SHELL OIL CO
SC 13D, 1998-07-10
PETROLEUM REFINING
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<PAGE>   1
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                  SCHEDULE 13D


                    UNDER THE SECURITIES EXCHANGE ACT OF 1934



                        The Meridian Resource Corporation
- ------------------------------------------------------------------------------
                                (Name of Issuer)

                          Common Stock, $.01 par value
- ------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    58977Q109
- ------------------------------------------------------------------------------
                                 (CUSIP Number)

                       J.B. Edrington, Corporate Secretary
                                Shell Oil Company
                              910 Louisiana Street
                              Houston, Texas 77252
                                 (713) 241-6161
- ------------------------------------------------------------------------------
                  (Name, Address and Telephone Number of Person
               Authorized to Receive Notices and Communications)

                                  June 30, 1998
- ------------------------------------------------------------------------------
             (Date of Event which Requires Filing of This Statement)

If the filing person has previously filed a statement on Schedule 13G to report
the acquisition which is the subject of this Schedule 13D, and is filing this
schedule because of Rule 13d-1(b)(3) or (4), check the following box [ ].

NOTE: Schedules filed in paper format shall include a signed original and five
copies of the schedule, including all exhibits. See Rule 13d-7(b) for other
parties to whom copies are to be sent.

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).

<PAGE>   2
                                  SCHEDULE 13D

CUSIP NO.: 58977Q109                                          

- --------------------------------------------------------------------------------

1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    Shell Oil Company
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]
         N/A                                                            (b) [ ]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS

     00
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEM  2(d) OR 2(e)                                                   [ ]

- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION


     Delaware
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES                -0-       
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING      24,919,458 or 13,487,394, depending on the matter put to a vote.
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                         -0-
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    -24,919,458-
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     24,919,458
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES                                                         [ ]

- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     42.5%
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON

     CO
- --------------------------------------------------------------------------------


                                      -1-

<PAGE>   3
                                  SCHEDULE 13D

CUSIP NO.: 58977Q109                                          

- --------------------------------------------------------------------------------

1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    Shell Louisiana Onshore Properties Inc.
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP
                                                                        (a) [ ]
         N/A                                                            (b) [ ]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS*

     AF
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEM 2(d) OR 2(e)                                                     [ ]

- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION


     Delaware
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES                -0-       
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING      24,919,458 or 13,487,394, depending on the matter put to a vote.
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                         -0-
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    -24,919,458-
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     24,919,458
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES                                                        [ ]

- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     42.5%
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON

     CO
- --------------------------------------------------------------------------------



                                       -2-

<PAGE>   4



ITEM 1.  SECURITY AND ISSUER.

         This statement relates to the common stock, $.01 par value (the "Common
Stock"), of The Meridian Resource Corporation, a Texas corporation (the
"Issuer"). The address of the principal executive office of the Issuer is
located at 15995 North Barkers Landing, Suite 300, Houston, Texas 77079.

ITEM 2.  IDENTITY AND BACKGROUND.

         This statement is being filed by Shell Louisiana Onshore Properties,
Inc., a Delaware corporation ("SLOPI"), and by Shell Oil Company, a Delaware
corporation ("Shell Oil"). Over 93% of the issued and outstanding common stock
of SLOPI is held by Shell Western E&P Inc. ("SWEPI"), which in turn is
controlled through indirect stock ownership by Shell Oil, which in turn is
wholly owned by Shell Petroleum Inc., also a Delaware corporation. The shares of
Shell Petroleum Inc. are directly or indirectly owned 60 percent by Royal Dutch
Petroleum Company, The Hague, The Netherlands, and 40 percent by The "Shell"
Transport and Trading Company, p.l.c., London, England. Royal Dutch Petroleum
Company and The "Shell" Transport and Trading Company, p.l.c., are holding
companies which together directly or indirectly own securities of companies of
the Royal Dutch/Shell group of companies, the members of which are severally
engaged throughout the greater part of the world in oil, natural gas, chemicals,
coal and other businesses.

         Shell Oil and its consolidated subsidiaries are engaged, principally in
the United States, in the exploration for, and development, production,
purchase, transportation and marketing of, crude oil and natural gas, and the
purchase, manufacture, transportation and marketing of oil and chemical
products. In addition, Shell Oil and its consolidated subsidiaries are engaged
in the exploration for, and production of, crude oil and natural gas outside the
United States. SLOPI is a holding 



                                       -3-

<PAGE>   5

company for companies engaged in oil and gas activities. SWEPI is engaged
primarily in the business of exploring for and producing oil, gas and other
minerals. SLOPI and Shell Oil are referred to herein as the "Reporting
Entities." 

        The address of the principal business and the principal office of SLOPI 
is 1105 North Market Street, Suite 1300, Wilmington, Delaware 19899. The address
of the principal business and the principal office of Shell Oil is One Shell
Plaza, Houston, Texas 77002. Schedule I attached hereto sets forth certain
additional information with respect to each director and each executive officer
of SLOPI and Shell Oil.

        Neither of the Reporting Entities nor, to their knowledge, any person
listed on Schedule I hereto, has been, during the last five years (i) convicted
in a criminal proceeding (excluding traffic violations or similar misdemeanors)
or (ii) a party to a civil proceeding and as a result of such proceeding was or
is subject to a judgment, decree or final order enjoining future violation of,
or prohibiting or mandating activities subject to, U.S. federal or state
securities laws or finding any violation with respect to such laws.

ITEM 3. SOURCE AND AMOUNT OF FUNDS OR OTHER CONSIDERATION.

        SLOPI obtained securities of the Issuer pursuant to an Agreement and 
Plan of Merger dated March 27, 1998 (the "Merger Agreement") among the Issuer,
LOPI Acquisition Corp., Louisiana Onshore Properties, Inc. ("LOPI"), and SLOPI.
In this transaction, a wholly-owned subsidiary of the Issuer named LOPI
Acquisition Corp. merged into LOPI, which had been a wholly-owned subsidiary of
SLOPI and which was the corporation surviving the merger (the "Merger").
Pursuant



                                       -4-

<PAGE>   6

to the terms of the Merger Agreement, (i) LOPI's treasury shares were canceled,
(ii) the issued and outstanding shares of LOPI common stock were converted into
an aggregate 12,082,030 duly authorized, validly issued, fully paid and
nonassessable shares of the Issuer's Common Stock and 3,982,906 duly authorized,
validly issued, fully paid and nonassessable shares of the Issuer's Series A
Preferred Stock, par value $1.00 per share (the "Preferred Stock") and (iii)
each issued and outstanding share of LOPI Acquisition Corp. was converted into
one fully paid and nonassessable share of common stock, par value $1.00 per
share, of LOPI. There are no other holders of the Preferred Stock. SLOPI also
obtained rights to acquire additional shares of Common Stock, as described below
in Items 6(A), 6(D)(6) and 6(D)(9).

         In connection with the Merger, SLOPI also took the following actions.
It eliminated or caused the elimination of all of LOPI's liabilities to persons
and entities which directly or indirectly controlled, were controlled by, or
were under direct or indirect common control with LOPI prior to the consummation
of the Merger (except for those liabilities related to the operation of LOPI in
the ordinary course of business and certain other liabilities associated with
the true-up accounting procedures described in Schedule III of the Merger
Agreement). SLOPI neither borrowed funds nor incurred indebtedness in connection
with the elimination of such liabilities. SLOPI also gave certain tax
indemnities set forth at Section 9.10 of the Merger Agreement and certain
post-closing indemnities set forth at Sections 12.1(c)(i) and 12.1(c)(ii) of the
Merger Agreement. SLOPI further caused SWEPI to guarantee the full and prompt
payment and performance by SLOPI of all of its obligations under the foregoing
tax indemnity, post-closing indemnities and true-up accounting procedures
pursuant to the Limited Joinder and Guaranty attached to the Merger Agreement.
Finally, SLOPI, SWEPI and Shell Onshore Ventures, Inc., a Delaware corporation
which is an affiliate of SLOPI, gave LOPI access to certain 3-D and 2-D seismic
data.



                                       -5-

<PAGE>   7


ITEM 4.  PURPOSE OF TRANSACTION.

         The transactions described in Item 3 above occurred as a result of
negotiations with the Issuer. The Common Stock, Preferred Stock, and the rights
to acquire Common Stock referenced above were acquired in connection with the
Merger and for investment purposes. SLOPI intends to review its investment in
the Issuer on an ongoing basis and, depending upon the price of, and other
market conditions relating to, the Common Stock, subsequent developments
affecting the Issuer, the Issuer's business and prospects, other investment and
business opportunities available to SLOPI, general stock market and economic
conditions, tax considerations and other factors deemed relevant, may decide to
increase or decrease the size of its investment in the Issuer.

         Other than as described Item 3 and Item 6 hereof, neither of the
Reporting Entities (nor, to their knowledge, any person listed on Schedule I
hereto) has any plan or proposal that would result in any of the consequences
listed in paragraphs (a) - (j) of Item 4 of Schedule 13D.

ITEM 5.  INTEREST IN SECURITIES OF THE ISSUER.

         Through its direct holdings, SLOPI beneficially owns and has the power
to dispose of 12,082,030, or nearly 26.4%, of the 45,803,419 shares of Common
Stock that are currently outstanding. Because SLOPI's 3,982,906 shares of
Preferred Stock are convertible into 12,837,428 shares of Common Stock at any
time at the holder's election, SLOPI is deemed under Rule 13d-3 to own
beneficially and have the power to dispose of such additional Common Stock as
well. SLOPI therefore beneficially owns and has the power to dispose of a total
of 24,919,458, or approximately 42.5%, of the 58,640,847 shares of Common Stock
which are deemed outstanding for purposes of Rule 13d-3(d).

         Voting power, however, does not directly track beneficial ownership.
Each of SLOPI's 3,982,906 shares of Preferred Stock is entitled to one vote per
share on all matters submitted to



                                       -6-

<PAGE>   8
holders of the Common Stock, and such shares are convertible into 12,837,428
shares of Common Stock. However, as explained further in Item 6(D)(5) below,
SLOPI agreed, subject to certain exceptions, (i) to exercise voting control over
no more than 23.0% of the votes entitled to be cast in any matter put to a
vote of the holders of Common Stock and (ii) to cast any excess votes it may
have pro rata with the votes of all other shares that are actually voted for or
against (or that abstain from voting) on each matter. Therefore, in voting upon
certain matters (see Item 6(D)(5) below), SLOPI's shares of Preferred Stock
would, after conversion and when aggregated with its direct holdings, entitle it
to cast 24,919,458 (or 42.5%) of the 58,640,847 then-outstanding votes. In votes
subject to the limitations described above, SLOPI may only vote (i) upon full
conversion of the Preferred Stock, up to 13,487,394 (or 23%) of the 58,640,847
shares of Common Stock which would then be outstanding and (ii) prior to the
conversion of any Preferred Stock, up to 11,450,855 (or 23%) of the 49,786,325
votes entitled to be cast. Therefore, SLOPI may exercise, upon conversion of the
Common Stock, voting power with respect to either 24,919,458 or 13,487,394 of
the outstanding shares. Because SLOPI is an indirect subsidiary of Shell Oil,
Shell Oil may also be deemed to own SLOPI's shares beneficially and to share in
its voting power with respect thereto. The foregoing share figures are accurate
as of the date of this statement but subject to adjustment in the event of
occurrences which trigger antidilution adjustments with respect to the Preferred
Stock and with respect to other changes in the Issuer's capitalization.

ITEM 6. CONTRACTS,  ARRANGEMENTS, UNDERSTANDINGS OR RELATIONSHIPS WITH RESPECT 
        TO SECURITIES OF THE ISSUER.

     A. Contingent Stock. 

     Exhibit H of the Merger Agreement, which is attached hereto within Exhibit
2, grants SLOPI the right to acquire, for no additional consideration, shares of
Common Stock having a value equal to 60% of the cash benefit which the Issuer's
consolidated federal 



                                      -7-
<PAGE>   9
income tax group may realize -- with respect to any consolidated federal income
tax return including LOPI for any period ending before June 30, 2008 -- as a
result of any increase in the tax basis of the transferred LOPI assets above $72
million. Such shares of Common Stock will be valued on the date of issuance at
the average trading price of such shares at the close of the 30 trading days
preceding the relevant date, or if not publicly traded, then the price as may be
determined by an investment bank selected by SLOPI.

         B. Certificate of Designation.

         The Preferred Stock has the dividend rights, voting rights and
liquidation preferences described in Sections 2, 3 and 4, respectively, of the
Certificate of Designation attached hereto as Exhibit 3 (the "Certificate of
Designation"). Section 3 provides that each share of Preferred Stock is entitled
to one vote with respect to all matters for which a vote of the holders of
Common Stock is taken. The affirmative vote or consent of the holders of a
majority of the shares of Preferred Stock outstanding at the time, voting as a
single class, is necessary to permit, effect or validate either (i) the
authorization, creation or issuance (or any increase in the authorized or issued
amount) of either any class or series of stock of the Issuer which has a
priority over shares of Preferred Stock as to payment of dividends or
distribution of assets or any stock of the Issuer ranking on a parity with the
Preferred Stock as to distribution of assets and payment of dividends or (ii)
the amendment, restatement, modification, alteration or repeal of any of the
provisions of the Certificate of Designation.

         The Certificate of Designation further provides that, until the earlier
of (a) the termination of the Stock Rights and Restrictions Agreement attached
hereto as Exhibit 4 (the "Stock Rights Agreement") or (b) SLOPI and its
affiliates beneficially own shares of Common Stock constituting less than 21% of
the then outstanding shares of Common Stock, the holders of Preferred Stock may
elect 20% of the directors constituting the entire board, and in no event less
than one director. The Certificate of Designation also provides for (i) the
resignation, removal or appointment of the board 


                                      -8-


<PAGE>   10
members elected by the holders of Preferred Stock as necessary to maintain such
percentage interest (each, a "Preferred Director") in the event of an election,
vacancy or expansion with respect to the board of directors, (ii) the removal of
the Preferred Directors upon the first to occur of the termination of the Stock
Rights Agreement or the complete conversion of the Preferred Stock, and (iii)
the appointment of a Preferred Director to the Audit Committee of the board of
directors.

         SLOPI's 3,982,906 shares of Preferred Stock may be converted into
Common Stock at the option of the holder upon the terms and conditions described
in Section 5 of the Certificate of Designation. The number of shares into which
a share of Preferred Stock may be converted is 3.22309, which is computed by
dividing its stated value of $33.894850 by the conversion price of $10.516125.
The conversion price will be adjusted from time to time as further described in
Section 5(b) of the Certificate of Designation. Such antidilution adjustments
are triggered by stock dividends, securities distributions, stock splits,
reverse stock splits, reclassifications of Common Stock, the issuance of certain
rights or warrants to acquire Common Stock for consideration below certain
minimum threshold values, the distribution of evidences of debt or assets or
rights to acquire any security, and similar events. In the event of a
reclassification of the Common Stock, the Preferred Stock may be converted into
the same amount of stock and other consideration that would have been received
or deemed to be held by shareholders owning an amount of Common Stock equal to
the amount into which the Preferred Stock could have been converted. Likewise,
upon certain business combination and reorganization events, the Preferred Stock
may be exchanged for amount of stock and other consideration which would have
been received by a shareholder who held an amount of Common Stock equal to the
amount into which the Preferred Stock could have been converted. The Issuer has
also agreed to reserve and keep available an amount of its authorized and
unissued Common Stock solely for the purpose of issuance upon conversion of the
outstanding Preferred Stock. If on or after June 30, 2001, (a) any shares of
Preferred Stock have not been converted into Common Stock and (b) the mean
average per share 


                                      -9-
<PAGE>   11
market value, as defined in Item 6(D)(7), exceeds 150% of the conversion price
for 75 consecutive Trading Days, as defined, then all Preferred Stock shall
automatically convert into Common Stock, except that SLOPI and its affiliates
may elect to retain one share of Preferred Stock among them.

         C. Registration Rights Agreement. 

                  The Issuer and SLOPI have entered into a registration rights 
agreement (the "Registration Rights Agreement") which grants SLOPI and certain
of its transferees certain demand and piggyback registration rights with
respect to Common Stock which from time to time (i) was issued pursuant to the
Merger Agreement, (ii) was issued upon the conversion of the Preferred Stock,
or (iii) was transferred or issued pursuant to the Stock Rights Agreement. The
Issuer agrees to file on demand no more than an aggregate of five registration
statements, plus any number of additional registration statements (not to
exceed an aggregate of an additional five) as to which the selling shareholders
and their underwriters have reasonably estimated the price to the public will
be at least $50 million. The Issuer may suspend sales under a registration
statement, and may refuse to file or amend a registration statement, for a
certain period of time not exceeding a cumulative 120 days in one year, if the
Issuer determines that such filing or sales would require premature disclosure
of information, to the detriment of the Issuer, not otherwise required to be
disclosed or would require disclosure which would materially and adversely
affect (i) a pending or proposed offering of securities of the Issuer, (ii) an
acquisition, merger, recapitalization, consolidation, reorganization, or
similar transaction relating to the Issuer, or (iii) negotiations with respect
thereto. The filing of a registration statement may not be deferred, and the
sale and distribution of shares may not be suspended, in each case, for more
than 60 days after the abandonment or consummation (or the completion of the
distribution of securities in the case of a public offering) of any of the
proposals or transactions described therein. In addition to these demand
registration rights, the Registration Rights Agreement also gives SLOPI and
certain of its transferees the right, from time to time, to include their
holdings of Common Stock in any firm commitment underwritten public offering of
Common Stock for cash pursuant to a registration



                                      -10-
<PAGE>   12


statement filed by the Issuer, if the registration statement would permit the
registration of their holdings of Common Stock. The number of shares includable
in such a registration statement is subject to certain cut-backs if the managing
underwriter determines that the offering would materially and adversely affect
the distribution of securities by the Issuer. Any shares registered pursuant to
the Registration Rights Agreement will be listed on the primary securities
exchange or other trading market where the Common Stock is listed.

         D.       Stock Rights and Restrictions Agreement.

         SLOPI and the Issuer have entered into the Stock Rights Agreement,
which addresses a number of matters.

                  1. Standstill. SLOPI agrees that it and its affiliates shall
not, until June 30, 2008 or the earlier termination of the Stock Rights
Agreement: (i) engage in or solicit others to engage in certain business
combination transactions with the Issuer (such as, if the transaction meets
certain conditions, a merger, consolidation, compulsory share exchange, event
defined in Part Thirteen of the Texas Business Corporation Act (the "TBCA"),
recapitalization, or other transaction involving the Issuer in which shares of
Common Stock are exchanged for cash, securities or other property, or the sale
of substantially all of the Issuer's and its subsidiaries' assets) (each, a
"Business Combination Transaction") or (ii) propose, or solicit any person to
make, a liquidation of the Issuer or a tender offer or exchange offer for shares
of Common Stock. Such actions may be taken, however, if either (i) it is after
June 30, 2001 and, on the date the transaction is proposed, either (x) no
Preferred Directors (as defined therein) or SLOPI Designee(s) (as defined
therein) shall be serving on the Issuer's board of directors or (y) SLOPI and
its affiliates collectively own beneficially less than 21% of the outstanding
Common Stock or (ii) the transaction is approved by a majority of the Continuing
Directors (as defined therein).

                  2. Takeover Defenses. The Issuer further agrees not to
implement any poison pill or takeover defense mechanism unless, in each case,
provision is made to exclude SLOPI and 


                                      -11-

<PAGE>   13
 its affiliates from the effects thereof. The foregoing agreement survives the
termination of the Stock Rights Agreement. In addition, the parties agree that,
notwithstanding the fact that a shorter period may apply, Article Eight of
Issuer's Articles of Incorporation (attached hereto as Exhibit 6) and Part
Thirteen of the TBCA will apply during the term of the Stock Rights Agreement to
any business combination transaction covered thereby between SLOPI and its
affiliates on the one hand and the Issuer on the other.

                  3. Board Representation; Restriction on Stock Acquisitions.

                  The Issuer and SLOPI have also agreed that, after the 
conversion of all of the Preferred Stock, and until either (i) the termination
of the Stock Rights Agreement or (ii) SLOPI and its affiliates beneficially own
less than 21% of the outstanding Common Stock, they will take certain actions
(such as filling vacancies, removing directors, and soliciting proxies)
relating to the maintenance of SLOPI's and its affiliates' board representation
and Audit Committee representation that are substantially similar to those
described in Item 6(B) above with respect to the Certificate of Designation.
The parties have also agreed that SLOPI and its affiliates will not acquire any
additional Common Stock without the consent of a majority of the Continuing
Directors, as defined, unless both (i) June 30, 2001 has occurred and (ii) at
the time of such acquisition, either no SLOPI Designee or Preferred Director
shall be serving on the Issuer's board or SLOPI and its affiliates would
beneficially own less than 21% of the outstanding Common Stock; but this
restriction does not affect (w) any conversion of Preferred Stock, (x) an
acquisition arising from stock dividends, stock splits, reclassifications or
the exercise of any other security received by SLOPI from the Issuer with
respect to the Common Stock and Preferred Stock received in connection with the
Merger, (y) any shares issuable in connection with a Deficiency Amount
described below in Item 6(D)(7), or (z) the exercise of any right to acquire,
pursuant to the Stock Rights Agreement, Common Stock or certain debt, equity,
warrants, or other rights issued by the Issuer or representing the right to
acquire voting stock of the Issuer (each, an "Exchangeable Security").


