<PAGE>
 
                                                                    Exhibit 4.11

                          UNITED MERIDIAN CORPORATION,

                           UMC PETROLEUM CORPORATION

                                      and

                 FIRST TRUST OF NEW YORK, NATIONAL ASSOCIATION
                                  successor to
                   BANK OF MONTREAL TRUST COMPANY, as Trustee


                                ________________

                          First Supplemental Indenture

                          Dated as of November 4, 1997

                                       to

                                   Indenture

                          Dated as of October 30, 1995
                                ________________

                                  $150,000,000


                   10.375% Senior Subordinated Notes due 2005
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                          FIRST SUPPLEMENTAL INDENTURE


     THIS FIRST SUPPLEMENTAL INDENTURE (this "SUPPLEMENTAL INDENTURE"), dated as
of November 4, 1997, is among United Meridian Corporation, a Delaware
corporation (the "COMPANY"), UMC Petroleum Corporation, a Delaware corporation
(the "SUBSIDIARY GUARANTOR"), and First Trust of New York, National Association,
a national banking association (the "SUCCESSOR TRUSTEE"). All terms used herein
but not defined herein shall have the meanings assigned to such terms in that
certain Indenture dated as of October 30, 1995, relating to the Company's
10.375% Senior Subordinated Notes due 2005 (the "INDENTURE").


                                    RECITALS

     A.  The Company and Bank of Montreal Trust Company, a New York banking
corporation (the "RESIGNING TRUSTEE"), executed the Indenture as of October 30,
1995.

     B.  On November 4, 1997 (the "RESIGNATION NOTICE DATE"), the Resigning
Trustee gave written notice, as required by Section 6.9(b) of the Indenture, to
the Company of its resignation as Trustee under the Indenture, such resignation
to become effective upon the acceptance of appointment by a successor Trustee
under Section 6.10 of the Indenture.

     C.  The parties hereto and the Resigning Trustee have entered into that
certain Resignation, Successor Appointment and Acceptance Agreement, dated as of
the date hereof (the "RESIGNATION AGREEMENT"), pursuant to which, among other
things, (i) the Company agrees to accept the resignation of the Resigning
Trustee, as Trustee