<PAGE>   1
                                                                   EXHIBIT 10.31

                                FOURTH AMENDMENT

                  FOURTH AMENDMENT, dated as of July 31, 1997 (this "Fourth
Amendment"), to the Credit Agreement, dated as of September 30, 1996 (as amended
by the Global Amendment and Assignment and Acceptance, dated as of October 9,
1996, the Second Amendment, dated as of April 23, 1997, the Third Amendment,
dated as of May 13, 1997 and as may be further amended, supplemented or
otherwise modified from time to time, the "Credit Agreement"), among RIGCO NORTH
AMERICA, L.L.C., a Delaware limited liability company (the "Borrower"), the
several banks and other financial institutions from time to time parties thereto
(the "Lenders"), LEHMAN COMMERCIAL PAPER INC. ("LCPI"), as Advisor, Syndication
Agent and Arranger, HIBERNIA NATIONAL BANK, as Collateral and Documentation
Agent and BHF-BANK AKTIENGESELLSCHAFT, as Administrative Agent.


                               W I T N E S S E T H

                  WHEREAS, pursuant to the Credit Agreement, the Lenders have
agreed to make, and have made, certain Loans to the Borrower; and

                  WHEREAS, the Borrower has requested that the Lenders amend,
and the Lenders have agreed to amend, certain of the provisions of the Credit
Agreement, upon the terms and subject to the conditions set forth below;

                  NOW, THEREFORE, the parties hereto hereby agree as follows:

                  1. Defined Terms. (a) As used herein, terms defined in this
Fourth Amendment or in the Credit Agreement are used herein as so defined.

                  (b) The definition of the term "Permitted Issuance" contained
in subsection 1.1 of the Credit Agreement is hereby amended by deleting the
amount "$5,000,000" in the fourth line thereof and substituting in lieu thereof
the amount "$20,000,000".

                  2. Amendment to Subsection 5.13. Subsection 5.13 of the Credit
Agreement is hereby amended by deleting the number "$48,000,000" in the last
line thereof and substituting in lieu thereof the number "$56,000,000".

                  3. Amendment to Subsection 6.1. Subsection 6.1 of the Credit
Agreement is hereby amended by deleting such subsection in its entirety and
substituting in lieu thereof the following:

                  "6.1  Financial Condition Covenants.

                  (a) Maintenance of Net Worth. Permit Net Worth at the last day
         of any fiscal quarter set forth below to be less than the amount set
         forth opposite such fiscal quarter below (provided, however, to the
         extent not included in Net Income in accordance with GAAP during the
         fiscal quarter then ended or in any previous fiscal quarter, Net Worth
         shall include any Mobilization Fees actually received by the Borrower
         during the fiscal quarter then ended and provided, further, to the
         extent deducted in computing Net Worth in accordance with GAAP during
         the fiscal 





<PAGE>   2

                                                                               2

         quarter then ended or in any previous fiscal quarter, Net Worth shall
         include the amount of any deferred corporate income taxes of the
         Borrower (less any reductions in deferred corporate income taxes of the
         Borrower during any of such periods) resulting from an election by the
         Borrower to be treated as a corporation for U.S. federal income tax
         purposes):

<TABLE>
<CAPTION>
              Fiscal Quarter Ending                       Amount
              ---------------------                       ------
<S>                                                       <C>       
              December 31, 1996                                $3,000,000
              March 31, 1997                                   $3,000,000
              June 30, 1997                                    $3,000,000
              September 30, 1997                               $5,000,000
              December 31, 1997                                $6,000,000
              March 31, 1998                                   $6,000,000
              June 30, 1998                                    $6,000,000
              September 30, 1998                               $6,000,000
</TABLE>

                  (b) Maintenance of EBITDA to Interest Expense Ratio. Permit
         the ratio of (i) EBITDA for any period of four consecutive fiscal
         quarters ending with any fiscal quarter set forth below to (ii) Cash
         Interest Expense for such period of four consecutive fiscal quarters to
         be less than the ratio set forth opposite such fiscal quarter below:

<TABLE>
<CAPTION>
              Fiscal Quarter Ending                 Ratio
              ---------------------                 -----
<S>                                                 <C>    
              March 31, 1997                         .50 to 1.00
              June 30, 1997                          .50 to 1.00
              September 30, 1997                    1.25 to 1.00
              December 31, 1997                     1.75 to 1.00
              March 31, 1998                        2.25 to 1.00
              June 30, 1998                         2.75 to 1.00
              September 30, 1998                    3.00 to 1.00
</TABLE>


                  (c) Maintenance of EBITDA. Permit EBITDA for any period of
         four consecutive fiscal quarters ending with any fiscal quarter set
         forth below to be less than the amount set forth opposite such fiscal
         quarter below:

<TABLE>
<CAPTION>
              Fiscal Quarter Ending                       Amount
              ---------------------                       ------
<S>                                                       <C>       
              March 31, 1997                               $ 1,750,000
              June 30, 1997                                $ 1,750,000
              September 30, 1997                           $ 9,000,000
              December 31, 1997                            $14,000,000
              March 31, 1998                               $20,000,000
              June 30, 1998                                $20,000,000
              September 30, 1998                           $21,000,000
</TABLE>

                  (d) Maintenance of Working Capital. Permit at any time prior
         to the date on which the Shoemaker is delivered to commence work under
         a Drilling Contract Working Capital to be less than $500,000."