                                      -12-
<PAGE>   14

                  4. Transfer Restrictions. 

                  The Issuer and SLOPI have also agreed that SLOPI and its 
affiliates will not sell, transfer or otherwise convey (each, a "Transfer")
beneficial ownership of any Common Stock or Preferred Stock without the consent
of a majority of the Continuing Directors, except as follows:

         (a) transfers may be made to a direct or indirect affiliate of Shell
         Oil which agrees in writing to be bound by the Stock Rights Agreement;

         (b) transfers may be made to the Issuer or a company with respect to
         which the Issuer directly or indirectly owns the majority of the voting
         power of the equity securities or voting interest;

         (c) transfers may be made pursuant to a merger, consolidation or 
         compulsory share exchange in which the Issuer is a constituent 
         corporation;

         (d) transfers may be made as a pro rata dividend or distribution to the
         holders of the common stock of SLOPI or its affiliates (provided that,
         except for dividends or distributions to any of the Royal Dutch/Shell
         Group of Companies, the holders agree in writing to be bound by the
         Stock Rights Agreement);

         (e) certain transfers may be made to persons or entities other than
         SLOPI or any affiliate of Shell Oil who has commenced a tender or
         exchange offer for Common Stock, if (i) SLOPI and its affiliates
         collectively beneficially own less than 21% of the then outstanding
         shares of Common Stock and no SLOPI Designee or Preferred Director is
         serving on the Issuer's board or (ii) SLOPI and its affiliates
         collectively beneficially own more than 21% of the then outstanding
         shares of Common Stock or any SLOPI Designee or Preferred Director is
         serving on the Issuer's board, if SLOPI and any of its affiliates first
         provide the Issuer a preferential right to purchase, for cash, all such
         shares which SLOPI and any of its affiliates would be willing to tender
         or exchange at a price of 105% of the tender offer price which SLOPI
         and any affiliate would be willing to accept (which shall be either the
         market value of the security to be exchanged on such date, if publicly
         traded, or the cash equivalent value as determined by SLOPI and its
         affiliates);

         (f) sales of Common Stock receivable in connection with the Merger or
         acquired upon conversion of the Preferred Stock may be made in certain
         types of transactions (namely, firm commitment underwritten public
         offerings, "Private Placements" defined in (g) below, and the transfers
         described in (h), (i) and (j) below), in the following amounts, from
         and after the following anniversaries of June 30, 1998:


<TABLE>
<CAPTION>

         ANNIVERSARY                      INCREMENTAL PERCENTAGE                AGGREGATE PERCENTAGE
        <S>                                   <C>                                    <C>
          Second                                 25%                                    25%
          Third                                  25%                                    50%
          Fourth                                 25%                                    75%
          Fifth                                  25%                                   100%
</TABLE>

                                      -13-

<PAGE>   15
         Common Stock received in connection with a Deficiency Amount, however,
         may be freely transferred, and such transfer will not reduce or delay
         the amounts otherwise permitted above.

         (g) from and after the following anniversaries of June 30, 1998,
         transfers may be made of the following percentages of the number of its
         Preferred Stock in Private Placements:


<TABLE>
<CAPTION>

          ANNIVERSARY                           INCREMENTAL PERCENTAGE                  AGGREGATE PERCENTAGE
          <S>                                  <C>                                    <C>
          Third                                         33 1/3%                                 33 1/3%
          Fourth                                        33 1/3%                                 66 2/3%
          Fifth                                         33 1/3%                                  100%
</TABLE>

         As used in the Stock Rights Agreement, a "Private Placement" is a
         Transfer in a transaction not involving a firm commitment underwritten
         public offering, other than (a) sales pursuant to tender or exchange
         offers, (b) Transfers to persons or entities having interests in
         businesses which explore for, develop or produce crude oil or natural
         gas, if such transferee would beneficially own, or have the right to
         acquire upon conversion of the Preferred Stock, ten percent or more of
         the then outstanding Common Stock, and if certain additional conditions
         are not met, (c) Transfers to any person or entity if such transferee
         would beneficially own or have the right to acquire upon conversion of
         the Preferred Stock more than 10% of the Common Stock unless such
         transferee agrees to be bound by terms substantially similar to
         those in the Stock Rights Agreement for a period of ten years;

         (h) subject to paragraphs (f) and (g) above, as such may be modified
         pursuant to paragraph (k) below, Transfers may be made in accordance
         with Rule 144 or Rule 145 promulgated under the Securities Act of 1933,
         as amended;

         (i) transfers in a firm commitment underwritten public offering or
         other public offering made pursuant to an effective registration
         statement involving a broad public distribution of the offered
         securities;

         (j) notwithstanding (f) or (g) above, Transfers may be made of any
         shares of Common Stock equal to the number of shares that SLOPI and its
         affiliates may have received from time to time in connection with a
         Deficiency Amount;

         (k) notwithstanding (f) and (g) above, if (1) the Issuer, in connection
         with a merger, consolidation, share exchange, or acquisition of a
         business or properties or similar transaction, sells or issues (or
         commits to sell or issue) 5 million shares (as adjusted for stock
         splits, reverse splits, reclassifications, and similar events) of
         Common Stock or Exchangeable Securities that, at the time of such
         issuance, sale or commitment (and assuming full conversion, exchange or
         exercise thereof) represent 5,000,000 or more (as adjusted for stock
         splits, reverse splits, reclassifications, and similar events) of the
         shares entitled to vote with respect to the election of directors and
         (2) prior to the approval of the transaction by the Issuer's board, no
         nationally recognized investment banking firm shall have given an
         opinion that the transaction is fair, from a financial point of view,
         to the


                                      -14-
<PAGE>   16

         Issuer, then in such event, SLOPI and its affiliates may also transfer
         a number of additional shares of Common Stock equal to the number of
         shares of Common Stock and/or the Common Stock equivalent of the voting
         shares represented by the transaction as to which such fairness opinion
         was not obtained; and if such transfers would exceed the limits in (f)
         and (g) above, then the limits will be accelerated in the following
         manner as of the date of such issuance, sale or commitment (the
         "Relevant Date"):

                  For paragraph (f):
<TABLE>
<CAPTION>

         DATE                                          INCREMENTAL PERCENTAGE             AGGREGATE PERCENTAGE
        <S>                                                   <C>                               <C>
         Immediately                                             25%                               25%
         1 year after the Relevant Date                          25%                               50%
         2 years after the Relevant Date                         25%                               75% 
         3 years after the Relevant Date                         25%                              100%


                  For paragraph (g):


         DATE                                          INCREMENTAL PERCENTAGE             AGGREGATE PERCENTAGE
         Immediately                                           33 1/3%                            33 1/3%
         1 year after the Relevant Date                        33 1/3%                            66 2/3%
         2 years after the Relevant Date                       33 1/3%                             100%
</TABLE>

                  5. Voting Restrictions. 

                  Prior to the conversion of all the Preferred Stock, the 
following provisions apply. SLOPI and its affiliates may vote the number of its
Common Stock that, when added to the votes represented by the Preferred Stock,
constitute an aggregate of up to 23% of the then outstanding votes eligible to
be cast for such matter. After the conversion of all of the Preferred Stock,
SLOPI and its affiliates shall be entitled to vote such number of shares of
Common Stock that constitute up to 23% of the then outstanding votes eligible
to be cast for such matter. If only a portion of the Preferred Stock has been
converted, the voting shall be prorated between the Common Stock and the
Preferred Stock for a total of up to 23% of the then outstanding votes eligible
to be cast for such matter. Common Stock in excess of the foregoing amounts, as
applicable, shall be voted pro rata with the votes of all shares (other than
the excess shares) that are actually voted for or against (or that abstain from
voting) on each matter. The foregoing provisions shall not apply to the voting
of Common Stock or Preferred Stock on any 


                                      -15-
<PAGE>   17


matter (i) constituting a Business Combination Transaction, (ii) that involves a
change of control of the Issuer, or (iii) with respect to any vote taken when
any of the following shall have occurred or exist: (w) the average per share
market value, as defined in Item 6(D)(7), of the Common Stock on the day of the
vote has been less than $5.50 for 30 days (as adjusted for stock splits, reverse
stock splits, stock dividends, reclassifications, share exchanges, dividends and
distributions for which adjustments to the conversion price of the Preferred
Stock may be made), (x) there are any accrued but unpaid dividends on any
Preferred Stock, (y) the issuer failed to issue additional Common Stock with
respect to Deficiency Amounts, (z) there is a continuing and uncured default by
the Issuer of any of its material obligations under the Stock Rights Agreement,
the Certificate of Designation, the Registration Rights Agreement, or the Merger
Agreement. In all circumstances, SLOPI may vote its Preferred Stock in its
complete discretion, notwithstanding the foregoing restrictions.

         6. Right to Purchase Stock. 

                  So long as SLOPI and its affiliates beneficially own shares 
of Common Stock that would constitute, after giving effect to the contemplated
transaction, less than 21% of the then outstanding shares of Common Stock, the
Issuer will not issue Common Stock or Exchangeable Securities without first
honoring the following rights. In the case of an offering that is not a firm
commitment underwritten public offering, SLOPI shall have the right to buy in
such offering a certain amount thereof. Such amount shall not exceed an amount
which would cause SLOPI and its affiliates to own beneficially, upon the
closing of the transaction, more than 21% of the Common Stock. If the terms of
the offering require that the subscription is not to be entirely paid in cash,
any noncash components thereof shall be valued by a third party in accordance
with the method described in the Stock Rights Agreement and SLOPI may tender an
equivalent amount in cash in satisfaction of that portion of the price. If,
however, the offering is a firm commitment underwritten public offering which
would result in SLOPI and its affiliates owning less than 21% of the
then-to-be-outstanding Common Stock, then the Issuer shall cause 



                                      -16-
<PAGE>   18

SLOPI to be offered the right to purchase a portion of the offered securities
sufficient to permit SLOPI and its affiliates to beneficially own, upon
consummation of the offering, 21% of the then-to-be-outstanding Common Stock.

                  7. Deficiency Amounts. 

                  If SLOPI, its affiliates, or any affiliate of Shell Oil shall 
sell any Common Stock issuable upon conversion of the Preferred Stock and
receive net proceeds, after commissions, discounts, placement fees and
incidental expenses, that result in a "Deficiency Amount" (defined below), then
the Issuer shall, at its option, either pay SLOPI cash equal to the Deficiency
Amount or issue fully paid and nonassessable shares of Common Stock equal in
value to the Deficiency Amount. A "Deficiency Amount" is the product of the
number of shares of Common Stock sold at less than the Allocated Price Per Share
(as defined) times the amount by which the per share sales price is less than
the Allocated Price Per Share, and the sales price of any shares sold in a
Private Placement or a transaction other than a firm commitment underwritten
offering shall be the greater of (i) the actual sales price or (ii) the average
per share market value of the Common Stock relating to the date of such sale.
The Allocated Price Per Share means the then existing conversion price of the
Preferred Stock (or if fully converted, the conversion price that would have
been in existence had the Preferred Shares not been converted), as the same may
be adjusted according to its terms. The average per share market value means the
average trading price of such shares at the close of the 30 trading days
preceding the relevant date, or if not publicly traded, then the price as may be
determined by an investment bank selected by SLOPI. Any shares so issued shall
be listed for trading on the principal stock exchange for the Common Stock.
Notwithstanding Section 2(C)(11)(g) of the Registration Rights Agreement, the
Issuer will pay the commissions, underwriter's discounts, certain legal expenses
and other expenses of sale payable by SLOPI and its affiliates in any sale of
Common Stock or Preferred Stock in certain circumstances.


                                      -17-
<PAGE>   19


                  8. Other Agreements. 

                  The Issuer agreed that, during the term of the Stock Rights
Agreement, it will not adopt any shareholder rights plan or amend any rights
plan without the approval of a majority of the SLOPI Designee(s) or the
Preferred Director(s) then on the board of directors of the Issuer, unless the
plan exempts SLOPI and its affiliates from all effects thereof. The Issuer
further agreed not to take any action without SLOPI's consent that would reduce
the number of shares of Common Stock held by persons or entities other than
SLOPI, the Issuer or any affiliate of either of them to less than the minimum
number required to maintain the Issuer's New York Stock Exchange listing.

                  9. Termination. 

                  The Stock Rights Agreement terminates on June 30, 2008 but may
be earlier terminated: (i) by the parties' mutual consent; (ii) by SLOPI or the
Issuer if SLOPI becomes the beneficial owner of less than 10% of the Common
Stock calculated on a fully diluted basis, (iii) by SLOPI if any person or
entity other than SLOPI or any of its affiliates proposes a Business Combination
Transaction and a majority of the Continuing Directors have either approved the
proposal or have retained an investment banking firm to solicit indications of
interest with respect to such transaction (but the Stock Rights Agreement shall
be reinstated upon the withdrawal, termination or expiration of any tender or
exchange offer which is the subject of such proposed transaction); (iv) by SLOPI
if any person or entity other than SLOPI or its affiliates acquires beneficial
ownership of 20% (or, if lower, the percentage specified in the definition of
"Affiliated Shareholder" in Part Thirteen of the TBCA, as amended from time to
time) or more of the Issuer's voting securities and such person or entity has
not entered into an agreement containing restrictions and other provisions at
least as favorable to the Issuer as those contained in the Stock Rights
Agreement; (v) by SLOPI if the Continuing Directors do not constitute a majority
of the board of directors of the Issuer; (vi) by SLOPI if the Issuer breaches
and fails timely to cure material provisions of the Stock Purchase Agreement,
the Merger Agreement, the Certificate of 


                                      -18-
<PAGE>   20

Designation or the Registration Rights Agreement; or (vii) by SLOPI if the
Issuer is subject to a voluntary or involuntary proceeding in the nature of
bankruptcy, insolvency, receivership and the like.

         E. Caveat; Incorporation by Reference.

         The foregoing descriptions of the Certificate of Designation, the 
Registration Rights Agreement, Exhibit H of the Merger Agreement, and the Stock
Rights Agreement summarize and abstract provisions which are complex and
detailed. As a necessary result, the summary descriptions are, in a manner which
is not essential to a general understanding of the agreements, imprecise or
lacking in certain detail. Accordingly, the exhibits to this statement
supplement the foregoing, are hereby incorporated by reference, and should be
directly referenced in order better to assess the precise scope, operation and
nature of the agreements reached between SLOPI and the Issuer with respect to
their subject matter. To the extent that any exhibit is inconsistent with or
supplements the summary descriptions, the summary descriptions are deemed
modified thereby.

         F. Amendment of Certificate of Incorporation. 

         In order to assure that sufficient Common Stock is available for 
issuance pursuant to the conversion of the Preferred Stock, the Issuer agreed to
amend its certificate of incorporation to increase the number of authorized
shares of Common Stock to 200,000,000 shares.

         G. Transactions during Past Sixty Days.

         Except as described herein, neither of the Reporting Entities, nor, to
their knowledge, any of the persons named in Schedule I hereto, has effected any
transactions in the Common Stock during the past sixty days.

                                      -19-
<PAGE>   21


ITEM 7.  MATERIAL TO BE FILED AS EXHIBITS
<TABLE>

        <S>               <C>
         Exhibit 1   -     Agreement that the Schedule 13D is filed on behalf of
                           each reporting person.

         Exhibit 2   -     Agreement and Plan of Merger dated March 27, 1998
                           among the Issuer, LOPI Acquisition Corp., LOPI, and
                           SLOPI (filed as Appendix A to the proxy statement
                           filed June 12, 1998 by the Issuer and incorporated
                           by reference herein pursuant to Rule 12b-32).

         Exhibit 3   -     Certificate of Designation of Series A Preferred
                           Stock of the Issuer.

         Exhibit 4   -     Stock Rights and Restrictions Agreement dated as of
                           June 30, 1998 between the Issuer and SLOPI.

         Exhibit 5   -     Registration Rights Agreement dated as of June 30,
                           1998 between the Issuer and SLOPI.

         Exhibit 6   -     Article Eight of the Issuer's Articles of
                           Incorporation
</TABLE>



                                      -20-
<PAGE>   22


                                    SIGNATURE

         After reasonable inquiry and to the best knowledge and belief of the
undersigned, the undersigned certify that the information set forth in this
statement is true, complete and correct.

July 10, 1998
                                       SHELL LOUISIANA ONSHORE PROPERTIES INC.


                                       By:    /s/ Y.N. YOUSSEF
                                          -------------------------------------
                                       Name:  Y.N. Youssef
                                       Title: Vice President


                                       SHELL OIL COMPANY


                                       By:    /s/ JACK B. EDRINGTON
                                          -------------------------------------
                                       Name:  Jack B. Edrington
                                       Title: Associate General Counsel
                                              and Corporate Secretary



                                      -21-

<PAGE>   23
                                                                      SCHEDULE I

                        DIRECTORS AND EXECUTIVE OFFICERS
                     SHELL LOUISIANA ONSHORE PROPERTIES INC.


<TABLE>
<CAPTION>

                                                    POSITION AND
      NAME AND ADDRESS            CITIZENSHIP       OCCUPATION

<S>                               <C>              <C>
S.P. Methvin                        U.S.A.           President
910 Louisiana Street                                 President & CEO, Shell
Houston, Texas 77252                                 Deer Park Refining    
                                                     Company

Y.N. Youssef                        U.S.A.           Vice President
910 Louisiana Street                                 Technical Manager, Shell
Houston, Texas 77252                                 Western E&P Inc.


J.N. Le Gault                       U.S.A.           Vice President and Treasurer
910 Louisiana Street                                 Manager, Customer Services
Houston, Texas 77252                                 Shell Services International Inc.

Jack E. Little                      U.S.A.           Chairman
910 Louisiana Street                                 Director, President, Chief
Houston, Texas 77252                                 Executive Officer and         
                                                     Executive Vice President
                                                     of Shell Oil Company

M.E. Acosta                         U.S.A.           Director
910 Louisiana Street                                 Vice President, Planning &
Houston, Texas 77252                                 Finance, Shell Exploration
                                                     & Production Company

J.M. Funk                           U.S.A.           Director
910 Louisiana Street                                 President, Shell Continental
Houston, Texas 77252                                 Companies
</TABLE>


                                      -22-

<PAGE>   24




                        DIRECTORS AND EXECUTIVE OFFICERS
                                SHELL OIL COMPANY
<TABLE>
<CAPTION>

                                                    POSITION AND 
NAME AND ADDRESS                    CITIZENSHIP     OCCUPATION

<S>                                 <C>             <C>
Joseph E. Antonini                    U.S.A.        Director
1800 W. Maple Road                                  Retired Chairman, President
Troy, Michigan 48084                                and CEO, KMart Corporation

Rand V. Araskog                       U.S.A.        Director
1330 Avenue of the Americas                         Retired Chairman and CEO
New York, New York 10019-5490                       ITT Corporation

Robert F. Daniell                     U.S.A.        Director
United Technologies Bldg.                           Retired Chairman, United
Hartford, Connecticut 06101                         Technologies Corporation

Jack E. Little                        U.S.A.        Director, President, Chief
910 Louisiana Street                                Executive Officer and
Houston, Texas 77252                                Executive Vice President

Vilma S. Martinez                     U.S.A.        Director
355 S. Grand Avenue                                 Attorney (Partner)
Los Angeles, California 90071-1560                  Munger, Tolles & Olson

Steve L. Miller                       U.S.A.        Director
Shell Centre                                        A Managing Director of
2 York Road                                         Royal Dutch Petroleum
London, England SE1 7NA                             Company

Mark Moody-Stuart                    England        Chairman
Shell Centre                                        Chairman and a Managing
2 York Road                                         Director of The "Shell"
London, England SEI 7NA                             Transport and Trading
                                                    Company p.l.c.

Harold A. Poling                      U.S.A.        Director Emeritus
Regent Court Bldg.                                  Retired Chairman and CEO,
16800 Executive Place Drive                         Ford Motor Company
Dearborn, Michigan  48126

Gordon R. Sullivan                    U.S.A.        Director
490 L'Enfont Plaza, S.W.                            President
Washington, D.C. 20024                              Association of the U.S. Army

John F. Woodhouse                     U.S.A.        Director
1390 Enclave Parkway                                Chairman
Houston, Texas 77077-2099                           Sysco Corporation
</TABLE>

                                      -23-

<PAGE>   25

<TABLE>
<CAPTION>
                                                          POSITION AND  
NAME AND ADDRESS                     CITIZENSHIP           OCCUPATION

<S>                                   <C>            <C>
L. E. Sloan                             U.S.A.       Senior Vice President -
910 Louisiana Street                                 Chemical
Houston, Texas 77252

Gaurdie E. Bannister                    U.S.A.       Vice President - Services
910 Louisiana Street
Houston, Texas 77252

D. Gardy                                France       Vice President - Finance
910 Louisiana Street
Houston, Texas 77252

S. A. Lackey                            U.S.A.       Vice President and General
910 Louisiana Street                                 Counsel
Houston, Texas 77252

B. W. Levan                             U.S.A.       Vice President - Human
910 Louisiana Street                                 Resources
Houston, Texas 77252

S. C. Stryker                           U.S.A.       Vice President and General
910 Louisiana Street                                 Tax Counsel
Houston, Texas 77252

S. E. Ward                              U.S.A.       Vice President - Government
1401 Eye Street, N.W., Suite 1030                    Affairs
Washington, D.C. 20005
</TABLE>


                                      -24-

<PAGE>   26

                               INDEX TO EXHIBITS

<TABLE>
        <S>               <C>
         Exhibit 1   -     Agreement that the Schedule 13D is filed on behalf of
                           each reporting person.

         Exhibit 2   -     Agreement and Plan of Merger dated March 27, 1998
                           among the Issuer, LOPI Acquisition Corp., LOPI, and
                           SLOPI.

         Exhibit 3   -     Certificate of Designation of Series A Preferred
                           Stock of the Issuer.

         Exhibit 4   -     Stock Rights and Restrictions Agreement dated as of
                           June 30, 1998 between the Issuer and SLOPI.

         Exhibit 5   -     Registration Rights Agreement dated as of June 30,
                           1998 between the Issuer and SLOPI.

         Exhibit 6   -     Article Eight of the Issuer's Articles of
                           Incorporation
</TABLE>


                                      -25-


<PAGE>   1

                                                                       EXHIBIT 1

                                    AGREEMENT

The undersigned reporting persons hereby agree that the statements filed
pursuant to this Schedule 13D dated July 10, 1998, to which this Agreement are
filed as an exhibit, are filed on behalf of each of them.

                                       SHELL LOUISIANA ONSHORE PROPERTIES INC.


                                       By: /s/ Y.N. YOUSSEF
                                          -------------------------------------
                                       Name:  Y.N. Youssef
                                       Title: Vice President

                                       SHELL OIL COMPANY


                                       By: /s/ JACK B. EDRINGTON
                                          -------------------------------------
                                       Name:  Jack B. Edrington
                                       Title: Associate General Counsel and
                                              Corporate Secretary









<PAGE>   1
                                                                       EXHIBIT 3

                        THE MERIDIAN RESOURCE CORPORATION

================================================================================
CERTIFICATE OF DESIGNATION, PREFERENCES AND RIGHTS OF A SERIES OF PREFERRED
STOCK BY RESOLUTION OF THE BOARD OF DIRECTORS PROVIDING FOR AN ISSUE OF
3,982,906 SHARES OF PREFERRED STOCK DESIGNATED SERIES A CUMULATIVE CONVERTIBLE
PREFERRED STOCK.
================================================================================

      The Meridian Resource Corporation, a Texas Corporation (the "Company"),
pursuant to the provisions of Article 2.12 of the Texas Business Corporation Act
("TBCA"), does hereby state and certify that, pursuant to the authority
expressly vested in the Board of Directors of the Company by the Second Amended
and Restated Articles of Incorporation of the Company, as amended, that the
Board of Directors, at a meeting thereof duly called and held on March 27, 1998,
at which meeting a quorum was present and acting throughout, duly adopted the
following resolutions providing for the issue of shares of Preferred Stock
hereinafter referred to, and further providing with respect to such issue of
shares of Preferred Stock for such powers, designations, preferences and
relative, participating, optional and other special rights, and the
qualifications, limitations or restrictions thereof, as are hereinafter set
forth, in addition to those set forth in said Articles of Incorporation;

      RESOLVED, that pursuant to Article Four of the Second Amended and Restated
Articles of Incorporation of the Company, as amended (which authorizes the
Company to issue up to 25,000,000 shares of Preferred Stock, par value $1.00 per
share), the Board of Directors hereby provides for the issue of a series of up
to 3,982,906 shares of Preferred Stock designated "Series A Cumulative
Convertible Preferred Stock"; and

      RESOLVED, that the powers, designations, preferences and relative,
participating, optional and other special rights, and the qualifications,
limitations or restrictions thereof, of the shares of the Series A Cumulative
Convertible Preferred Stock shall be as follows:

      SECTION 1. DESIGNATION AND RANK. The designation of the series of
Preferred Stock created by this resolution shall be "Series A Cumulative
Convertible Preferred Stock", and the number of shares constituting this Series
shall have a stated value of $33.894850 per share (the "Stated Value"). The
shares of this Series shall rank prior to the Junior Stock (as defined in
Section 8) as to distribution of assets and payments of dividends.
<PAGE>   2
      SECTION 2. DIVIDENDS.

      (a) Shares of this Series shall be entitled to receive, when and as
declared by the Board of Directors, a cash dividend at the dividend rate of four
percent (4%) per annum (the "Dividend Rate") on the Stated Value per share of
this Series, and no more; provided, however, that dividends shall cease to
accrue on shares of the Series on the following schedule: 1,327,635 shares on
the third anniversary of the date of original issuance (the "Sub-Series A-I");
1,327,636 shares on the fourth anniversary of the date of original issuance (the
"Sub-Series A-II"); and 1,327,635 shares on the fifth anniversary of the date of
original issuance (the "Sub-Series A-III") (collectively, the "Sub-Series"). The
certificates evidencing shares of the Series will specify whether the shares
represented thereby are designated Sub-Series A-I, Sub-Series A-I or Sub- Series
A-III. Dividends shall be cumulative, shall accrue (whether or not declared and
whether or not there shall be funds legally available for the payment of
dividends) from the data of original issuance and shall be payable in arrears,
out of assets legally available therefor, when and as declared by the Board of
Directors of the Company, on January 1, April 1, July 1, and October 1 of each
year in which dividends are payable, commencing October 1, 1998, (except that if
any such date is a Saturday, Sunday or a Business Day then such dividend shall
be payable without interest on the next day that is not a Saturday, Sunday or
Business Day) (each three-month period expiring on a dividend payment date being
referred to herein as a "Dividend Period"). Dividends shall be paid to the
holders of record of shares of each Sub-Series entitled thereto as they appear
on the stock register of the Company on such record dates, not exceeding 30 days
preceding the payment dates thereof, as shall be fixed by the Board of
Directors. Dividends on account of arrears for any past Dividend Periods (an
"Arrearage") may be declared and paid at any time, without reference to any
regular dividend payment date, to holders of record on such date, not exceeding
45 days preceding the payment date thereof, as may be fixed by the Board of
Directors. Until paid in full, each Arrearage shall also accrue dividends at the
rate of 4% per annum. All dividends and Arrearages respectively, shall be
declared and paid pro rata on all Sub-Series, based on the aggregate of the
accrued dividends, Arrearages and dividends on Arrearages, respectively, for the
various Sub-Series.

      (b) No dividends (other than a dividend in Junior Stock or other than as
provided in Section 2(b)) shall be declared or paid or set apart for payment on
Junior Stock for any period unless full cumulative dividends have been or
contemporaneously are declared and paid or declared and a sum sufficient for the
payment thereof set apart for such payment on this Series for all Dividend
Periods terminating on or prior to the date of payment of such full cumulative
dividends Holders of shares of this Series shall not be entitled to any
dividend, whether payable in cash, property or stock, in excess of full
cumulative dividends.

      (c) So long as any shares of this Series are outstanding, no dividend
(other than a dividend in Junior Stock or other than as provided in Section
2(b)) shall be declared or paid or set aside for payment or other distribution
declared or made upon the Junior Stock, nor shall any Junior Stock be redeemed,
purchased or otherwise acquired for any consideration (or any moneys be paid to
or made available for a 

                                      -2-
<PAGE>   3
sinking fund for the redemption of any shares of Junior Stock) by the Company
(except by conversion into or in exchange for Junior Stock) unless, in each
case, full cumulative dividends on all outstanding shares of this Series then
payable shall have been paid.

      (d) Dividends payable on this Series for a period less than a full
Dividend Period shall be computed on the basis of the ratio of the number of
days in such partial period to the actual number of days in such full Dividend
Period.

      SECTION 3. VOTING AND ELECTION OF DIRECTORS.

      (a) The holders of outstanding shares of this Series shall be entitled to
vote, with the Common Stock and any other capital stock voting with the Common
Stock, with respect to all matters for which a vote of the holders of Common
Stock is taken. Each holder of outstanding shares of this Series shall be
entitled to that number of votes as are equal to the number of shares of this
Series held by such holder. The record date for holders of shares of the Series
entitled to vote on any matters submitted to the holders of Common Stock for
their vote, whether at an annual or special meeting of shareholders or by
unanimous written consent, shall be the same date as the record date established
for the Common Stock.

      (b) So long as any shares of this Series remain outstanding, the
affirmative vote or consent of the holders of a majority of the shares of this
Series outstanding at the time, voting as a single class, given in person or by
proxy, either in writing or at a meeting, shall be necessary to permit, effect
or validate any of the following: (i) the authorization, creation or issuance,
or any increase in the authorized or issued amount, of any class of series of
Senior Stock or Parity Stock (both as defined in Section 8) or (ii) the
amendment, restatement, modification, alteration or repeal of any of the
provisions of this Certificate of Designation.

      (c) Until the earlier of (i) the termination of the Stock Rights and
Restrictions Agreement to be entered into on or about June 30, 1998, as it may
be amended from time to time (the "SLOPI Agreement"), between the Company and
Shell Louisiana Onshore Properties, Inc., a Delaware Corporation ("SLOPI") or
(ii) SLOPI and its Affiliates shall Beneficially Own shares of Common Stock
constituting less than 21% of the then outstanding shares of Common Stock, then,
in connection with each election of directors of the Company, whether at an
annual or special meeting, the holders of this Series shall be entitled to elect
at such meeting a number of directors (the "Preferred Directors") such that,
after giving effect to the election of such persons to the Board of Directors of
the Company, the number of Preferred Directors then serving on the Board of
Directors of the Company shall equal the product (rounded downward to the
nearest whole number, but, in any event, not less than one) of (i) the total
number of directors constituting the entire Board of Directors multiplied by
(ii) 20% (the "Director Percentage").

      (d) If at any time the number of directors constituting the Board of
Directors of the Company shall decrease so that the holders of the Series would
be entitled to designate fewer directors than are then serving as Preferred
Directors, the holders of 

                                      -3-
<PAGE>   4
the Series, one or more of the Preferred Directors shall resign so that the
percentage of the Board of Directors consisting of Preferred Directors does not
exceed the Director Percentage (rounded downward to the nearest whole number but
in no event less than one); provided, that, if a Preferred Director does not
resign, the members of the Board of Directors who are not Preferred Directors
shall be entitled to remove such Preferred Director. Further, (i) upon
termination of the SLOPI Agreement in accordance with its terms or (ii) the
conversion of all outstanding shares of this Series into Common Stock, all
Preferred Directors then serving as directors of the Company shall immediately
cease to be members of the Company's Board of Directors and shall be deemed to
have resigned on the date of such termination.

      (e) (i) In the event that any Preferred Director shall cease to serve as a
director for any reason (other than as set forth in Section (d) immediately
above), the vacancy resulting thereby shall be filled by appointment by any
Preferred Director remaining, and in the absence of action by the remaining
Preferred Directors, by the holders of the Series, and such Preferred Director
shall thereafter serve until the expiration of the term of the Preferred
Director replaced by such new Preferred Director.

          (ii) Subject to the provisions of Section 3(f) below, if there shall
exist at any time any vacancy or vacancies on the Board of Directors of the
Company as a result of any increase in the number of directors that constitutes
the entire Board of Directors of the Company, which the directors of the Company
then in office intend to fill in accordance with the Company's then existing
Articles of Incorporation, by-laws and applicable law, the holders of the Series
shall be entitled to designate one or more persons to fill such vacancy or
vacancies if and to the extent necessary so that, after giving effect to the
filling of such vacancy or vacancies, the number of Preferred Directors then
serving on the Board of Directors of the Company shall equal the Director
Percentage (rounded downward to the nearest whole number but in no event less
than one).

      (f) Notwithstanding anything to the contrary contained herein, no
Preferred Director may be a person who previously has been a director of the
Company and was properly removed for cause from the Board of Directors of the
Company or a person who has been convicted of a felony or a crime involving
moral turpitude.

      (g) At all times when there is a Preferred Director on the Company's Board
of Directors, at least one shall be a member of each Audit Committee of the
Board of Directors. All members of the Audit Committee shall have access to the
Company's independent accountants and all audit and tax work papers to the same
extent as any other member of the Audit Committee.

      (h) The Preferred Directors will be furnished with all information that is
provided to all other directors of the Company (in their capacities as such) at
the same time as such information is furnished to such other directors (in their
capacities as such).

                                      -4-
<PAGE>   5
      (i) All Preferred Directors shall comply with the retirement policies of
the Company as in effect on the date hereof or as hereafter amended or modified
from time to time by the Board of Directors of the Company or its stockholders;
provided that no such amendment or modification to such policies shall be
binding upon a Preferred Director unless at least one Preferred Director shall
have voted in favor of such amendment or modification at the meeting, or in the
action in lieu of a meeting, of the Board of Directors of the Company at or in
which it is considered.

      (j) The election of Preferred Directors or approval under paragraph (b)
above shall be by holders of a majority of the issued and outstanding Series as
reflected on the stock books of the Company on the applicable record date, or if
by written consent, on the date of such consent. The record date for holders of
shares of the Series entitled to vote on matters pursuant to this Section 3 at a
meeting of the holders of the Series shall be established by the Board of
Directors of the Company and shall not precede 60 days before such meeting.
Special meetings of the holders of the Series may be called by any holder of
more than 25% of the outstanding shares of the Series, except that the Company
may call a special meeting of the holders of the Series in connection with any
action to be voted on pursuant to paragraph (b) above. Any action taken by
written consent of the holders of the Series need not be unanimous and such
action will be effective upon delivery of such written consent to the Secretary
of the Company.

      SECTION 4. LIQUIDATION. In the event of any complete liquidation,
dissolution or winding-up of the Company, whether voluntary or involuntary the
holders of shares of this Series shall each be entitled to receive out of assets
of the Company, whether such assets are capital or surplus, for each share of
this Series a sum equal to the Stated Value plus the amount of any accrued and
unpaid dividends on such share plus interest accrued but unpaid on any
Arrearage, before any distribution shall be made to the holders of Junior Stock
of the Company, and if the assets of the Company shall be insufficient to pay in
full such amounts, then such assets shall be distributed among the holders of
this Series ratably in accordance with the respective amounts that would be
payable on such shares if all amounts payable thereon were paid in full.

      SECTION 5. CONVERSION.

      (a) Each share of this Series shall be convertible at the option of the
record holder thereof at any time by presentation of the certificate
representing such share by the record holder in person or by registered mail,
return receipt requested with postage prepaid thereof, at the principal office
of the Company, and at such other offices, if any, as the Board of Directors may
determine, into the number of fully paid and nonassessable shares of Common
Stock determined by dividing the Stated Value by the Conversion Price in effect
on the Conversion Date.

      (b) The conversion price initially shall be $10.516125 (the "Conversion
Price") and shall be subject to adjustment from time to time as follows:

                                      -5-
<PAGE>   6
            (i) If the Company, at any time while any shares of this Series are
      outstanding, shall (A) pay a stock dividend or stock dividends or
      otherwise make a distribution or distributions on shares of its capital
      stock payable in shares of Common Stock (or in securities convertible into
      shares of Common Stock), (B) except as set forth in clause (A) above, pay
      a stock dividend or make a distribution on shares of its capital stock
      payable in shares of its capital stock of any class other than Common
      Stock or a class convertible into Common Stock, (C) subdivide outstanding
      shares of Common Stock into a larger number of shares, (D) combine
      outstanding shares of Common Stock into a smaller number of shares, or (E)
      issue by reclassification of shares of Common Stock any shares of capital
      stock of the Company of any class or classes, the Conversion Price in
      effect immediately prior to such action shall be adjusted so that the
      holder of any shares of this Series thereafter surrendered for conversion
      shall be entitled to receive the number and class or classes of shares of
      the capital stock of the Company which he would have owned or have been
      entitled to receive immediately after the happening of any of the events
      described above, had such shares of this Series been converted on or
      immediately prior to the record date for such dividend or distribution or
      the effective date of such subdivision, combination or reclassification,
      as the case may be. An adjustment made pursuant to this subsection 5(b)(i)
      shall become effective immediately after the record date in the case of a
      dividend or distribution and shall become effective immediately after the
      effective date in the case of a subdivision, combination or
      reclassification.

            (ii) If the Company, at any time while any shares of this Series are
      outstanding, shall issue rights or warrants to all holders of Common Stock
      entitling them (for a period expiring within 45 days after the record date
      mentioned below) to subscribe for or purchase shares of Common Stock at a
      price per share less than the Per Share Market Value of Common Stock at
      the record date mentioned below, the Conversion Price at which each share
      of this Series shall thereafter be convertible shall be reduced by
      multiplying the Conversion Price in effect immediately prior to such
      record date by a fraction, of which the denominator shall be the number of
      shares of Common Stock (excluding treasury shares, if any) outstanding on
      the date of issuance of such rights or warrants plus the number of
      additional shares of Common Stock offered for subscription or purchase,
      and of which the numerator shall be the number of shares of Common Stock
      (excluding treasury shares, if any) outstanding on the date of issuance of
      such rights or warrants plus the number of shares which the aggregate
      offering price of the total number of shares so offered would purchase at
      such Per Share Market Value. Such adjustment shall be made whenever such
      rights or warrants are issued, and shall become effective immediately
      after the record date for the determination of stockholders entitled to
      receive such rights or warrants. However, upon the expiration of any right
      or warrant to purchase Common Stock the issuance of which resulted in an
      adjustment in the Conversion Price of the shares of this Series pursuant
      to this Subsection 5(b)(ii), if any such right or warrant shall expire and
      shall not have been fully exercised, the Conversion Price per share of
      Common Stock at which 

                                      -6-
<PAGE>   7
      each share of this Series shall thereafter be convertible shall
      immediately upon such expiration be recomputed and effective immediately
      upon such expiration be increased to the price which it would have been
      (but reflecting any other adjustments in the Conversion Price made
      pursuant to the provisions of this Section 6 after the issuance of such
      rights or warrants) had the adjustment of the Conversion Price made upon
      the issuance of such rights or warrants been made on the basis of offering
      for subscription or purchase only that number of shares of Common Stock
      actually purchased upon the exercise of such rights or warrants which were
      actually exercised. No adjustment shall be made pursuant to this Section
      5(b)(ii) if rights and warrants are also distributed to the holders of
      this Series on the basis of the number of shares of Common Stock then
      issuable on conversion of the shares of this Series.

            (iii) If the Company, at any time while shares of this Series are
      outstanding, shall distribute to all holders of Common Stock evidences of
      its indebtedness or assets (excluding cash dividends or cash distributions
      paid out of earned surplus) or rights or warrants to subscribe for or
      purchase any security (excluding those referred to in Subsection 5(b)(ii)
      above) then in each such case the Conversion Price per share of Common
      Stock at which each share of this Series shall thereafter be convertible
      shall be determined by multiplying the Conversion Price in effect
      immediately prior to the record date fixed for determination of
      stockholders entitled to receive such distribution by a fraction, of which
      the denominator shall be the Per Share Market Value of Common Stock
      determined as of the record date mentioned above, and of which the
      numerator shall be such Per Share Market Value of the Common Stock, less
      the then fair market value (as determined by the Board of Directors of the
      Company (the "Board") in good faith, whose determination shall be
      conclusive if made in good faith; provided, however, that in the event of
      a distribution or series of related distributions exceeding 10% of the net
      assets of the Company, then such fair market value shall be determined by
      a nationally recognized or major regional investment banking firm or firm
      of independent certified public accountants of recognized standing (which
      may be the firm that regularly examines the financial statements of the
      Company) selected in good faith by the Board, and in either case shall be
      described in a statement provided to all registered holders of this
      Series) of the portion of assets or evidences of indebtedness so
      distributed or such subscription rights applicable to one share of Common
      Stock. Such adjustment shall be made whenever any such distribution is
      made and shall become effective immediately after the record date
      mentioned above. No adjustment shall be made pursuant to this subsection
      5(b)(iii) if such evidence of indebtedness or assets are also distributed
      to the holders of this Series on the basis of the number of shares of
      Common Stock then issuable on the conversion of the shares of this Series.

            (iv) No notification to the holders of any adjustment in the
      Conversion Price otherwise required by this Section 5 shall be required
      unless such adjustment would require an increase or decrease of at least
      1% in such price; provided, however, that any adjustment which by reason
      of this 

                                      -7-
<PAGE>   8
      subsection 5(b)(iv) is not required to be made shall be carried forward
      and taken into account in any subsequent adjustments, and that upon
      presentment of shares of this Series for conversion, all adjustment shall
      be made calculating the conversion rights of such holder. All calculations
      under this Section 5 shall be made to the nearest cent or the nearest
      1/100th of a share, as the case may be.

            (v) Subject to (iv) above, whenever the Conversion Price is
      adjusted, as herein provided, the Company shall promptly mail to each
      registered holder of shares of this Series a notice setting forth the
      Conversion Price after such adjustment and setting forth a brief statement
      of the facts requiring such adjustment. Such notice prepared in good faith
      shall be conclusive evidence of the correctness of such adjustment absent
      manifest error.

            (vi) In case:

                  (A) the Company shall declare a dividend (or any other
            distribution) on the Common Stock payable otherwise than in cash out
            of its earned surplus; or

                  (B) the Company shall declare a special nonrecurring cash
            dividend on or a redemption of its Common Stock; or

                  (C) the Company shall authorize the granting to the holders of
            the Common Stock of rights or warrants to subscribe for or purchase
            any shares of capital stock of any class or of any other rights; or

                  (D) the approval of any stockholders of the Company shall be
            required in connection with any reclassification of the Common Stock
            of the Company (other than a subdivision or combination of the
            outstanding shares of Common Stock), any consolidation or merger to
            which the Company is a party, any sale or transfer of all or
            substantially all of the assets of the Company, or any compulsory
            share exchange whereby the Common Stock is converted into other
            securities, cash or property; or

                  (E) of the voluntary or involuntary dissolution, liquidation
            or winding up of the affairs of the Company,

then the Company shall cause to be filed at each office or agency maintained for
the purpose of conversion of the shares of this series, and shall cause to be
mailed to the holders of record of the shares of this Series at their last
addresses as they shall appear upon the stock books of the Company, at least 10
days prior to the applicable record date hereinafter specified, a notice stating
(x) the date on which a record is to be taken for the purpose of such dividend,
distribution, redemption, rights or warrants, or, if a record is not to be
taken, the date as of which the holders of Common Stock of record to be entitled
to such dividend, distribution, redemption, rights or warrants are to be
determined, or (y) the date on which such reclassification, consolidation,
merger, sale, transfer, share exchange, dissolution, liquidation or winding up
is expected to become 

                                      -8-
<PAGE>   9
effective, and the date as of which it is expected that holders of Common Stock
of record shall be entitled to exchange their shares of Common Stock for
securities or other property deliverable upon such reclassification,
consolidation, merger, sale, transfer, share exchange, dissolution, liquidation
or winding up (but no failure to mail such notice or any defect therein or in
the mailing thereof shall affect the validity of the corporate action required
to be specified in such notice).

      (c) In case of any reclassification of the Common Stock, then the holders
of the shares of this Series then outstanding shall have the right thereafter to
convert such shares only into the kind and amount of shares of stock and other
securities and property receivable upon or deemed to be held following such
reclassification by a holder of a number of shares of the Common Stock of the
Company into which such shares of this Series could have been converted
immediately prior to such reclassification. This provision shall similarly apply
to successive reclassifications.

      (d) In case of any consolidation or merger of the Company with or into
another Person in which the Company is not the surviving entity or any
compulsory share exchange pursuant to any of which the Common Stock is converted
into other securities, cash or property (any such event being hereinafter
referred to as "Reorganization"), then the terms of such Reorganization shall
provide that each holder of share of this Series then outstanding shall have the
right to receive in exchange therefor the kind and amount of shares of stock and
other securities and property receivable upon such Reorganization
("Reorganization Consideration") by a holder of the number of shares of the
Common Stock of the Company into which (x) a share of this Series (or
Sub-Series) could have been converted as of the effective date of the
Reorganization, plus (y) the Arrearage (if any) on a share of this Series could
have been exchanged as of the effective date of the Reorganization.

      (e) In case at any time conditions shall arise by reason of action taken
by the Company, which, in the opinion of the Board of Directors of the Company,
are not adequately covered by the other provisions hereof and which might
materially and adversely affect the rights of the holders of shares of this
Series, the Board of Directors of the Company shall appoint a firm of
independent certified public accountants of recognized standing (which may be
the firm that regularly examines the financial statements of the Company), who
shall give their opinion as to the adjustment, if any (not inconsistent with the
standards established in this Section 5, of the Conversion Price (including, if
necessary, any adjustment as to the securities into which shares of this Series
may thereafter be convertible) which is or would be required to preserve the
rights of the holders of shares of this Series. The Board of Directors of the
Company shall make the adjustment recommended forthwith upon the receipt of such
opinion or the taking of any such action contemplated, as the case may be;
provided, however, that no such adjustment of the Conversion Price shall be made
which in the opinion of the investment banking firm or firm of accountants
giving the aforesaid opinion would result in an increase of the Conversion Price
to more than the Conversion Price then in effect.

                                      -9-
<PAGE>   10
      Section 6. MATTERS RELATING TO ISSUANCE OF COMMON STOCK. The following
provisions shall be applicable to issuances of Common Stock upon conversion of
shares of this Series.

      (a) The Company covenants that it will at all times reserve and keep
available, out of its authorized and unissued Common Stock solely for the
purpose of issuance upon conversion of this Series as herein provided, free from
preemptive rights or any other actual or contingent purchase rights of Persons
other than the holders of shares of this Series, such number of shares of Common
Stock as shall then be issuable upon the conversion of all outstanding shares of
this Series. The Company covenants that all shares of Common Stock that shall be
so issuable shall upon issue be duly and validly issued and fully paid and
nonassessable.

      (b) The Company shall not be required to issue stock certificates
representing fractions of shares of Common Stock, but may, if otherwise
permitted, make a cash payment in respect of any final fraction of a share based
on the Per Share Market Value at such time. If the Company elects not, or is
unable, to make such a cash payment, the holder of a share of this Series shall
be entitled to receive, in lieu of the final fraction of a share, one whole
share of Common Stock.

      (c) The issuance of certificates for shares of Common Stock on conversion
of this Series shall be made without charge to the holders thereof for any
documentary stamp or similar taxes that may be payable in respect of the issue
or delivery of such certificate, provided, that the Company shall not be
required to pay any tax that may be payable in respect of any transfer involved
in the issuance and delivery of any such certificate in a name other than that
of the holder of the shares of this Series converted was made and the Company
shall not be required to issue or deliver such certificates unless or until the
Person or Persons requesting the issuance thereof shall have paid to the Company
the amount of such tax or shall have established to the satisfaction of the
Company that such tax has been paid.

      (d) The exercise by a holder of shares of this Series of the conversion
rights granted herein is subject in all respects to and conditioned upon
compliance by the parties with the HSR Act, and rules and regulations
promulgated pursuant thereto, to the extent that said act, rules and regulations
are applicable to such exercise. The Company and such holder agree to make such
filings with and provide such information to the Federal Trade Commission and
the Department of Justice with respect to such exercise as are required in
connection with the HSR Act in a timely manner and to join each others request
for early termination. The Company and such holder will use such reasonable
efforts to obtain all governmental approval required to permit such exercise and
to cause early termination of the waiting period under the HSR Act.

      SECTION 7. AUTOMATIC CONVERSION. If on or after June 30, 2001 (a) any
shares of this Series have not been converted into shares of Common Stock and
(b) the mean average Per Share Market Value exceeds 150% of the Conversion Price
for 75 consecutive Trading Days, then all such shares of this Series shall
automatically be converted into the number of shares of Common Stock determined
by dividing the 

                                      -10-
<PAGE>   11
Stated Value by the Conversion Price in effect at the time of conversion;
provided that SLOPI and its Affiliates may elect to retain an aggregate of one
share of Preferred Stock that will not be automatically converted pursuant to
this Section 7.

      SECTION 8. DEFINITIONS. For the purposes hereof, the following terms shall
have the following respective meanings:

      "Affiliate" shall mean, with respect to any specified Person, any other
Person, directly or indirectly controlling or controlled by or under direct or
indirect common control with such specified Person. For the purposes of this
definition, "control" (including, with correlative meanings, "controlling,"
"controlled by," and "under common control with") means the power to direct or
cause the direction of the management and policies of such Person, directly or
indirectly, whether through the ownership of voting securities, by contract, or
otherwise and, and with respect to a corporation or partnership, control shall
mean direct or indirect ownership of more than fifty percent (50%) of the voting
stock or general partnership interest or voting interest in any such corporation
or partnership.

      "Arrearage" has the meaning specified in Section 2(a).

      "Beneficially Own" shall have the meaning assigned to such term in Rule
13d-3 under the Exchange Act in effect on the date hereof. "Beneficial Owner"
and "Beneficial Ownership" shall have correlative meanings.

      "Business Day" shall mean any day that commercial banks located in
Houston, Texas are legally open for business.

      "Change of Control" shall mean the acquisition by a Person other than
SLOPI or its Affiliates of Beneficial Ownership of more than 50% of the then
outstanding shares of Common Stock.

      "Common Stock" means shares now or hereafter authorized of the class of
Common Stock, $0.01 par value, of the Company presently authorized and stock of
any other class into which such shares may hereafter have been reclassified or
changed.

      "Conversion Date" means the date the stock certificate is received by the
Company for conversion in accordance with Section 5(a).

      "Conversion Price" has the meaning specified in Section 5(b).

      "Dividend Period" has the meaning specified in Section 2(a).

      "Dividend Rate" has the meaning specified in Section 2(a).

      "Fully Diluted Shares" means, at any time, the sum of (i) the shares of
Common Stock then outstanding plus (ii) the number of shares of Common Stock
reserved for issuance or issuable in connection with the exercise, exchange or
conversion of options, 

                                      -11-
<PAGE>   12
warrants or securities of the Company then outstanding which are exercisable or
exchangeable for shares of Common Stock or are convertible into shares of Common
Stock (including, without limitation, this Series).

      "HSR Act" means the Hart-Scott-Rodino Antitrust Improvements Act of
1976, as amended.

      "Junior Stock" means the Common Stock of the Company and any other stock
of the Company over which shares of this Series has a preference as to
distribution of assets and payment of dividends.

      "Parity Stock" means any stock of the Company ranking as to distribution
of assets and payment of dividends on a parity with this Series.

      "Per Share Market Value" means on any particular date (a) the last sale
price per share of the Common Stock on such date on the principal stock exchange
on which the Common Stock has been listed or, if there is no such price on such
date, then the last sale price on such exchange on the date nearest preceding
such date, or (b) if the Common Stock is not listed on any stock exchange, the
final bid price for a share of Common Stock in the over-the-counter market, as
reported by The Nasdaq Stock Market at the close of business on such date, or
the last sales price if such price is reported and final ibid prices are not
available, or (c) if the Common Stock is not quoted on The Nasdaq Stock Market,
the bid price for a share of Common Stock in the over-the-counter market as
reported by the National Quotation Bureau Incorporated (or any similar
organization or agency succeeding to its functions of reporting prices), or (d)
if the Common Stock is no longer publicly traded, as determined by one of the
investment banking firms listed on Schedule I to the SLOPI Agreement selected in
good faith by the Board of Directors of the Company, provided, that none of the
transactions related to the foregoing shall include purchases by any "affiliate"
(as such term is defined in the General Rules and Regulations under the
Securities Act of 1933) of the Company.

      "Person" means any individual, firm, partnership, association, group (as
such term is defined in Section 13(d)(3) of the Exchange Act, as in effect on
the date hereof), corporation, trust, business trust or other entity, and
includes any successor (by merger or otherwise) of any such entity.

      "Preferred Stock" means the Company's Preferred Stock, par value $0.01
per share.

      "Reorganization" has the meaning specified in Section 5(d).

      "Reorganization Consideration" has the meaning specified in
Section 5(d).

      "Senior Stock" means any stock of the Company which has a priority over
shares of this Series as to payment of dividends or distribution of assets of
the Company.

                                      -12-
<PAGE>   13
      "SLOPI" means Shell Louisiana Onshore Properties, Inc., a Delaware
corporation.

      "SLOPI Agreement" has the meaning assigned thereto in Section 3.C.

      "Stated Value" has the meaning specified in Section 1.

      "Trading Day" means (a) a day on which the Common Stock is traded on the
principal stock exchange on which the Common Stock has been listed, or (b) if
the Common Stock is not listed on any stock exchange, a day on which the Common
Stock is quoted in the over-the-counter market, as reported by National
Association of Securities Dealers Automated Quotation System ("NASDAQ"), or (c)
if the Common Stock is not quoted by NASDAQ, a day on which the Common Stock is
quoted in the over-the-counter market as reported by the National Quotation
Bureau Incorporated (or any similar organization or agency succeeding to its
functions of reporting prices).


      IN WITNESS WHEREOF, The Meridian Resource Corporation has caused this
Certificate to be signed by a duly authorized officer, this 30th day of June,
1998.

                              THE MERIDIAN RESOURCE CORPORATION

                              By: /s/ JOSEPH A. REEVES, JR.
                                      Joseph A. Reeves, Jr.
                                      Chief Executive Officer and
                                      Chairman of the Board
ATTEST:

By:  /s/ MELINDA FREW

                                      -13-


<PAGE>   1

                                                                       EXHIBIT 4

                     STOCK RIGHTS AND RESTRICTIONS AGREEMENT

      STOCK RIGHTS AND RESTRICTIONS AGREEMENT, dated as of June 30, 1998,
between The Meridian Resource Corporation, a Texas corporation ("TMR"), and
Shell Louisiana Onshore Properties Inc., a Delaware corporation ("SLOPI").

                                    RECITALS:

      A. After giving effect to the Closing (as defined below), SLOPI owns
 12,082,030 shares of Common Stock (the "Common Shares") and 3,982,906 shares
of Preferred Stock (the "Preferred Shares") (together with any additional Common
Shares or Preferred Shares which SLOPI or any Affiliate of Shell (as defined
below) may from time to time own (collectively, the "Shares")).

      B. After giving effect to the Closing, the number of directors
constituting the whole Board of Directors of TMR is seven (7) and the following
person is the initial Preferred Director (as defined below): J.M. Funk.

      C. The Boards of Directors of TMR and SLOPI deem it advisable to establish
certain rights and restrictions with respect to the Shares.

      ACCORDINGLY, premises considered, the parties have entered into this
Agreement.

      1.    DEFINITIONS. For purposes of this Agreement, the following terms
have the meanings indicated:

            (a) "Affiliate" shall mean, with respect to any specified Person,
any other Person, directly or indirectly controlling or controlled by or under
direct or indirect common control with such specified Person. For the purposes
of this definition, "control" (including, with correlative meanings,
"controlling," "controlled by," and "under common control with") means the power
to direct or cause the direction of the management and policies of such Person,
directly or indirectly, whether through the ownership of voting securities, by
contract, or otherwise and, with respect to a corporation or partnership,
control shall mean direct or indirect ownership of more than fifty percent (50%)
of the voting stock or general partnership interest or voting interest in any
such corporation or partnership.
<PAGE>   2
            (b) "Allocated Price Per Share" shall mean the then existing
conversion price of the Preferred Shares (or if all of the Preferred Shares
shall have been converted, the conversion price that would have then been in
existence had the Preferred Shares not been so converted) as the same may be
adjusted from time to time in accordance with the terms thereof.

            (c) "Applicable Percentage" shall mean 21%.

            (d) "Average Per Share Market Value" of shares of Common Stock shall
mean the average of the Per Share Market Value of such shares for the 30 Trading
Days immediately preceding (and excluding) the relevant date.

            (e) "Beneficially Own" shall have the meaning assigned to such term
in Rule 13d-3 under the Exchange Act in effect on the date hereof. "Beneficial
Owner" and "Beneficial Ownership" shall have correlative meanings.

            (f) "Business Combination Transaction" shall mean a merger,
consolidation, "business combination" as defined in Part Thirteen of the TBCA as
in effect on the date hereof, compulsory share exchange, recapitalization or
other transaction in which TMR is a constituent corporation or to which TMR is a
party and pursuant to which the shares of Common Stock are exchanged for cash,
securities or other property or a sale of all or substantially all of the assets
of TMR and its Subsidiaries, taken as a whole; provided that none of the
following shall be deemed a Business Combination Transaction for purposes of
this Agreement: (i) a merger, consolidation, compulsory share exchange,
recapitalization or other transaction in which the Beneficial Ownership of the
capital stock of TMR or the surviving corporation of the transaction (or of the
ultimate parent of TMR or of such surviving corporation) immediately after the
consummation of such transaction is substantially the same as the ownership of
the capital stock of TMR immediately prior to the consummation of the
transaction or (ii) a merger (A) in which TMR is the surviving corporation, (B)
in which all shares of Common Stock immediately prior to the consummation of
such merger remain outstanding immediately after the consummation thereof, (C)
as a result of the consummation of which no Person will own a majority of the
then outstanding shares of Common Stock and (D) following the consummation of
which the Continuing Directors will represent a majority of the Board of
Directors of TMR.

            (g) "Certificate of Designation" for the Preferred Shares shall have
the meaning assigned to such term in the Merger Agreement.

            (h) "Closing" shall have the meaning assigned to such term in the
Merger Agreement.

            (i)   "Common Shares" shall have the meaning set forth in Recital
A.

            (j) "Common Stock" shall mean TMR's common stock, par value $0.01
per share, and any shares of common stock or similar securities into which the
common stock of TMR are hereafter reclassified into or exchanged for.

                                    -2-
<PAGE>   3
            (k) "Continuing Director" shall mean (i) any member of the Board of
Directors of TMR, while such person is a member of such Board of Directors, who
(1) was a member of the Board of Directors of TMR prior to the Effective Time or
(2) is recommended or elected to the Board of Directors by a majority of the
Continuing Directors to fill a vacancy arising as a result of an increase in the
number of directors of TMR occurring after the date hereof, and (ii) any
successor of a Continuing Director, while such successor is a member of the
Board of Directors of TMR, who is recommended or elected to succeed the
Continuing Director by a majority of the Continuing Directors. Notwithstanding
anything to the contrary in this definition, for purposes of this Agreement, the
SLOPI Designee(s) or Preferred Director(s) shall not be considered Continuing
Directors.

            (l) "Deficiency Amount" shall mean with respect to any sale by SLOPI
or its Affiliates of Common Shares which were issued upon the conversion of
Preferred Shares, (i) the product of (x) the number of Common Shares sold by
SLOPI or its Affiliates in such sale at a per share price that is less than the
Allocated Price Per Share, times (y) the amount by which the per share sales
price is less than the Allocated Price Per Share. If Common Shares are sold in a
Public Offering, then the net proceeds to selling shareholder (after reasonable
and customary underwriting discounts, commissions, placement fees and expenses
of sale, excluding expenses for Security Holder's legal counsel) shall be deemed
to be the sales price. If Common Shares are sold in a Private Placement or any
transaction other than Public Offering, then the sales price shall be deemed to
be the greater of (i) the actual sales price or (ii) the Average Per Share
Market Value of the Common Stock relating to the date of such sale.

            (m) "Director Election Date" shall have the meaning set forth in
Section 2.2(b).

            (n) "Director Percentage" shall have the meaning set forth in
Section 2.2(b).

            (o) "Effective Time" shall have the meaning assigned to such term in
the Merger Agreement.

            (p) "E&P Company" shall have the meaning set forth in the definition
of Private Placement.

            (q) "Excess Shares" shall have the meaning set forth in Section 2.5.

            (r) "Exchangeable Security" shall mean a security of any type,
including but not limited to debt, equity, warrants or other rights, issued by
TMR or representing the right to acquire Voting Shares from TMR upon exchange,
conversion or exercise thereof.

                                    -3-
<PAGE>   4
            (s) "Exchange Act" shall mean the Securities Exchange Act of 1934,
as amended, or any successor federal statute as in effect from time to time.

            (t) "Fully Diluted Shares" shall mean, at any time, the sum of (i)
the shares of Common Stock then outstanding plus (ii) the number of shares of
Common Stock reserved for issuance or issuable in connection with the exercise,
exchange or conversion of options, warrants or securities of TMR then
outstanding which are exercisable or exchangeable for shares of Common Stock or
are convertible into shares of Common Stock (including, without limitation, the
Preferred Shares).

            (u) "Merger Agreement" shall mean the Agreement and Plan of Merger
dated March 27, 1998 among TMR, LOPI Acquisition Corp., SLOPI, and Louisiana
Onshore Properties Inc.

            (v) "Per Share Market Value" means on any particular date (a) the
last sale price per share of the Common Stock on such date on the principal
stock exchange on which the Common Stock has been listed or, if there is no such
price on such date, then the last price on such exchange on the date nearest
preceding such date, or (b) if the Common Stock is not listed on any stock
exchange, the final bid price for a share of Common Stock in the
over-the-counter market, as reported by The Nasdaq Stock Market at the close of
business on such date, or the last sales price if such price is reported and
final bid prices are not available, or (c) if the Common Stock is not quoted on
The Nasdaq Stock Market, the bid price for a share of Common Stock in the over-
the-counter market as reported by the National Quotation Bureau Incorporated (or
any similar organization or agency succeeding to its functions of reporting
prices), or (d) if the Common Stock is no longer publicly traded, as determined
by one of the investment banking firms listed on Schedule I, as selected by
SLOPI.

            (w) "Person" shall mean any individual, firm, partnership,
association, group (as such term is defined in Section 13(d)(3) of the Exchange
Act, as in effect on the date hereof), corporation, trust, business trust or
other entity, and includes any successor (by merger or otherwise) of any such
entity.

            (x) "Preferred Director" shall have the meaning assigned to such
term in the Certificate of Designation for the Preferred Stock.

            (y) "Preferred Shares" shall have the meaning set forth in Recital 
A.

            (z) "Preferred Stock" shall mean TMR's Series A Cumulative
Convertible Preferred Stock, par value $1.00 per share.

            (aa) "Private Placement" shall mean a Transfer of Shares pursuant to
a transaction not involving a Pubic Offering; provided, however, that (A) the
sale of Shares pursuant to a tender or exchange offer is not a Private
Placement; (B) a Private Placement shall not include a Transfer to any Person
who, directly or indirectly, has as one of its material businesses the
exploration, development or production of crude oil or natural gas (an "E&P
Company") if, as a result of such Private Placement, such E&P Company would
Beneficially Own and/or have the right to acquire upon conversion of shares of
Preferred Stock, such 

                                      -4-
<PAGE>   5
number of shares of Common Stock as would constitute 10% or more of the then
outstanding shares of Common Stock, (x) unless any such E&P Company acquiring
such amount of securities enters into an agreement with TMR limiting the
Transfer of such shares on substantially the same terms as this Agreement except
that the term of such agreement shall be 10 years from the date of such
agreement and (y) if any such E&P Company is acquiring registration rights under
the Registration Rights Agreement (as defined in the Merger Agreement), it must
agree that, although any underwriter for such E&P Company shall have customary
access to TMR to perform its due diligence obligations, such underwriter will be
subject to confidentiality obligations that prohibit the sharing or disclosure
of non-public information with such E&P Company; and (C) a private placement
shall not include a Transfer of Shares to any Person in which following such
Transfer such Person Beneficially Owns or has the right to acquire upon
conversion of the Preferred Stock more than 10% of the Common Stock of TMR
unless such Person enters into an agreement with TMR with terms and conditions
restricting the Transfer of such Shares substantially similar to those contained
herein except that the term of such agreement shall be for 10 years from the
date of such agreement. For purposes of the foregoing, in determining whether
any Person Beneficially Owns shares of Common Stock or shares of Preferred
Stock, SLOPI and its Affiliates shall be entitled to rely exclusively on the
existence or non-existence of any reports on Schedule 13D that may have been
filed by such Person with the SEC, without having to make any inquiry of such
Person or otherwise.

            (ab) "Public Offering" shall mean a firm commitment underwritten
public offering pursuant to a registration statement which has been declared
effective by the SEC under the Securities Act.

            (ac)  "Relevant Date" shall have the meaning set forth in Section
2.4(k).

            (ad) "Rule 144" and "Rule 145" shall mean Rule 144 and Rule 145
adopted by the SEC under the Securities Act, or any successor rule.

            (ae)  "SEC" shall mean the Securities and Exchange Commission.

            (af) "Securities Act" shall mean the Securities Act of 1933, as
amended, or any successor federal statute as in effect from time to time.

            (ag)  "Shares" shall have the meaning set forth in Recital A.

            (ah) "Shell" shall mean Shell Oil Company, a Delaware corporation,
which is an Affiliate of SLOPI.

            (ai) "Subsidiary" shall mean, with respect to any Person, any other
Person of which at least a majority of the voting power of the voting equity
securities or voting equity interest is owned, directly or indirectly, by such
Person.

                                      -5-
<PAGE>   6
            (aj) "SLOPI" shall have the meaning set forth in the first paragraph
hereof; and the term "SLOPI" shall include SLOPI and its Affiliates unless the
context otherwise requires.

            (ak) "SLOPI Designee(s)" shall have the meaning set forth in Section
2.2(b) hereof.

            (al)  "TBCA" shall have the meaning set forth in Section 2.1(c).

            (am) "TMR" shall have the meaning set forth in the first paragraph
of this Agreement.

            (an) "Trading Days" means (a) a day on which the Common Stock is
traded on the principal stock exchange on which the Common Stock has been
listed, or (b) if the Common Stock is not listed on any stock exchange, a day on
which the Common Stock is quoted in the over-the-counter market, as reported by
The Nasdaq Stock Market, or (c) if the Common Stock is not quoted on The Nasdaq
Stock Market, a day on which the Common Stock is quoted in the over-the-counter
market as reported by the National Quotation Bureau Incorporated (or any similar
organization or agency succeeding to its functions of reporting prices).

            (ao)  "Transfer" shall have the meaning set forth in Section 2.4
hereof.

            (ap) "Voting Shares" shall mean the Common Stock and any other
securities of TMR having voting power under ordinary circumstances with respect
to the election of directors of TMR.

      2.    SHARE RIGHTS AND RESTRICTIONS.

            2.1   LIMITATION ON CERTAIN TRANSACTIONS.

                  (a) Except as otherwise permitted by this Agreement, SLOPI
agrees that SLOPI shall not, during the period from the date of this Agreement
until its termination, (i) engage, or propose to engage, in any Business
Combination Transaction with TMR, or (ii) make any proposal to TMR, the Board of
Directors of TMR or the shareholders of TMR with respect to a tender offer or
exchange offer for shares of Common Stock or a liquidation of TMR, unless either
(A) such transaction shall have been approved by a majority of the Continuing
Directors or (B) (x) the third anniversary of the date of this Agreement shall
have occurred and (y) on the date when such transaction is proposed, either no
Preferred Director(s) or SLOPI Designee(s) shall be serving on the Board of
Directors of TMR or SLOPI and its Affiliates collectively shall Beneficially Own
less than 21% of the then outstanding Common Stock.

                  (b) Except as otherwise permitted by this Agreement, SLOPI
agrees that SLOPI shall not, during the period from the date of this Agreement
until its termination, (i) request or solicit any Person (A) to make a tender or
exchange offer for shares of Common Stock or (B) to make a proposal for a
Business Combination 

                                      -6-
<PAGE>   7
Transaction, unless either (A) a majority of the Continuing Directors shall have
approved of SLOPI taking such action or (B) (x) the third anniversary of the
date of this Agreement shall have occurred on the date when such action is first
requested or solicited by SLOPI and (y) either no SLOPI Designee(s) or Preferred
Director(s) shall be serving on the Board of Directors of TMR or SLOPI and its
Affiliates shall collectively Beneficially Own less than 21% of the then
outstanding Common Stock.

                  (c) In connection with the Merger, TMR's Board of Directors
has taken all action to assure that (i) no state takeover statute or similar
statute will apply to the Merger or to any of the transactions contemplated in
the Merger Agreement or the items referenced to in Section 2.3(w), (x), (y) and
(z), (ii) Article Eight of TMR's Articles of Incorporation will not apply to the
Merger or any of the transactions contemplated in the Merger Agreement or in the
documents attached thereto, and (iii) Part Thirteen of the Texas Business
Corporation Act ("TBCA") will not apply to the Merger or any of the transactions
contemplated in the Merger Agreement or the items referenced to in Section
2.3(w), (x), (y) and (z). Further, TMR has no "poison pill" or takeover defense
mechanism other than Article Eight of TMR's Articles of Incorporation except
those that exclude SLOPI and its Affiliates from all effects thereof. TMR shall
not amend or modify any of the foregoing actions nor shall TMR implement any
new, additional, amended or modified poison pill or takeover defense mechanism,
unless, in each and every such case, provision shall be made to exclude SLOPI
and its Affiliates from all effects thereof. This Section 2.1(c) shall survive
the termination of this Agreement.

                  (d) TMR and SLOPI agree that the operative provisions, as
presently in effect, of Article Eight of TMR's Articles of Incorporation and
Part Thirteen of the TBCA will apply to any business combination transaction
covered by said Article Eight or Part Thirteen between SLOPI and its Affiliates
and TMR for the term of this Agreement, notwithstanding that the operative
provisions of said Article Eight and Part Thirteen might otherwise be applicable
for a shorter period of time.

            2.2   TMR BOARD OF DIRECTORS.

                  (a) Subject to restrictions of applicable law and unless this
Agreement has been terminated, on the Director Election Date (defined below),
TMR shall appoint SLOPI Designee(s) (defined below) to fill the vacancies
created by the removal of the Preferred Director(s) in accordance with the
Certificate of Designation for the Preferred Stock, to serve until their
successors are elected or their earlier resignation or removal.

                  (b) From and after the date on which all the Preferred Shares
shall have been converted into Common Stock (the "Director Election Date") and
until the earlier of (i) termination of this Agreement or (ii) SLOPI and its
Affiliates shall Beneficially Own Shares constituting less than 21% of the then
outstanding shares of Common Stock, then, in connection with each election of
directors of TMR, whether at an annual or special meeting, TMR will nominate,
and, subject to the fiduciary obligations of the TMR directors, solicit proxies
for, in accordance with its procedures 

                                      -7-
<PAGE>   8
for the nomination of, and solicitation of proxies for, management-slate
directors, a number of persons designated by SLOPI (all such persons who, at any
time, are or were designated by SLOPI for purposes of this Agreement are
referred to herein as the "SLOPI Designee(s)") such that, after giving effect to
the election of such persons to the Board of Directors of TMR, the number of
SLOPI Designees then serving on the Board of Directors of TMR shall equal the
product (rounded downward to the nearest whole number, but, in any event, not
less than one) of (i) the total number of directors constituting the entire
Board of Directors of TMR multiplied by (ii) 20% (the "Director Percentage").

                  (c) If at any time the number of directors constituting the
Board of Directors of TMR shall decrease so that SLOPI would be entitled to
designate fewer directors than are then serving as SLOPI Designees, SLOPI shall
cause one or more of the SLOPI Designees serving as TMR directors to resign so
that the percentage of the Board of Directors consisting of SLOPI Designees does
not exceed the Director Percentage (rounded downward to the nearest whole
number, but, in any event, not less than one); provided, that in no event will
there ever be less than one SLOPI Designee. Further, upon termination of this
Agreement in accordance with its terms, SLOPI shall cause all SLOPI Designees
then serving as directors of TMR to resign immediately.

                  (d) (i) In the event that any SLOPI Designee shall cease to
serve as a director for any reason (other than as set forth in Section 2.2(c)),
the vacancy resulting thereby shall be filled by the remaining directors of the
Company in accordance with its Articles of Incorporation, by-laws and applicable
law by a new SLOPI Designee and such new SLOPI Designee shall thereafter serve
until the expiration of the term of the SLOPI Designee replaced by such new
SLOPI Designee.

                      (ii)  Subject to the provisions of Section 2.2(e), if, 
after the Director Election Date, there shall exist at any time any vacancy or
vacancies on the Board of Directors of TMR as a result of any increase in the
number of directors that constitutes the entire Board of Directors of TMR, which
the directors of TMR then in office intend to fill in accordance with TMR's
Articles of Incorporation, by-laws and applicable law, SLOPI shall be entitled
to designate one or more persons as SLOPI Designees to fill such vacancy or
vacancies if and to the extent necessary so that, after giving effect to the
filling of such vacancy or vacancies, the number of SLOPI Designees then serving
on the Board of Directors of TMR shall equal the Director Percentage (rounded
downward to the nearest whole number, but, in any event, not less than one). TMR
agrees to take all actions appropriate or necessary to ensure that any SLOPI
Designees designated pursuant to the preceding sentence are appointed to the
Board of Directors of TMR to fill any such vacancy or vacancies filled by the
Board of Directors of TMR as provided in the preceding sentence.

                  (e) Notwithstanding anything to the contrary contained herein,
no SLOPI Designee may be a person who previously has been a director of TMR and
was properly removed for cause from the Board of Directors of TMR or a person
who has been convicted of a felony or a crime involving moral turpitude.

                                      -8-
<PAGE>   9
                  (f) The SLOPI Designees will be furnished with all information
that is provided to all other directors of TMR (in their capacities as such) at
the same time as such information is furnished to such other directors (in their
capacities as such).

                  (g) SLOPI shall cause all SLOPI Designees serving as directors
of TMR to comply with the retirement policies of TMR as in effect on the date
hereof or as hereafter amended or modified from time to time by the Board of
Directors of TMR or its shareholders; provided that no such amendment or
modification to such policies shall be binding upon SLOPI or the SLOPI Designees
unless at least one SLOPI Designee shall have voted in favor of such amendment
or modification at the meeting, or in the action in lieu of a meeting, of the
Board of Directors of TMR at or in which it is considered.

                  (h) At all times when there is a SLOPI Designee on TMR's Board
of Directors, at least one SLOPI Designee shall be a member of each Audit
Committee of the Board of Directors. Each SLOPI Designee who is a member of the
Audit Committee shall have unrestricted access to TMR's independent accountants
and all audit and tax work papers to the same extent as any other member of the
Audit Committee.

            2.3 LIMITATION ON ACQUISITION OF ADDITIONAL SHARES BY SLOPI. From
and after the date hereof, SLOPI shall not acquire any shares of Common Stock,
other than the Common Shares and the Preferred Shares owned by SLOPI as of the
Effective Time and after giving effect to the Closing, (i) without the prior
written consent of a majority of the Continuing Directors or (ii) unless (A) the
third anniversary of the date of this Agreement shall have occurred and (B) at
the time of such acquisition no SLOPI Designee(s) or Preferred Director(s) shall
be serving on the Board of Directors of TMR or SLOPI and its Affiliates would
collectively Beneficially Own less than 21% of the then outstanding Common
Stock; provided, however, that nothing in this Section 2.3 shall limit SLOPI's
power and right (w) to convert shares of Preferred Stock into shares of Common
Stock, or (x) to purchase or acquire shares as a result of any stock dividend or
stock split, reclassification of the Common Stock, or the exercise or conversion
of any security received by SLOPI from TMR in respect of its Shares, or (y) to
receive shares of Common Stock pursuant to Section 2.7 to make up a Deficiency
Amount or (z) to acquire shares of Common Stock or any TMR Exchangeable Security
pursuant to Section 2.6 or to convert, exchange or exercise any such TMR
Exchangeable Security.

            2.4 RESTRICTIONS ON TRANSFER. From and after the date hereof until
the termination of this Agreement, SLOPI and its Affiliates shall not sell,
transfer or otherwise convey (when used as a verb, "Transfer" and, any sale,
transfer or other conveyance, a "Transfer") Beneficial Ownership of any Shares
(including Shares subject to Exchangeable Securities), without the prior written
consent of a majority of the Continuing Directors, which consent shall not be
unreasonably withheld, except that, in any event, any and all of the following
Transfers shall be permitted:

                                      -9-
<PAGE>   10
                  (a) One or more Transfers to Shell or a direct or indirect
Affiliate of Shell, provided that Shell and each such Affiliate of Shell agrees
in writing with TMR to be bound by the same restrictions as are applicable to
SLOPI hereunder.

                  (b) One or more Transfers to TMR or a to a direct or indirect
Subsidiary of TMR (pursuant to a tender offer or otherwise).

                  (c) One or more Transfers pursuant to a merger, consolidation
or compulsory share exchange, in which TMR is a constituent corporation.

                  (d) One or more Transfers made as a pro rata dividend or
distribution to the holders of the common stock of SLOPI or its Affiliates,
provided, unless such dividend or distribution is to the public shareholders of
any of the Royal Dutch/Shell Group of Companies, such holders agree in writing
with TMR to be bound by the same restrictions as SLOPI hereunder.

                  (e) One or more Transfers to any Person (other than SLOPI or
any Affiliate of Shell) who shall have commenced a tender or exchange offer for
shares of Common Stock if, at the time of public announcement of the tender or
exchange offer: (i) SLOPI and its Affiliates collectively Beneficially Own less
than 21% of the then outstanding shares of Common Stock and no SLOPI Designee or
Preferred Director is serving on the TMR Board of Directors, or (ii) SLOPI and
its Affiliates collectively Beneficially Own more than 21% of the then
outstanding shares of Common Stock or any SLOPI Designee or Preferred Director
is serving on the TMR Board of Directors, unless SLOPI and any Affiliates first
provide to TMR a preferential right to purchase, for cash, all such shares which
SLOPI and any Affiliates would be willing to tender or exchange at a price of
105% of the tender offer price which SLOPI and any Affiliates would be willing
to accept (which shall be the market value of the security to be exchanged on
such date if publicly traded or the cash equivalent value as reasonably
determined in good faith by SLOPI and its Affiliates). With respect to clause
(ii) above, SLOPI and its Affiliates shall give TMR notice of its willingness to
accept the tender or exchange offer at least 10 calendar days prior to its then
stated expiration date and, if TMR desires to exercise its preferential purchase
right, it must so notify SLOPI and its Affiliates in writing within said 10
calendar day period. Once TMR has given notice to SLOPI and its Affiliates that
TMR will exercise such preferential right, then, on such then stated expiration
date of the tender or exchange offer, TMR will be obligated to close the
purchase and pay in full in cash, and SLOPI and its Affiliates will be obligated
to sell, at the applicable 105% price notwithstanding anything that may
otherwise occur with respect to the tender or exchange offer, including, without
limitation, withdrawal, extension, modification, or increase or decrease in the
tender or exchange price or other consideration. Once TMR has not exercised a
preferential right to purchase with respect to a particular tender or exchange
offer made by a particular Person, then SLOPI and its Affiliates shall not
thereafter be required to make any additional preferential purchase rights
available to TMR with respect to such particular tender or exchange offer, even
if in such tender or exchange offer there is an extension or modification of or
an increase or decrease in price or other consideration, in any tender or
exchange offer made by such particular Person; provided, however, that SLOPI
will 

                                      -10-
<PAGE>   11
be required to provide to TMR a preferential purchase right with respect to any
tender or exchange offer made by each other Person or with respect to any new
tender or exchange offer by such particular Person which SLOPI and its
Affiliates would be willing to accept.

                  (f) From and after the following anniversaries of the date of
this Agreement, SLOPI and its Affiliates may, collectively, sell the following
percentages of the number of their Common Shares in one or more Public
Offerings, Private Placements and/or transactions described below in paragraphs
(h), (i), or (j):


<TABLE>
<CAPTION>
                                        PERCENTAGE OF
                                        COMMON SHARES
      ANNIVERSARY OF               PERMITTED TO TRANSFER*
                                -----------------------------
      THIS AGREEMENT            INCREMENTAL*       AGGREGATE*
      --------------            ------------       ----------
<S>                                  <C>               <C>
      Second                         25%               25%
      Third                          25%               50%
      Fourth                         25%               75%
      Fifth                          25%              100%
</TABLE>

      --------------------
      *These time restrictions and percentages will also apply to any shares of
      Common Stock acquired by SLOPI and its Affiliates upon conversion of any
      Preferred Shares into Common Shares, which will result in additional
      Common Shares that can be Transferred based on the percentage limitations
      being applied to a greater number of Common Shares.

Notwithstanding the above, if, at any time or from time to time, SLOPI or any of
its Affiliates receive Common Shares pursuant to Section 2.7 to make up a
Deficiency Amount, then immediately the same number of Common Shares will be
available for Transfer . Such increased availability for Transfer and any actual
Transfer(s) will not reduce or delay other Transfers otherwise permitted to be
made in accordance with the foregoing.

                  (g) From and after the following anniversaries of the date of
this Agreement, SLOPI may sell the following percentages of the number of its
Preferred Shares in one or more Private Placements:

                                      -11-
<PAGE>   12


<TABLE>
<CAPTION>
                                        PERCENTAGE OF
                                      PREFERRED SHARES
   ANNIVERSARY OF                   PERMITTED TO TRANSFER
                                -----------------------------
   THIS AGREEMENT               INCREMENTAL         AGGREGATE
   --------------               -----------         ---------
<S>                               <C>                 <C>
      Third                       33 1/3%             33 1/3%
      Fourth                      33 1/3%             66 2/3%
      Fifth                       33 1/3%             100%
</TABLE>


                  (h) Subject to paragraphs (f) and (g), as such may be modified
pursuant to paragraph (k) below, one or more Transfers in accordance with Rule
144 or Rule 145.

                  (i) Subject to paragraphs (f) and (g) as such may be modified
pursuant to paragraph (k) below, one or more Transfers of Shares in a Public
Offering or in a public offering (other than a Public Offering) made pursuant to
a registration statement which has been declared effective by the SEC under the
Securities Act (any such Public Offering or public offering, a "Registered
Transaction"); provided, however, that, in connection with any such Registered
Transaction, SLOPI and the Company shall obtain from the managing underwriter of
such Public Offering or from each broker through which such public offering is
made, as the case may be, a commitment to use its reasonable best efforts to
make a broad public distribution of the Shares (including an indirect
distribution of Shares as a result of a distribution of Exchangeable Securities)
to be Transferred in such Registered Transaction. The managing underwriter or
broker, as the case may be, will be advised that, for purposes of this
Agreement, a "broad public distribution" means a distribution such that no
Person is allocated for purchase in such Registered Transaction a number of
Shares in excess of (A) 5% of the then outstanding shares of Common Stock (after
giving effect to the offering of the Common Shares and any other securities
being offered by TMR concurrently therewith in such Registered Offering) or (B)
in the case of a Public Offering, in excess of 20% of the number of shares of
Common Shares being offered in such Public Offering, provided that, in the case
of this clause (B), there shall be disregarded Common Shares allocated for
purchase by a mutual fund, a pension fund, an investment adviser (which
investment adviser shall be registered under the Investment Advisers Act of
1940, as amended) for any mutual fund or pension fund, or any party who is
entitled to report such party's holdings of Common Stock on Schedule 13G
promulgated under the Exchange Act in light of that party's investment intent.

                  (j) Notwithstanding paragraphs (f) or (g), as such may be
modified pursuant to paragraph (k) below, such numbers of shares of Common Stock
as are equal to the numbers of shares that SLOPI and its Affiliates may from
time to time have received pursuant to Section 2.7 to make up a Deficiency
Amount.

                                      -12-
<PAGE>   13
                  (k) Notwithstanding paragraphs (f) and (g) above, if (i) TMR
shall ever, in connection with a merger, consolidation, share exchange, or
acquisition of a business or properties or similar transaction, sell or issue or
commit to sell or issue 5,000,000 (as adjusted for stock splits, reverse splits,
reclassifications, and similar actions) or more shares of Common Stock or TMR
Exchangeable Securities that, at the time of issuance, sale or commitment and
assuming full conversion, exchange or exercise thereof, represent 5,000,000 (as
adjusted for stock splits, reverse splits, reclassifications, and similar
actions) or more of the Voting Shares and (ii) at or prior to the meeting of the
TMR Board of Directors approving any such transaction the TMR Board of Directors
shall not have received an opinion letter from an investment banking firm of
national recognition to the effect that the contemplated transaction is fair,
from a financial point of view, to TMR, then (x) SLOPI and its Affiliates will,
immediately or at any time thereafter, be permitted to Transfer an additional
number of Common Shares equal to the number of shares of Common Stock and/or the
Common Stock equivalent of the Voting Shares represented by the transaction as
to which the requisite fairness opinion was not obtained, and (y) if such would
result in earlier or greater Transfers by SLOPI and its Affiliates, the tables
in paragraphs (f) and (g) shall upon the date of issuance, sale or commitment
(the "Relevant Date") be revised to read, in their entirety:

      For paragraph (f):

<TABLE>
<CAPTION>
                                                 PERCENTAGE OF COMMON      
                                             SHARES PERMITTED TO TRANSFER*
                                           --------------------------------
            DATE                           INCREMENTAL*         AGGREGATE *
            ----                           ------------         -----------
<S>                                             <C>                 <C>
            Immediately                         25%                 25%
            
            1 year after Relevant Date          25%                 50%
            
            2 years after Relevant Date         25%                 75%
            
            3 years after Relevant Date         25%                100%
</TABLE>

            --------------------
            *These time restrictions and percentages will also apply to any
            shares of Common Stock acquired by SLOPI upon conversion of any
            Preferred Shares into Common Shares, which will result in additional
            Common Shares that can be Transferred based on the percentage
            limitations being applied to a greater number of Common Shares.

                                      -13-
<PAGE>   14
      For paragraph (g):


<TABLE>
<CAPTION>
                                                     PERCENTAGE OF PREFERRED
                                                  SHARES PERMITTED TO TRANSFER
                                                 -----------------------------
            DATE                                 INCREMENTAL         AGGREGATE
            ----                                 -----------         ---------
<S>                                                <C>                 <C>
            Immediately                            33 1/3%             33 1/3%
            
            1 year after Relevant Date             33 1/3%             66 2/3%
            
            2 years after Relevant Date            33 1/3%              100%
</TABLE>

            
            2.5 VOTING OF COMMON SHARES. During the term of this Agreement and
prior to the conversion of all of the Preferred Shares, the following provisions
will apply: SLOPI and its Affiliates shall be entitled to vote, in its or their
complete discretion, and on all matters, such number of its Common Shares that,
when added to the votes represented by the Preferred Shares, constitute an
aggregate of up to 23% of the then outstanding votes eligible to be cast for
such matter. After the conversion of all the Preferred Shares, SLOPI and its
Affiliates shall be entitled to vote, in its or their complete discretion, and
on all matters, such number of its Common Shares that constitute up to 23% of
the then outstanding votes eligible to be cast for such matter. If only a
portion of the Preferred Shares has been converted, the voting shall be prorated
between the Common Stock and Preferred Stock for a total of up to 23% of the
then outstanding eligible votes to be cast for such matter. With respect to
those Common Shares, if any, that are in excess of the above amounts of the then
outstanding votes eligible to be cast for such matter (the "Excess Shares"),
SLOPI shall vote such Excess Shares pro rata with the votes of all shares, other
than the Excess Shares, that are actually voted for, against or abstain from
voting on each matter. Notwithstanding the previous sentence, SLOPI shall have
complete discretion in voting all of its Common Shares and Preferred Shares on
any matter (i) that constitutes a Business Combination Transaction, (ii) that
would involve a change of control of TMR (for purposes of this section a change
in control shall mean the acquisition by a Person other than SLOPI or its
Affiliates of Beneficial Ownership of more than 50% of the then outstanding
shares of Common Stock), or (iii) with respect to which a vote is taken when any
of the following shall have occurred or shall exist: (w) the Average Per Share
Market Value for TMR's Common Stock with respect to the day in which the matter
is voted upon has been less than $5.50 per share (such amount to be
appropriately adjusted to give effect to stock splits, reverse splits, stock
dividends, reclassifications, share exchanges, dividends and distributions for
which adjustments to the conversion price of the Preferred Shares may be made),
(x) there are any accrued but unpaid dividends on any Preferred Shares, (y) TMR
shall have failed to issue the additional shares of Common Stock required to be
issued pursuant to Section 2.7, or (z) there shall be a continuing and uncured
default by TMR of any of its material obligations under this Agreement, the
Certificate of Designation or Registration Rights Agreement (both as defined in
the Merger Agreement) or the Merger Agreement. The 

                                      -14-
<PAGE>   15
foregoing does not limit or restrict SLOPI's or its Affiliates' complete
discretion in voting its or their Preferred Shares.

            2.6 RIGHT TO PARTICIPATE IN CERTAIN ISSUANCES BY TMR.

                  (a) If, when, and for so long as, SLOPI and its Affiliates
Beneficially Own shares of Common Stock that would constitute, after giving
effect to the proposed transaction (but not prior to the proposed transaction),
less than the Applicable Percentage of the then outstanding shares of Common
Stock, TMR shall not issue any shares of Common Stock or any Exchangeable
Securities, for any consideration or in any type of transaction, unless TMR
shall have first complied with, in the case of an issuance other than pursuant
to Public Offering, the provisions of Section 2.6(b) or, in the case of a Public
Offering, the provisions of Section 2.6(c).

                  (b) If TMR determines to issue any shares of Common Stock or
any Exchangeable Security, other than in a Public Offering, then TMR shall
provide written notice of such determination to SLOPI, which notice shall
include all the terms of such issuance and shall offer to SLOPI the right to
purchase, at the same price and on the same terms as TMR proposes to issue such
shares of Common Stock or Exchangeable Security to others (or, if TMR proposes
to issue such shares of Common Stock or any Exchangeable Security other than for
cash, at a cash price equal to the current market price of the Common Stock or
if a Exchangeable Security, such value to be determined by agreement between TMR
or SLOPI, or if the parties are unable to agree, by an investment banking firm
or other asset valuation firm of national reputation selected by SLOPI from
Schedule I attached hereto (as such Schedule I may be amended in writing from
time to time by both TMR and SLOPI) with the consent of a majority of the
Continuing Directors, which consent shall not be unreasonably withheld, the cost
of which shall be borne by TMR) a number or amount of the shares of Common Stock
or Exchangeable Securities proposed to be issued that represents the right to
acquire upon exercise, exchange or conversion of such Exchangeable Securities a
number of Voting Shares so that, upon closing of the transaction, SLOPI and its
Affiliates will Beneficially Own the Applicable Percentage of the then to be
outstanding Common Stock (the "Offer Notice"). If SLOPI determines to accept the
offer contained in the Offer Notice, SLOPI shall deliver a written notice to TMR
indicating its acceptance within 10 days after its receipt of the Offer Notice,
which notice shall indicate whether SLOPI has accepted such offer in whole or in
part, and, if accepted in part, the number or amount of shares of Common Stock
or Exchangeable Securities as to which such offer has been accepted (an
"Acceptance Notice"). Any acceptance of the offer contained in an Offer Notice
by delivery of an Acceptance Notice shall be irrevocable and shall constitute a
commitment by SLOPI to purchase from TMR, and by TMR to sell to SLOPI, the
number or amount of shares of Common Stock or Exchangeable Securities covered by
such Acceptance Notice upon the terms contained in the Offer Notice.

                  (c) If at any time and from time to time, (i) TMR determines
to issue any shares of Common Stock or any Exchangeable Security in a Public
Offering, and (ii) as a result thereof SLOPI and its Affiliates would
Beneficially Own less than 

                                      -15-
<PAGE>   16
the Applicable Percentage of the then to be outstanding shares of Common Stock,
then (y) TMR shall provide written notice of such determination to SLOPI, which
notice shall include the proposed size and other terms of such issuance, to the
extent then known, the name or names of any managing underwriter or placement
agent(s) and the date when it is proposed that any such issuance will be made,
and (z) TMR shall either sell directly or cause the underwriters or placement
agent(s) to offer to SLOPI the right to purchase from TMR directly or from the
underwriters or placement agent(s), at the applicable offering price, a number
or amount of the shares of Common Stock, Exchangeable Securities or other
securities proposed to be issued that, if purchased by SLOPI, would permit SLOPI
and its Affiliates to Beneficially Own a number of shares of Common Stock equal
to Applicable Percentage of the then to be outstanding Common Stock after
closing the proposed issuance.

            2.7   TMR SUPPORT OF CERTAIN STOCK SALES.

            (a) In the event that, from time to time, SLOPI and/or any Affiliate
of SLOPI or of Shell shall sell any of the Common Shares to be issued upon
conversion of Preferred Shares and the net proceeds (after reasonable and
customary commissions, underwriters discounts, placement fees and expenses of
sale, excluding expenses of legal counsel for the selling shareholder(s))
received by SLOPI or such Affiliate for such Common Shares shall result in a
Deficiency Amount, then TMR shall, at its option, (i) pay to SLOPI an amount of
cash equal to the Deficiency Amount or (ii) issue to SLOPI or such Affiliate
additional fully paid and non-assessable shares of Common Stock equal in value
to the Deficiency Amount. All shares of Common Stock issued by TMR in respect of
a Deficiency Amount (i) shall be valued in the manner set forth in the
definition of Deficiency Amount and (ii) shall be issued as of the closing of
such sale. If TMR issues shares of Common Stock in respect of a Deficiency
Amount, then TMR will cause such shares to be listed for trading on the
principal stock exchange for the Common Stock.

                  (b) In the event, (i) SLOPI shall propose to Transfer Shares
to a person who has committed to purchase such Shares pursuant to a transaction
not involving a Public Offering at a time when SLOPI is authorized to sell such
Shares, (ii) under the terms of this Agreement, such person would be required to
enter into an agreement with TMR and such person and TMR are unable to effect
such agreement, and (iii) SLOPI shall subsequently sell such Shares pursuant to
a Public Offering, TMR shall pay the reasonable and customary commissions,
underwriters discounts and expenses of sale payable by SLOPI in such sale,
excluding expenses of legal counsel for SLOPI. If this Section 2.7(b) shall be
applicable in the circumstances, then this Section shall control over Section
2.C (11) g of the Registration Rights Agreement.

                                      -16-
<PAGE>   17
      3.    STOCK CERTIFICATES AND OTHER RESTRICTIONS.

            3.1 ENDORSEMENT OF CERTIFICATES.

                  (a) All certificates representing Shares shall, subject to
Section 3.1(c), bear the following legend:

            "THIS CERTIFICATE IS SUBJECT TO THE PROVISIONS OF A STOCK RIGHTS AND
      RESTRICTIONS AGREEMENT BETWEEN THE MERIDIAN RESOURCE CORPORATION AND SHELL
      LOUISIANA ONSHORE PROPERTIES, INC. DATED AS OF JUNE 30, 1998. A COPY OF
      SUCH AGREEMENT IS ON FILE AT THE PRINCIPAL BUSINESS OFFICE OF THE MERIDIAN
      RESOURCE CORPORATION."

                  (b) All certificates representing Shares shall, subject to
Section 3.1(c), bear the following legend:

            "THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
      REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "ACT"), AND
      MAY NOT BE SOLD, TRANSFERRED OR OTHERWISE CONVEYED EXCEPT PURSUANT TO AN
      EFFECTIVE REGISTRATION STATEMENT UNDER THE ACT OR PURSUANT TO RULE 144
      UNDER THE ACT, UNLESS THE COMPANY SHALL HAVE BEEN FURNISHED WITH AN
      OPINION OF COUNSEL, WHICH OPINION SHALL BE REASONABLY SATISFACTORY TO
      COUNSEL FOR TMR ENERGY CORPORATION, THAT REGISTRATION UNDER THE ACT IS NOT
      REQUIRED."

                  (c) After such time as either of the legends set forth in
Sections 3.1(a) and (b) is no longer required hereunder (including without
limitation as a result of the termination of this Agreement in accordance with
its terms) or if the securities represented by a certificate have been
registered under the Securities Act pursuant to an effective registration
statement or are to be sold pursuant to Rule 144, or if the Company shall have
been furnished with an opinion of counsel, which opinion shall be reasonably
satisfactory to counsel for TMR, that registration under the Securities Act is
not required, as the case may be, then, in any such event, upon the request of
SLOPI, TMR shall cause such certificate or certificates to be exchanged for a
certificate or certificates that do not bear any legend.

            3.2 IMPROPER TRANSFER. Any attempt by SLOPI or its Affiliates to
Transfer any Shares other than in accordance with this Agreement shall be null
and void and neither TMR nor any transfer agent for such securities shall be
required to give any effect to such attempted Transfer in its stock records.

                                      -17-
<PAGE>   18
      4.    GENERAL PROVISIONS.

            4.1 REPRESENTATIONS AND WARRANTIES.

                  (a) TMR represents and warrants to SLOPI that (i) TMR is a
corporation duly organized, validly existing and in good standing under the laws
of the State of Texas and has the corporate power and authority to enter into
this Agreement and to carry out its obligations hereunder, (ii) the execution
and delivery of this Agreement by TMR and the consummation by TMR of the
transactions contemplated hereby have been duly authorized by all necessary
corporate action on the part of TMR and no other corporate proceedings on the
part of TMR are necessary to authorize this Agreement or any of the transactions
contemplated hereby, and (iii) this Agreement has been duly executed and
delivered by TMR and constitutes a valid and binding obligation of TMR, and,
assuming this Agreement constitutes a valid and binding obligation of SLOPI, is
enforceable against TMR in accordance with its terms, subject to applicable
bankruptcy, reorganization, insolvency, moratorium, fraudulent conveyance and
similar laws affecting creditors' rights generally from time to time and to
general principles of equity.

                  (b) SLOPI represents and warrants to TMR that (i) SLOPI is a
corporation duly organized, validly existing and in good standing under the laws
of the State of Delaware and has the corporate power and authority to enter into
this Agreement and to carry out its obligations hereunder, (ii) the execution
and delivery of this Agreement by SLOPI and the consummation by SLOPI of the
transactions contemplated hereby have been duly authorized by all necessary
corporate action on the part of SLOPI and no other corporate proceedings on the
part of SLOPI are necessary to authorize this Agreement or any of the
transactions contemplated hereby, and (iii) this Agreement has been duly
executed and delivered by SLOPI and constitutes a valid and binding obligation
of SLOPI, and, assuming this Agreement constitutes a valid and binding
obligation of TMR, is enforceable against SLOPI in accordance with its terms,
subject to applicable bankruptcy, reorganization, insolvency, moratorium,
fraudulent conveyance and similar laws affecting creditors' rights generally
from time to time and to general principles of equity.

            4.2 AMENDMENT AND MODIFICATION; WAIVER OF COMPLIANCE. This Agreement
may be amended or waived only by written instrument duly executed by the
parties. In the event of the amendment or modification of this Agreement in
accordance with its terms, the Board of Directors of TMR shall adopt any
amendment to the by-laws of TMR that may be required as a result of such
amendment or modification to this Agreement, and, if required, shall propose any
amendment to the Certificate of Incorporation that may be required as a result
of such amendment or modification to this Agreement to the TMR shareholders
entitled to vote thereon at a meeting duly called and held for such purpose, and
shall recommend that the TMR shareholders vote in favor of such amendment to the
Certificate of Incorporation.

            4.3 INJUNCTIVE RELIEF. Each of the parties hereto hereby
acknowledges that in the event of a breach by any of them of any material
provision of this 

                                      -18-
<PAGE>   19
Agreement, the aggrieved party may be without an adequate remedy of law. Each of
the parties therefore agrees that in the event of a breach of any material
provision of this Agreement the aggrieved party may elect to institute and
prosecute proceedings in any court of competent jurisdiction to enforce specific
performance or to enjoin the continuing breach of such provision, as well as to
obtain damages for breach of this Agreement. By seeking or obtaining any such
relief, the aggrieved party will not be precluded from seeking or obtaining any
other relief to which it may be entitled in equity or at law.

            4.4 BYLAWS. At all times while this Agreement shall be in effect,
TMR shall cause its Bylaws to conform to the provisions of this Agreement,
including by causing its Bylaws to be amended.

            4.5 NO ADOPTION OR AMENDMENT OF RIGHTS PLAN. During the term of this
Agreement, TMR's Board of Directors shall not adopt any shareholder rights plan
or amend any rights plan without the approval of a majority of the SLOPI
Designee(s) or Preferred Director(s) then on the Board of Directors of TMR
unless such plan exempts SLOPI and its Affiliates from all effects thereof.

            4.6 LIMITATION ON REDUCTIONS OF PUBLIC FLOAT BY TMR. TMR shall not
take any action, including without limitation an acquisition by TMR or any of
its Affiliates of shares of Common Stock then outstanding, or a recapitalization
by TMR, which would reduce the number of shares of Common Stock held by Persons
other than SLOPI, TMR or any Affiliate of either SLOPI or TMR to less than the
minimum number required to maintain TMR's listing on the New York Stock
Exchange, without the prior written consent of SLOPI.

            4.7 GOVERNING LAW. This Agreement and the legal relations between
the parties shall be governed by and construed in accordance with the laws of
the State of Texas, without regard to the principles of conflicts of law
thereof.

            4.8   TERMINATION.

                  (a)   This Agreement may be terminated:

                        (i) by the mutual written consent of the parties hereto;

                        (ii) by SLOPI or TMR if SLOPI shall have become the
Beneficial Owner of less than 10% of the Fully Diluted Shares; or

                        (iii) by SLOPI if any Person (other than SLOPI or any
Affiliate of SLOPI) shall have proposed to TMR a Business Combination
Transaction and a majority of the Continuing Directors shall have approved such
proposal or shall have retained (or authorized TMR to retain) the services of an
investment banking firm and shall have instructed such investment banking firm
to solicit indications of interest with respect to a Business Combination
Transaction; provided that, if a proposal with respect to a Business Combination
Transaction referred to in this clause (iii) shall have 

                                      -19-
<PAGE>   20
been terminated or withdrawn by the Person who made such proposal and SLOPI
shall have withdrawn, terminated or permitted to expire any tender or exchange
offer or proposal with respect to a Business Combination Transaction made by
SLOPI, then the provisions of this Agreement shall thereafter be reinstated
(without liability to any party for any failure to have complied with the terms
and provisions of this Agreement during the period when it shall have been
terminated in accordance with this Section 4.8(a)(iii)) and this Agreement shall
thereafter continue in full force and effect in accordance with its terms; or

                        (iv) by SLOPI if (A) any Person other than SLOPI or
its Affiliates shall have acquired Beneficial Ownership of 20% (or, if lower,
the percentage specified in the definition of "Affiliated Shareholder" in Part
Thirteen of the TBCA, as amended from time to time), or more of the Voting
Shares and such Person shall not have entered into an agreement with TMR
containing restrictions and other provisions at least as favorable to TMR as
those contained in this Agreement; or

                        (v) by SLOPI if the Continuing Directors shall not
constitute a majority of the Board of Directors of TMR; or

                        (vi) by SLOPI if TMR shall have breached any
material provision of this Agreement, the Merger Agreement, or the Certificate
of Designation or the Registration Rights Agreement (both as defined in the
Merger Agreement) and SLOPI shall have delivered a written notice of such breach
to TMR; provided that, if such breach is reasonably susceptible of cure and TMR
shall proceed diligently to cure such breach, then this Agreement shall not be
terminated unless such breach shall not have been cured on or prior to the fifth
day after the delivery of written notice by SLOPI to TMR that TMR has breached a
material provision of any such instrument; or

                        (vii) by SLOPI if (x) TMR shall seek relief under any
bankruptcy, insolvency, receivership, custodianship, trusteeship, liquidation,
reorganization, composition, readjustment, moratorium or similar law (an
"Insolvency Law"); or (y) a proceeding or case shall be commenced under an
Insolvency Law by a third party against TMR and such proceeding or case shall
continue undismissed or unstayed for 60 days; or (z) an order for relief under
an Insolvency Law shall be entered against TMR.

                  (b) Unless this Agreement shall have been earlier terminated
as provided in Section 4.8(a), this Agreement shall terminate on the 10th
anniversary of the date of this Agreement.

            4.9 NOTICES. All notices, requests, demands or other communications
required or permitted by this Agreement shall be in writing and effective when
received, and delivery shall be made personally or by registered or certified
mail, return receipt requested, postage prepaid, or overnight courier or
confirmed facsimile transmission, addressed as follows:

                                      -20-
<PAGE>   21
                  (a) If to TMR:

                      The Meridian Resource Corporation
                      15995 N. Barkers Landing, Suite 300
                      Houston, Texas 77079
                      Attention: Joseph A. Reeves, Jr., Chairman and
                                 Chief Executive Officer
                      Fax:  (281) 558-5595

                      with a copy to:

                      Fulbright & Jaworski L.L.P.
                      1301 McKinney Street, Suite 5100
                      Houston, Texas  77010
                      Attention: Curtis W. Huff
                      Fax: (713) 651-5246

                  (b) If to SLOPI:

                      Shell  Louisiana Onshore Properties Inc.
                      P.O. Box 7986
                      Newark, Delaware 19714
                      Attention: Corporate Secretary

                      with a copy to:

                      Shell Oil Company Legal Firm
                      P.O. Box 2463
                      Houston, Texas 77252
                      Attention: Danna M. Walton
                      Fax: 713-241-5056

            4.10 SEVERABILITY. If any term or other provision of this Agreement
is invalid, illegal or incapable of being enforced by any rule of law, or public
policy, all other conditions and provisions of this Agreement shall nevertheless
remain in full force and effect so long as the economic or legal substance of
the transactions contemplated hereby is not affected in any manner adverse to
any party. Upon such determination that any term or other provision is invalid,
illegal or incapable of being enforced, the parties hereto shall negotiate in
good faith to modify this Agreement so as to effect the original intent of the
parties as closely as possible in an acceptable manner to the end that the
transactions contemplated hereby are fulfilled to the fullest extent possible.

            4.11 ENTIRE AGREEMENT. Except as otherwise expressly stated herein,
this Agreement constitutes the entire agreement among the parties with respect
to the subject matter hereof and supersedes all prior agreements and
undertakings, both written and oral, among the parties, or any of them, with
respect to the subject matter 

                                      -21-
<PAGE>   22
hereof. Except for the permitted Transfers to Shell and Affiliates of Shell or
SLOPI and except as otherwise expressly permitted or contemplated herein, the
rights and obligations under this Agreement shall not be assigned by operation
of law or otherwise. Nothing in this Agreement shall be construed as prohibiting
TMR from effecting a merger, consolidation or other similar transaction with
another entity, provided that (i) the operative terms of this Agreement shall be
applied in respect of any such transaction and (ii) under the express terms of
such transaction this Agreement will be continued in effect by TMR or any
successor thereto.

            4.12 PARTIES IN INTEREST. This Agreement shall be binding upon and
inure solely to the benefit of each party hereto and to Shell and the Affiliates
of Shell and SLOPI if they receive Permitted Transfers in accordance with this
Agreement. Nothing in this Agreement, express or implied, is intended to or
shall confer upon any other person any rights, benefits or remedies of any
nature whatsoever under or by reason of this Agreement, except as expressly
otherwise contemplated herein.

            4.13 HEADINGS. The descriptive headings contained in this Agreement
are included for convenience of reference only and shall not affect in any way
the meaning or interpretation of this Agreement.

            4.14 COUNTERPARTS. This Agreement may be executed in one or more
counterparts, and by the different parties hereto in separate counterparts, each
of which when executed shall be deemed to be an original but all of which taken
together shall constitute one and the same agreement.

            4.15 AUDIT RIGHTS. SLOPI shall have the right to perform, directly
or through its representatives, periodic audits of TMR and its subsidiaries. The
audits may cover financial transactions, operational matters, and other areas
deemed appropriate. The audit frequency will not be more than once a year. The
scope of the audits will be determined by SLOPI. SLOPI will utilize TMR's
independent auditor, Ernst & Young LLP or such other firm as may then be TMR's
outside auditors ("E&Y"), to conduct the audits as long as E&Y performs to
SLOPI's satisfaction. SLOPI reserves the right to use a different E&Y partner to
conduct any audit. SLOPI personnel or representatives may participate in the
audit and/or review all audit work papers. SLOPI will bear the cost of the
audits.

                                      -22-
<PAGE>   23
      IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
executed as of the date first written above by their respective officers
thereunto duly authorized.

                              THE MERIDIAN RESOURCE CORPORATION

                              By: /s/ JOSEPH A. REEVES, JR.
                              Name:   JOSEPH A. REEVES, JR.
                              Title:  CEO


                              SHELL LOUISIANA ONSHORE PROPERTIES INC.

                              By: /s/ S. P. METHVIN
                              Name:   S. P. METHVIN
                              Title: PRESIDENT

                                      -23-
<PAGE>   24
                                   SCHEDULE I

                      LIST OF ACCEPTABLE INVESTMENT BANKING
                            AND ASSET VALUATION FIRMS



1.    Goldman Sachs

2.    CS First Boston

3.    Merrill Lynch

4.    Chase Securities

5.    Smith Barney

6.    Donaldson Lufkin Jenrette

7.    Petrie Parkman

8.    Dain Rauscher

9.    Morgan Stanley

10.   Howard Weil

The above list may be revised from time to time by a written instrument signed
by both TMR and SLOPI.

                                      -24-


<PAGE>   1

                                                                       EXHIBIT 5

                          REGISTRATION RIGHTS AGREEMENT

      REGISTRATION RIGHTS AGREEMENT, dated June 30, 1998 by and between The
Meridian Resource Corporation, a Texas corporation (the "Company"), and Shell
Louisiana Onshore Properties Inc., a Delaware corporation ("Security Holder").

                             W I T N E S S E T H:

      WHEREAS, the Company and Security Holder have entered into an Agreement
and Plan of Merger dated as of March 27, 1998 (the "Merger Agreement") which
provides, among other things, for the execution of this Agreement;

      NOW THEREFORE, in consideration of the mutual covenants and agreements set
forth herein and in the Merger Agreement the parties hereto agree as follows:

      Section 1. DEFINITIONS. The terms defined in this Section, whenever used
in this Agreement, shall, unless the context otherwise requires, have the
respective meanings hereinafter specified. Terms not defined in this Agreement,
and defined in the Merger Agreement have the meanings assigned them in the
Merger Agreement.

      "Agreement" shall mean this Registration Rights Agreement.

      "Commission" shall mean the United States Securities and Exchange
Commission.

      "Common Stock" shall mean the Company's authorized Common Stock, par value
$0.01 per share.

      "Company" shall mean The Meridian Resource Corporation, a Texas
corporation, and any successor corporation by merger, consolidation or otherwise
and any parent corporation resulting from the merger or consolidation of the
Company with or into a subsidiary of another corporation.

      "Eligible Stock" means the issued and outstanding shares of Common Stock
(i) that have been issued pursuant to the Agreement and Plan of Merger (the
"Merger Agreement") by and among the Company, the Security Holder, LOPI
Acquisition Corp. and Louisiana Onshore Properties, Inc., (ii) that have been
issued upon conversion of the Series A Convertible Preferred Stock issued
pursuant to the Merger Agreement; (iii) that have been purchased by the Security
Holder upon the exercise of its rights pursuant to the Stock Rights and
Restrictions Agreement; and (iv) that may be issued pursuant to Section 2.7 of
the Stock Rights and Restriction Agreement.
<PAGE>   2
      "Exchange Act" shall mean the Securities Exchange Act of 1934, and the
rules and regulations of the Commission thereunder, all as the same shall be in
effect at the time.

      "Person" shall mean an individual, a corporation, a partnership, a trust,
an unincorporated organization or a government or any agency or political
subdivision thereof.

      "Public Offering" shall mean a firm commitment underwritten public
offering pursuant to a registration statement under the Securities Act.

      "Registrable Securities" shall mean that portion of the shares of Eligible
Stock that any Security Holder is permitted to sell under Section 2.4(f) of the
Stock Rights and Restriction Agreement, as such Section may be adjusted in
accordance with terms of such Agreement.

      "Registration" shall mean the registration under the Securities Act of
Registrable Securities pursuant to either Section 2.A hereof or 2.B hereof.

      "Registration Statement" shall mean a registration statement filed under
the Securities Act or a similar document filed pursuant to any other statute
then in effect corresponding to the Securities Act.

      "Securities Act" shall mean the Securities Act of 1933, and the rules and
regulations of the Commission thereunder, all as the same shall be in effect at
the time.

      "Security Holder" shall mean Shell Louisiana Onshore Properties Inc., a
Delaware corporation, its permitted assigns, or any affiliate thereof holding
Common Stock or any successor corporation to any of the foregoing by merger or
consolidation or otherwise.

      "Stock Rights and Restrictions Agreement" means that certain Stock Rights
and Restrictions Agreement of even date herewith between the Company and the
Security Holder.

      Section 2. REGISTRATION RIGHTS.

      A. DEMAND REGISTRATIONS. Subject to the provisions of Section 5 in the
event of assignment of this Agreement, if the Company shall receive a written
request from Security Holder requesting that the Company file a Registration
Statement relating to Registrable Securities, the Company will as promptly as
practicable prepare and file a Registration Statement and use reasonable best
efforts to cause the Registration Statement to become effective; subject,
however, to the following provisions:

            (1) the Company shall be required to file no more than an aggregate
of 5 Registration Statements on behalf of Security Holder (or Security Holders
in the event of an assignment of this Agreement) pursuant to this Subsection
2.A, plus 

                                      -2-
<PAGE>   3
any number of additional Registration Statements (not to exceed an aggregate of
an additional 5) as to which, at the time of the first filing with the SEC, the
Security Holder (or Security Holders in the event of an assignment of this
Agreement) and its underwriter(s) have reasonably estimated that the price to
the public of the Registrable Securities to be sold (before discounts,
commissions, and expenses) will be equal to or greater than $50,000,000;

            (2) the Company shall not be obligated (i) to file a requested
Registration in the event that the aggregate number of Registrable Securities to
be included in such requested Registration is less than 2 1/2% of the issued and
outstanding Common Stock; or (ii) to prepare or file such Registration Statement
or an amendment or supplement thereto, and may suspend sales, at any time when
the Company reasonably determines (by action of the Company's Board of Directors
or an officer duly authorized by the Board of Directors to make such decision)
that the filing thereof at the time requested, or the offering of Registrable
Securities pursuant thereto, would materially and adversely affect a pending or
proposed offering of securities of the Company, an acquisition, merger,
recapitalization, consolidation, reorganization or similar transaction relating
to the Company or negotiations, discussions or pending proposals with respect
thereto or require premature disclosure of information not otherwise required to
be disclosed to the potential detriment of the Company; PROVIDED, HOWEVER, that
such period of sale or distribution shall resume after any such suspension for a
number of days necessary to keep such Registration effective for permitted sales
thereunder for a term of 90 days. The filing of a Registration Statement, or any
amendment or supplement thereto, by the Company may not be deferred, and the
sale and distribution of shares may not be suspended, in each case pursuant to
the foregoing provisions, for more than 60 days after the abandonment or
consummation (or the completion of the distribution of securities in the case of
a public offering) of any of the proposals or transactions described therein or,
in any event, for more than 120 days during any one year;

            (3) a Registration Statement filed pursuant to a request of Security
Holder shall first include all Registrable Securities requested to be included
by Security Holder and, only after such inclusion, may, include securities of
the Company being sold for the account of the Company provided, however, that
securities to be offered on behalf of the Company will be included in such
Registration Statement only to the extent that, in the reasonable opinion of the
managing underwriter for the Public Offering of Registrable Securities on behalf
of Security Holder, such inclusion will not materially adversely affect the
distribution of Registrable Securities on behalf of Security Holder;

            (4) the selection of an underwriter for a Public Offering of
Registrable Securities by Security Holder shall be subject to the approval of
the Company, which shall not be unreasonably withheld;

            (5) for purposes of paragraph (1) of this Subsection A, if a
requested Registration Statement is filed and the Company otherwise complies
with its obligations hereunder, but the Registration Statement is withdrawn by
Security Holder due to a 

                                      -3-
<PAGE>   4
delay in the offering requested by the Company for a period of more than 15
business days pursuant to Section 2, then no requested Registration Statement
shall be deemed to have been filed; and

            (6) no Other Holder (as defined below) shall be entitled to include
securities or piggyback in any Registration demanded by Security Holder.

      B. INCIDENTAL/"PIGGY-BACK" REGISTRATIONS. If the Company at any time
proposes to file a Registration Statement (other than a Registration Statement
filed pursuant to Subsection A of this Section) under the Securities Act
relating to a Public Offering of Common Stock to be sold for cash that would
permit the registration of Registrable Securities, it will give Security Holder
as much advance notice, in writing, as is reasonably practicable under the
circumstances, but in any event not less than 5 days, before the filing with the
Commission of such Registration Statement, which notice shall set forth the
securities proposed to be registered. The notice shall offer to include in such
filing such amount of Registrable Securities as Security Holder may request. If
Security Holder wishes to have Registrable Securities registered for sale in the
Public Offering pursuant to this Subsection B, it shall advise the Company in
writing within 20 days after the date of receipt of such offer from the Company
(or such shorter period, but in any event not less than 5 days, as the Company
shall specify in its notice to Security Holder), setting forth the amount of
Registrable Securities for which registration is requested. If the managing
underwriter of the proposed Public Offering of Common Stock by the Company shall
advise the Company in writing that, in the reasonable opinion of the managing
underwriter, the distribution of the Registrable Securities requested by
Security Holder to be included in the Registration Statement concurrently with
securities being registered for sale by the Company would materially adversely
affect the distribution of such securities by the Company and Security Holder,
then the Company shall so advise the Security Holder and the number of
securities that are entitled to be included in the registration and underwriting
shall be allocated as follows: (i) in the event a Registration Statement is
being filed in connection with the exercise of registration rights by a security
holder other than the Security Holder (an "Other Holder"), all of any Other
Holder's shares of Common Stock shall be included in the registration and the
remaining number of securities that are entitled to be included in the
registration shall be allocated (A) 80% to the Company and any other
shareholders (not including the Other Holder or the Security Holder) whose
shares are to be included in such Registration Statement and (B) 20% to the
Security Holder, and (ii) in the event the registration is not being filed in
connection with the exercise of registration rights of any Other Holder (a) 80%
to the Company and any other shareholders (not including Security Holder) whose
shares are to be included in such Registration Statement and (b) 20% to Security
Holder. If any Person does not agree to the terms of any such underwriting, such
Person shall be excluded therefrom by written notice from the Company or the
underwriter.

            Nothing contained in this Subsection B shall, however, limit the
Company's right to cancel, postpone or withdraw any such registration proposed
by the Company for any reason.

                                      -4-
<PAGE>   5
            Any obligation of the Company to effect a registration pursuant to
this Subsection B shall be conditioned upon Security Holder entering into an
underwriting agreement with the Company and the managing underwriters of the
registered offering of the type described in paragraph (10) of Subsection C.

      C. REGISTRATION PROCEDURES. If the Company is required by the provisions
of Subsections A or B of this Section 2 to effect the Registration of any of the
Registrable Securities under the Securities Act, the Company will, as soon as in
reasonably practicable:

            (1) Prepare and file with the Commission a Registration Statement
with respect to such securities and use its reasonable best efforts to cause
such Registration Statement to become and, subject to paragraph (2) of this
Subsection C, remain effective.

            (2) Keep such Registration effective, and the prospectus used in
connection therewith, current for a period of ninety (90) days or until the
Security Holder has completed the distribution described in the Registration
Statement relating thereto, whichever first occurs (the "Selling Period");
provided, however, that (a) the Selling Period shall be extended for a period of
time equal to any period that Security Holder refrains from selling any
securities included in such registration pursuant to a suspension under
Subsection A.

            (3) Prepare and file with the Commission such amendments and
supplements to such Registration Statement and the prospectus used in connection
therewith as may be necessary to keep such Registration Statement effective and
such prospectus current in compliance with Section 10 of the Securities Act, and
to comply with the provisions of the Securities Act with respect to the sale or
other disposition of all Common Stock covered by such Registration Statement;
provided, however, that the Company shall have no obligation under this
paragraph (3) after the period required by paragraph (2) of this Subsection C
has lapsed.

            (4) Furnish to Security Holder such number of copies of such
Registration Statement and of each amendment and supplement thereto (in each
case including all exhibits), such number of copies of the prospectus included
in such Registration Statement (including each preliminary prospectus, summary
prospectus and prospectus supplement), in conformity with the requirements of
the Securities Act, and such other documents, as Security Holder may reasonably
require in order to facilitate the public offering, sale or other disposition of
the Registrable Securities owned by Security Holder.

            (5) Use reasonable best efforts to register or qualify the Common
Stock covered by such Registration Statement under such other securities or blue
sky laws of jurisdictions in the United States of America as Security Holder
shall reasonably request (excluding however any jurisdiction in which the filing
would subject the Company to additional tax liability, and any jurisdiction in
which the Company would be required to execute a general consent to service of
process in effecting such 

                                      -5-
<PAGE>   6
registration or qualification which consent would not be required but for this
paragraph (5)), and do such other acts and things as may be required to enable
Security Holder to consummate the public sale or other disposition in such
jurisdictions of the Registrable Securities owned by Security Holder.

            (6) Otherwise use reasonable best efforts to comply with all
applicable rules and regulations of the Commission, and make available to its
security holders, as soon as reasonably practicable, an earnings statement which
satisfies the provisions of Section 11(a) of the Securities Act.

            (7) Immediately notify Security Holder at any time when a prospectus
is required to be delivered under the Securities Act within the Selling Period
referred to in paragraph (2) of this Subsection C, of the Company becoming aware
that the prospectus included in the Registration Statement, or as such
prospectus may be amended or supplemented, includes an untrue statement of a
material fact or omits to state any material fact required to be stated therein
or necessary in order to make the statements therein not misleading in light of
the circumstances then existing, and at the request of Security Holder to
promptly prepare and furnish to Security Holder a number of copies of an amended
or supplemental prospectus as may be necessary so that, as thereafter delivered
to the purchasers of such Registrable Securities, such prospectus shall not
include an untrue statement of a material fact or omit to state a material fact
required to be stated therein or necessary in order to make the statements
therein not misleading in the light of the circumstances then existing. In the
event the Company shall give any such notice, Security Holder shall immediately
suspend use of the prospectus and the Selling Period shall be extended by the
number of days during the period from and including the date of the giving of
such notice to and including the date when Security Holder shall have received
the copies of such supplemented or amended prospectus.

            (8) In the event that the Company suspends use by Security Holder of
a prospectus relating to an offering of Registrable Securities pursuant to a
suspension under Subsection A, because the Company is conducting negotiations
for a material business combination or due to pending material developments or
events that have not yet been publicly disclosed and as to which the Company
believes public disclosure will be prejudicial to the Company, the Company shall
deliver notice in writing to the effect of the foregoing and, upon receipt of
such notice, the Security Holder shall not use the prospectus, and the Selling
Period shall cease to run or will not commence, until such Security Holder has
received copies of the supplemented or amended prospectus provided for in
paragraph 3 of this Subsection C, or until it is advised in writing by the
Company that the prospectus may be used, and has received copies of any
additional or supplemental filings that are incorporated or deemed incorporated
by reference in such prospectus. The Company will use reasonable best efforts to
ensure that the use of the prospectus may be resumed, and the Selling Period
will commence, as promptly as is practicable and, in any event, promptly after
the earlier of (x) public disclosure of such material business combination or
pending material development or event sufficient to permit an affiliate of the
Company to sell Common Stock or (y) in the judgment of 

                                      -6-
<PAGE>   7
the Company, public disclosure of such material business combination or material
development or event would not be prejudicial to the Company.

            (9) Use its reasonable best efforts to list such Registrable
Securities on the primary securities exchange or other trading market on which
the Common Stock is then listed, if such Registrable Securities are not already
so listed and if such listing is then permitted under the rules of such exchange
or other trading market, and to provide a transfer agent and registrar for such
Registrable Securities covered by such Registration Statement not later than the
effective date of such Registration Statement.

            (10) Enter into such agreements (including an underwriting agreement
in customary form and containing customary provisions relating to legal opinions
and accountants' letters and customary representations and warranties and
customary provisions for mutual indemnification and contribution between the
Company and the underwriters for Security Holder) and take such other actions as
Security Holder may reasonably request in order to expedite or facilitate the
disposition of such Registrable Securities.

            (11) Make available for inspection by Security Holder, by any
underwriter participating in any disposition to be effected pursuant to such
Registration Statement and by any attorney, accountant or other agent retained
by Security Holder or any such underwriter, all customary financial and other
records, customary corporate documents and properties of the Company, and cause
all of the Company's officers, directors and employees to supply all customary
information requested by Security Holder, such underwriter, attorney, accountant
or agent, as is reasonably needed in connection with such Registration
Statement; provided such parties execute confidentiality agreements reasonably
acceptable to the Company.

            Except as otherwise provided in Section 2.7(b) of the Stock Rights
and Restriction Agreement, underwriting discounts and commissions attributable
to securities offered on behalf of Security Holder plus the fees and expenses of
separate counsel for Security Holder incurred in connection with effecting a
Registration pursuant to this Section 2 shall be borne by Security Holder. All
other expenses incurred in connection with the Registration Statement shall be
borne by the Company.

            It shall be a condition precedent to the obligation of the Company
to take any action pursuant to this Section 2 in respect of the Registrable
Securities which are to be registered at the request of Security Holder that
Security Holder shall furnish to the Company such information regarding the
securities held by it and the intended method of disposition thereof as the
Company shall reasonably request and as shall be required in connection with the
action taken by the Company.

      D.    INDEMNIFICATION.

            (1) In the event of any Registration of any Registrable Securities
under the Securities Act pursuant to this Section 2, the Company agrees to
indemnify and hold harmless Security Holder, its directors, officers and
employees, and each other 

                                      -7-
<PAGE>   8
Person, if any, who controls Security Holder within the meaning of Section 15 of
the Securities Act, against any losses, claims, damages or liabilities, joint or
several, to which Security Holder or any such director, officer, employee or
controlling Person may become subject under the Securities Act or any other
statute or at common law, insofar as such losses, claims, damages or liabilities
(or actions in respect thereof) arise out of or are based upon (i) any alleged
untrue statement of any material fact contained, on the effective date thereof,
in any Registration Statement under which such securities were registered under
the Securities Act, any preliminary prospectus or final prospectus contained
therein, or any amendment or supplement thereto, or (ii) any alleged omission to
state therein a material fact required to be stated therein or necessary to make
the statements therein not misleading, and shall reimburse Security Holder or
such director, officer, employee or controlling Person for reasonable legal or
any other expenses reasonably incurred by Security Holder or such director,
officer, employee or controlling Person in connection with investigating or
defending any such loss, claim, damage, liability or action; provided, however,
that the Company shall not be liable in any such case to the extent that any
such loss, claim, damage or liability arises out of or is based upon any alleged
untrue statement or alleged omission made in such Registration Statement,
preliminary prospectus, prospectus, or amendment or supplement in reliance upon
and in conformity with written information furnished to the Company in writing
for use therein; and provided, further, that the Company shall not be liable in
any such case to the extent that any such loss, claim, damage, liability or
expense arises out of or is based upon an untrue statement or alleged untrue
statement or omission or alleged omission in the prospectus if such untrue
statement or alleged untrue statement or omission or alleged omission has been
the subject of a notice given to Security Holder pursuant to paragraph (7) of
Subsection C if Security Holder after receipt of such notice and prior to the
receipt of a corrected prospectus sold a Registrable Security to the Person
asserting such loss, claim, damage, liability or expense who purchased such
Registrable Security which is the subject thereof form Security Holder. Such
indemnity shall remain in full force and effect regardless of any investigation
made by or on behalf of Security Holder or such director, officer, employee or
participating Person or controlling Person, and shall survive the transfer of
such securities by Security Holder.

            (2) Security Holder agrees to indemnify and hold harmless the
Company, its directors, officers and employees and each other Person, if any,
who controls the Company against any losses, claims, damages or liabilities
joint or several, to which the Company or any such director, officer, or
employee or any such Person may become subject under the Securities Act or any
other statute or at common law, insofar as such losses, claims, damages or
liabilities (or actions in respect thereof) arise out of or are based upon (i)
any alleged untrue statement of any material fact contained, on the effective
date thereof, in any Registration Statement under which Registrable Securities
were registered under the Securities Act at the request of Security Holder, any
preliminary prospectus or final prospectus contained therein, or any amendment
or supplement thereto, or (ii) any alleged omission to state therein a material
fact required to be stated therein or necessary to make the statements therein
not misleading, in each case to the extent, but only to the extent, that such
alleged untrue statement or alleged omission was made in such Registration
Statement, 

                                      -8-
<PAGE>   9
preliminary prospectus, prospectus, amendment or supplement in reliance upon and
in conformity with written information furnished to the Company in writing by
Security Holder for use therein, and shall reimburse the Company or such
director, officer, employee or other Person for any reasonable legal or any
other expenses reasonably incurred in connection with investigating or defending
any such loss, claim, damage, liability or action.

            (3) Promptly after receipt by an indemnified party hereunder of
written notice of the commencement of any action or proceeding involving a claim
referred to in the preceding paragraphs of this Subsection E, such indemnified
party will, if a claim in respect thereof is to be made against an indemnifying
party, give written notice to the latter of the commencement of such action;
provided, that the failure of any indemnified party to give notice as provided
herein shall not relieve the indemnifying party of its obligation under this
Subsection D to the extent the indemnifying party is not materially prejudiced
by such failure. In case any such action is brought against an indemnified
party, the indemnified party shall permit the indemnifying party to assume the
defense of such action or proceeding, provided that counsel for the indemnifying
party, who shall conduct the defense of such action or proceeding shall be
approved by the indemnified party (whose approval shall not be unreasonably
withheld) and the indemnified party may participate in such defense at such
indemnified party's expense unless in the opinion of counsel to such indemnified
party a conflict of interest between such indemnified and indemnifying parties
may exist in respect of such claim that would prevent the indemnified party's
counsel from adequately representing both parties, in which event the
indemnifying party shall pay the reasonable fees and expense of separate counsel
for the indemnified party. No indemnifying party will consent to entry of any
judgment or enter into any settlement which does not include as an unconditional
term thereof the giving by the claimant or plaintiff to such indemnified party
of a release from all liability in respect to such claim or litigation. The
indemnifying party shall not, in connection with any proceeding or related
proceedings in the same jurisdiction, be liable for the fees and expenses of
more than one separate firm for all indemnified parties. The indemnifying party
shall not be liable for any settlement of any proceeding effected without its
written consent.

            (4) Indemnification similar to that specified in the preceding
paragraphs of this Subsection E shall be given by the Company and Security
Holder (with such modifications as shall be appropriate) with respect to
liability related to any required registration or other qualification of
Registrable Securities under any Federal or state law or regulation of
governmental authority other than the Securities Act.

            (5) If the indemnification provided for in this Subsection D is
unavailable or insufficient to hold harmless an indemnified party under
paragraphs (1) or (2) above, then the indemnifying party shall contribute to the
amount paid or payable by such indemnified party as a result of the losses,
claims, damages or liabilities referred to in paragraphs (1) or (2) above, in
such proportion as is appropriate to reflect the relative fault of the Company
on the one hand and Security Holder on the other in connection with the
statements or omissions which resulted in such losses, claims, damages or
liabilities, as well as any other relevant equity considerations. The relative

                                      -9-
<PAGE>   10
fault shall be determined by reference to, among other things, whether the
untrue or alleged untrue statement of a material fact or the omission or alleged
omission to state a material fact relates to information supplied by the Company
or Security Holder and the parties' relative intent, knowledge, access to
information and opportunity to correct or prevent such untrue statement or
omission. The Company and Security Holder agree that it would not be just and
equitable if contributions pursuant to this paragraph (5) were to be determined
by pro rata allocation or by any other method of allocation which does not take
account of the equitable considerations referred to in the first sentence of
this paragraph (5). The amount paid by an indemnified party as a result of the
losses, claims, damages or liabilities referred to in the first sentence of this
paragraph (5) shall be deemed to include any legal or other expenses reasonably
incurred by such indemnified party in connection with investigating or defending
any action or claim (which shall be limited as provided in paragraph (3) above
if the indemnifying party has assumed the defense of any such action in
accordance with the provisions thereof) which is the subject of this paragraph
(5). Notwithstanding the provisions of this paragraph (5), in respect of any
loss, claim, damage or liability based upon any untrue or alleged untrue
statement of a material fact or omission or alleged omission to state a material
fact which relates to information other than information supplied by Security
Holder, Security Holder shall not be required to contribute any amount in excess
of the amount by which the total price at which the Registrable Securities
offered by it and distributed to the public were offered to the public exceeds
the amount of any damages which Security Holder has otherwise been required to
pay by reason of such untrue or alleged untrue statement or omission or alleged
omission. No Person guilty of fraudulent misrepresentation (within the meaning
of Section 11(f) of the Act) shall be entitled to contribution from any Person
who was not guilty of such fraudulent misrepresentation. Promptly after receipt
by an indemnified party under this paragraph (5) of notice of the commencement
of any action against such party in respect of which a claim for contribution
may be made against an indemnifying party under this paragraph (5), such
indemnified party shall notify the indemnifying party in writing of the
commencement thereof if the notice specified in paragraph (3) above has not been
given with respect to such action; but the omission so to notify the
indemnifying party shall not relieve it from any liability which it may have to
any indemnified party under this paragraph (5) to the extent such omission is
not prejudicial.

      E. PUBLIC AVAILABILITY OF INFORMATION. The Company shall comply with all
public information reporting requirements of the Commission, to the extent
required from time to time to enable Security Holder to sell Registrable
Securities without Registration under the Securities Act within the limitation
of the exemptions provided by (i) Rule 144 under the Securities Act, as such
Rule may be amended from time to time, or (ii) any similar rule or regulation
hereafter adopted by the Commission. Upon the request of Security Holder, the
Company will deliver to Security Holder a written statement as to whether it has
complied with such requirements.

      F. SUPPLYING INFORMATION. The Company shall cooperate with Security Holder
in supplying such information as may be necessary for Security Holder to
complete and file any information reporting forms presently or hereafter
required by the Commission 

                                      -10-
<PAGE>   11
as a condition to the availability of an exemption from the Securities Act for
the sale of any Registrable Securities.

      G. SPECIFIC PERFORMANCE. Each party hereto acknowledges and agrees that
each other party hereto would be irreparably harmed and would have no adequate
remedy of law if any of the provisions of this Agreement were not performed in
accordance with their specific terms or were otherwise breached. Accordingly, it
is agreed that, in addition to any other remedies by law or in equity which may
be available, the parties hereto shall be entitled to obtain temporary and
permanent injunctive relief with respect to any breach or threatened breach of,
or otherwise obtain specific performance of the covenants and other agreements
contained in this Agreement.

      Section 3. REPRESENTATIONS AND WARRANTIES OF THE COMPANY. The Company
represents and warrants to Security Holder that (a) the Company is a corporation
duly organized, validly existing and in good standing under the laws of the
State of Texas and has the corporate power and authority to enter into this
Agreement and to carry out its obligations hereunder, (b) the execution and
delivery of this Agreement by the Company and the consummation by the Company of
the transactions contemplated hereby have been duly authorized by all necessary
corporate action on the part of the Company and no other corporate proceedings
on the part of the Company are necessary to authorize this Agreement or any of
the transactions contemplated hereby, and (c) this Agreement has been duly
executed and delivered by the Company and constitutes a valid and binding
obligation of the Company, and, assuming this Agreement constitutes a valid and
binding obligation of Security Holder is enforceable against the Company in
accordance with its terms, subject to applicable bankruptcy, reorganization,
insolvency, moratorium, fraudulent conveyance and similar laws affecting
creditors, rights generally from time to time and to general principles of
equity, and except as the enforceability thereof may be limited by
considerations of public policy.

      Section 4. REPRESENTATIONS AND WARRANTIES OF SECURITY HOLDER. Security
Holder represents and warrants to the Company that (a) it is a corporation duly
organized, validly existing and in good standing under the laws of the State of
Delaware and has the corporate power and authority to enter into this Agreement
and to carry out its obligations hereunder, (b) the execution and delivery of
this Agreement by Security Holder and the consummation by Security Holder of the
transactions contemplated hereby have been duly authorized by all necessary
corporate action on the part of Security Holder and no other corporate
proceedings on the part of Security Holder are necessary to authorize this
Agreement or any of the transactions contemplated hereby, and (c) this Agreement
has been duly executed and delivered by Security Holder and constitutes a valid
and binding obligation of Security Holder, and, assuming this Agreement
constitutes a valid and binding obligation of the Company, is enforceable
against Security Holder in accordance with its terms subject to applicable
bankruptcy, reorganization, insolvency, moratorium, fraudulent conveyance and
similar laws affecting creditors' rights generally from time to time and to
general principles of equity, and except as the enforceability thereof may be
limited by considerations of public policy.

                                      -11-
<PAGE>   12
      Section 5. STOCK RIGHTS AND RESTRICTIONS AGREEMENT. This Agreement shall
be in all respects subject to the terms and conditions of the Stock Rights and
Restrictions Agreement between the parties hereto and of even date herewith. As
provided in the next sentence, this Agreement may be assigned by Security
Holder, in whole or in part, in connection with any transfer (one or more) of
Registrable Securities that is permitted under the Stock Rights and Restrictions
Agreement except for transfers (i) in a Public Offering or (ii) pursuant to Rule
144 or Rule 145; provided, however, that any such transferee who is not an
Affiliate of Security Holder must acquire from the Security Holder a number of
Registrable Securities equal to at least 25% of the Eligible Stock then held by
Security Holder and its Affiliates. In order for any such transferee to be
entitled to the benefits of this Agreement and thereby become a "Security
Holder," such transferee must agree to be bound by this Agreement by executing a
counterpart of this Agreement. In the event of an assignment or partial
assignment of this Agreement pursuant to this Section 5, notices and requests to
and from the Company pursuant to this Agreement shall continue to be made only
to and from the Security Holder until such time as Security Holder shall
otherwise advise the Company in writing from time to time that a
transferee-Security Holder(s) will give and receive notices and requests.

      In the event that any such transferee-Security Holder is an E&P Company
(as defined in the Stock Rights and Restriction Agreement), then any underwriter
for such E&P Company shall have customary access to perform its due diligence
obligations with respect to any Registration Statement subject to
confidentiality obligations that prohibit the sharing or disclosure of
information with such E&P Company, and no such E&P Company shall, by virtue of
this Agreement, have access to non-public information of the Company.

      No transfer or assignment of this Agreement shall increase the number of
Registrations which the Company is obligated to make under this Agreement.

      Section 6. NOTICES. All notices and other communications hereunder shall
be in writing and shall be deemed given if delivered personally or transmitted
by telex, telegram or facsimile transmission or mailed by registered or
certified mail (return receipt requested) to the parties at the following
addresses (or at such other address for a party as shall be specified by like
notice):

             (a)  if to Security Holder, to:

                  Shell Louisiana Onshore Properties Inc.
                  P.O. Box 7986
                  Newark, Delaware 19714
                  Attention:  Corporate Secretary

                                      -12-
<PAGE>   13
                  with a copy to:

                  Shell Oil Company Legal Firm
                  P.O. Box 2463
                  Houston, Texas 77252
                  Attention:  Danna M. Walton
                  Fax: 713-241-5056

            (b)   if to the Company, to:

                  The Meridian Resource Corporation
                  15995 N. Barkers Landing, Suite 300
                  Houston, Texas  77079
                  Attention:  Joseph A. Reeves, Jr., Chairman and
                              Chief Executive Officer
                  Fax: (281) 558-5595

                  with a copy to:

                  Fulbright & Jaworski L.L.P.
                  1301 McKinney Street, Suite 5100
                  Houston, Texas  77010
                  Attention:  Curtis W. Huff
                  Fax:  (713) 651-5246

      Section 7. GOVERNING LAW. This Agreement shall be governed by and
construed in accordance with the laws of the State of Texas.

      Section 8. COUNTERPARTS. This Agreement may be executed in any number
of counterparts, which together shall constitute a single agreement.

                                      -13-
<PAGE>   14
      IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed by their officers thereunto duly authorized.

                              THE MERIDIAN RESOURCE CORPORATION


                              By /s/ JOSEPH A. REEVES, JR.
                              Name   JOSEPH A. REEVES, JR.
                              Title  CEO


                              SHELL LOUISIANA ONSHORE PROPERTIES INC.

                              By /s/ S.P. METHVIN
                              Name   S. P. METHVIN
                              Title  PRESIDENT

                                      -14-


<PAGE>   1
                                                                      EXHIBIT 6


                                 ARTICLE EIGHT

     The following provisions of this Article Eight shall apply to a business
combination (as defined herein).

     1.   Notwithstanding any other provisions of these Articles of
Incorporation, the Corporation shall not engage in any business combination
with any interested shareholder for a period of three (3) years following the
date that such shareholder became an interested shareholder, unless: (a) prior
to such date the Board of Directors of the Corporation approved either the
business combination or the transaction which resulted in the shareholder
becoming an interested shareholder; (b) upon consummation of the transaction
which resulted in the shareholder becoming an interested shareholder, the
interested shareholder owned at least eighty-five percent (85%) of the voting
stock of the Corporation outstanding at the time the transaction commenced,
excluding for purposes of determining the number of shares outstanding those
shares owned (i) by persons who are directors and also officers and (ii)
employee stock plans in which employee participants do not have the right to
determine confidentially whether shares held subject to the plan will be
tendered in a tender or exchange offer; or (c) on or subsequent to such date
the business combination is approved by the Board of Directors and authorized
at an annual or special meeting of shareholders, and not by written consent,
by the affirmative vote of at least two-thirds of the outstanding voting stock
which is not owned by the interested shareholder.

     2.   The restrictions contained in this Article Eight shall not apply if:
<PAGE>   2
          (a) the Corporation, by action of its shareholders, adopts an
amendment to these Articles of Incorporation expressly electing not to be
governed by this Article Eight; provided that, in addition to any other vote
required by law, such amendment to these Articles of Incorporation must be
approved by the affirmative vote of eighty-five percent (85%) of the shares
entitled to vote. An amendment adopted pursuant to this paragraph shall not be
effective until twelve (12) months after the adoption of such amendment and
shall not apply to any business combination between the Corporation and any
person who became an interest shareholder of the Corporation on or prior to
such adoption;

          (b) a shareholder becomes an interested shareholder inadvertently and
(i) as soon as practicable divests sufficient shares so that the shareholder
ceases to be an interested shareholder and (ii) would not, at any time within
the three (3) year period immediately prior to a business combination between
the Corporation and such shareholder, have been an interested shareholder but
for the inadvertent acquisition; or

          (c) the business combination is proposed prior to the consummation or
abandonment of and subsequent to the earlier of the public announcement or the
notice required hereunder of a proposed transaction which (i) constitutes one
of the transactions described in the following sentence, (ii) is with or by a
person who either was not an interested shareholder during the previous three
(3) years or who became an interested shareholder with the approval of the
Corporation's Board of Directors, and (iii) is approved or not opposed by a
majority of the members of the Board of Directors then in office (but not less
than one (1)) who were directors prior to any person becoming an interested
shareholder during the previous three (3) years or were recommended for
election or elected to succeed such directors by a majority of such directors.
The proposed transactions referred to in the preceding sentence are limited to
(x) a merger or consolidation of the Corporation (except for a merger in
respect of which, pursuant to Article 5.03 of the TBCA, no vote of the
shareholders of the Corporation is required); (y) a sale, lease, exchange,
mortgage, pledge, transfer or other disposition (in one transaction or a
series of transactions), whether as part of a dissolution or otherwise, of
assets of the Corporation or of any direct or indirect majority-owned
subsidiary of the Corporation (other than to any direct or indirect
wholly-owned subsidiary or to the Corporation) having an aggregate market value
equal to fifty percent (50%) or more of either the aggregate market value of
all of the assets of the Corporation determined on a consolidated basis or the
aggregate market value of all the outstanding stock of the Corporation; or (z)
a proposed tender or exchange offer for fifty percent (50%) or more of the
outstanding voting stock of the Corporation. The Corporation shall give not
less than twenty (20) days notice to all interested shareholders



<PAGE>   3
prior to the consummation of any of the transactions described in clauses (x) or
(y) of the second sentence of this paragraph.

     3.   As used in this Article Eight only, the term:

          (a)  "affiliate" means a person that directly, or indirectly through
one or more intermediaries, controls, or is controlled by, or is under common
control with, another person.

          (b)  "Associate," when used to indicate a relationship with any
person, means (i) any corporation or organization of which such person is a
director, officer or partner or is, directly or indirectly, the owner of twenty
percent (20%) or more of any class of voting stock; (ii) any trust or other
estate in which such person has at least a twenty percent (20%) beneficial
interest or as to which such person serves as trustee or in a similar fiduciary
capacity; and (iii) any relative or spouse of such person, or any relative of
such spouse, who has the same residence as such person.

          (c)  "Business combination," when used in reference to the
Corporation and any interested shareholder of the Corporation, means:

               (i)   any merger or consolidation of the Corporation or any
direct or indirect majority-owned subsidiary of the Corporation with (A) the
interested shareholder, or (B) any other Corporation if the merger or
consolidation is caused by the interested shareholder and as a result of such
merger or consolidation subsection 1 of this section is not applicable to the
surviving corporation;

               (ii)  any sale, lease, exchange, mortgage, pledge, transfer or
other disposition (in one transaction or a series of transactions), except
proportionately as a shareholder of the Corporation, to or with the interested
shareholder, whether as part of a dissolution or otherwise, of assets of the
Corporation or of any direct or indirect majority-owned subsidiary of the
Corporation, which assets have an aggregate market value equal to ten percent
(10%) or more of either the aggregate market value of all of the assets of the
Corporation determined on a consolidated basis or the aggregate market value of
all of the outstanding stock of the Corporation;

               (iii) any transaction which results in the issuance or transfer
by the Corporation or by any direct or indirect majority-owned subsidiary of
the Corporation of any stock of the Corporation or of such subsidiary to the
interested shareholder, except (A) pursuant to the exercise, exchange or
conversion of securities exercisable for, exchangeable for or convertible into
stock of the Corporation or any such subsidiary, which securities    
<PAGE>   4
were outstanding prior to the time that the interested shareholder became such;
(B) pursuant to a dividend or distribution paid or made, or the exercise,
exchange or conversion of securities exercisable for, exchangeable for or
convertible into stock of the Corporation or any such subsidiary, which
security is distributed pro rata to all holders of a class or series of stock of
the Corporation subsequent to the time the interested shareholder became such;
(C) pursuant to an exchange offer by the Corporation to purchase stock made on
the same terms to all holders of said stock; or (D) any issuance or transfer of
stock by the Corporation, provided however, that in no case under (B) through
(D) above shall there be an increase in the interested shareholder's
proportionate share of the stock of any class or series of the Corporation or of
the voting stock of the Corporation;

          (iv) any transaction involving the Corporation or any direct or
indirect majority-owned subsidiary of the Corporation which has the effect,
directly or indirectly, of increasing the proportionate share of the stock of
any class or series, or securities convertible into the stock of any class or
series, of the Corporation or of any such subsidiary which is owned by the
interested shareholder, except as a result of immaterial changes due to
fractional share adjustments or as a result of any purchase or redemption of any
shares of stock not caused, directly or indirectly, by the interested
shareholder; or

          (v)  any receipt by the interested shareholder of the benefit,
directly or indirectly (except proportionately as a shareholder of the
Corporation), of any loans, advances, guarantees, pledges, or other financial
benefits (other than those expressly permitted in subparagraphs (i) through
(iv) above) provided by or through the Corporation or any direct or indirect
majority owned subsidiary.

     (d)  "Control," including the term "controlling," "controlled by" and
"under common control with," means the possession, directly or indirectly,
of the power to direct or cause the direction of the management and policies of
a person, whether through the ownership of voting stock, by contract, or
otherwise. A person who is the owner of twenty percent (20%) or more of a
corporation's outstanding voting stock shall be presumed to have control of
such corporation, in the absence of proof by a preponderance of the evidence to
the contrary. Notwithstanding the foregoing, a presumption of control shall not
apply where such person holds voting stock, in good faith and not for the
purpose of circumventing this section, as an agent, bank, broker, nominee,
custodian or trustee for one or more owners who do not individually or as a
group have control of such corporation.
<PAGE>   5
     (e)  "Interested shareholder" means any person (other than the Corporation
and any direct or indirect majority-owned subsidiary of the Corporation) that
(i) is the owner of fifteen percent (15%) or more of the outstanding voting
stock of the Corporation, or (ii) is an affiliate or associate of the
Corporation and was the owner of fifteen percent (15%) or more of the
outstanding voting stock of the Corporation at any time within the three (3)
year period immediately prior to the date on which it is sought to be
determined whether such person is an interested shareholder; and the affiliates
and associates of such person; provided, however, that the term "interested
shareholder" shall not include any person whose ownership of shares in excess
of the fifteen percent (15%) limitation set forth herein is the result of
action taken solely by the Corporation provided that such person shall be an
interested shareholder if thereafter he acquires additional shares of voting
stock of the Corporation, except as a result of further corporate action not
caused, directly or indirectly, by such person. For the purpose of determining
whether a person is an interested shareholder, the voting stock of the
Corporation deemed to be outstanding shall include stock deemed to be owned by
the person through application of paragraph (h) of this subsection but shall
not include any other unissued stock of the Corporation which may be issuable
pursuant to any agreement, arrangement or understanding, or upon exercise of
conversion rights, warrants or options, or otherwise.

     (f)  "Person" means any individual, corporation, partnership,
unincorporated association or other entity.

     (g)  "Voting stock" means stock of any class or series entitled to vote
generally in the election of directors.

     (h)  "Owner" including the terms "own" and "owned" when used with respect
to any stock means a person that individually or with or through any of its
affiliates or associates;

          (i)   beneficially owns such stock, directly or indirectly; or

          (ii)  has (A) the right to acquire such stock (whether such right is
exercisable immediately or only after the passage of time) pursuant to any
agreement, arrangement or understanding, or upon the exercise of conversion
rights, exchange rights, warrants or options, or otherwise; provided, however,
that a person shall not be deemed the owner of stock tendered pursuant to a
tender or exchange offer made by such person or any of such person's affiliates
or associates until such tendered stock is accepted for purchase or exchange;
or (B) the right to vote such stock pursuant to any agreement, arrangement or
understanding; provided, however, that a person shall not be deemed the owner of
<PAGE>   6
any stock because of such person's right to vote such stock if the agreement,
arrangement or understanding to vote such stock arises solely from a revocable
proxy or consent given in response to a proxy or consent solicitation made to
ten (10) or more persons; or

     (iii) has any agreement, arrangement or understanding for the purpose of
acquiring, holding, voting (except voting pursuant to a revocable proxy or
consent as described in item (B) of clause (ii) of this paragraph), or disposing
of such stock with any other person that beneficially owns, or whose affiliates
or associates beneficially own, directly or indirectly, such stock.


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