<PAGE>   3


                                                                               3


                  4. Consent. The Lenders hereby consent to the amendment of the
Charter with respect to the Pincay (the "Pincay Charter") to the extent such
amendment (i) increases the daily payments by the Borrower to the Charterer
thereunder from $2,800 to $5,000 and (ii) eliminates the participation discount
rate in the event the Pincay is deployed for drilling activities on behalf of
affiliates of the Borrower.

                  5. Waiver. The Lenders hereby waive any Default or Event of
Default which may have occurred prior to the date hereof resulting solely from
the failure of the upgrade contemplated by the Shoemaker Upgrade Agreement to be
completed by June 15, 1997 (it being a condition to such waiver that such
upgrade was completed on July 9, 1997).

                  6. Effectiveness. The amendments provided for herein shall
become effective on the date (the "Effective Date") of satisfaction of the
following condition precedent:

                  (a) The Administrative Agent shall have received counterparts
         of this Fourth Amendment, duly executed and delivered by the Borrower
         and each of the other parties hereto.

                  (b) The Lenders shall have received and be reasonably
         satisfied with the amendment to the Pincay Charter referred to in
         paragraph 4.

                  (c) The Lenders shall have received satisfactory revised
         financial projections of the Borrower for the period of July 1997
         through June 1998.

                  (d) All governmental and third party approvals (including
         landlords' and other consents) necessary or advisable in connection
         with this Fourth Amendment shall have been obtained and be in full
         force and effect, and all applicable waiting periods shall have expired
         without any action being taken or threatened by any competent authority
         which would restrain, prevent or otherwise impose materially adverse
         conditions on the Credit Agreement as amended by this Fourth Amendment.

                  (e) All limited liability company and other proceedings, and
         all documents, instruments and other legal matters in connection with
         the transactions contemplated by this Fourth Amendment shall be
         satisfactory in form and substance to the Arranger and the
         Administrative Agent.

                  7. Representations and Warranties. After giving effect to the
amendments contained herein, on the Effective Date, the Borrower hereby
confirms, reaffirms and restates the representations and warranties set forth in
Section 3 of the Credit Agreement; provided that each reference in such Section
3 to "this Agreement" shall be deemed to be a reference both to this Fourth
Amendment and to the Credit Agreement as amended by this Fourth Amendment.

                  8. Continuing Effect; No Other Amendments. Except as expressly
amended or waived hereby, all of the terms and provisions of the Credit
Agreement and the other Loan Documents are and shall remain in full force and
effect. The amendments contained herein shall not constitute an amendment or
waiver of any other provision of the Credit Agreement or the other Loan
Documents or for any purpose except as expressly set forth herein.


<PAGE>   4

                                                                               4


                  9. No Default. Other than as contemplated by paragraph 5
above, no Default or Event of Default shall have occurred and be continuing as
of the Effective Date after giving effect to this Fourth Amendment.

                  10. Costs and Expenses. The Borrower agrees to pay the
reasonable costs and expenses of the Administrative Agent, the Collateral and
Documentation Agent and the Arranger in connection with this Fourth Amendment,
including, without limitation, legal fees and expenses.

                  11. Counterparts. This Fourth Amendment may be executed in any
number of counterparts by the parties hereto, each of which counterparts when so
executed shall be an original, but all the counterparts shall together
constitute one and the same instrument.

                  12. GOVERNING LAW. THIS FOURTH AMENDMENT SHALL BE GOVERNED BY,
AND CONSTRUED AND INTERPRETED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW
YORK.


<PAGE>   5
                                                                               5




                  IN WITNESS WHEREOF, the parties have caused this Fourth
Amendment to be duly executed and delivered by their respective proper and duly
authorized officers as of the day and year first above written.

                                   RIGCO NORTH AMERICA, L.L.C.


                                   By:
                                      Title:


                                   BHF-BANK AKTIENGESELLSCHAFT, as 
                                   Administrative Agent and as a Lender


                                   By:
                                     Title:



                                   By:
                                     Title:


                                   HIBERNIA NATIONAL BANK, as Collateral and
                                   Documentation Agent and as a Lender


                                   By:
                                     Title:


                                   LEHMAN COMMERCIAL PAPER INC., as 
                                   Syndication Agent and as a Lender


                                   By:
                                     Title:


                                   VAN KAMPEN AMERICAN CAPITAL PRIME   
                                   RATE INCOME TRUST


                                   By:
                                     Title:



<PAGE>   6

                                                                               6


                                   PROTECTIVE LIFE INSURANCE COMPANY


                                   By:
                                     Title:

                                   MERRILL LYNCH PRIME RATE PORTFOLIO

                                   By: MERRILL LYNCH ASSET MANAGEMENT L.P., 
                                   as Investment Adviser


                                   By:
                                     Title:

                                   MERRILL LYNCH SENIOR FLOATING RATE
                                   FUND, INC.


                                   By:
                                     Title:

                                   MERRILL LYNCH DEBT STRATEGIES PORTFOLIO

                                   By: MERRILL LYNCH ASSET MANAGEMENT L.P.,
                                   as Investment Adviser


                                   By:
                                     Title:

                                   ML CBO IV (CAYMAN) LTD.

                                   By: Protective Asset Management, L.L.C.,
                                   as Collateral Manager


                                   By:
                                     Title: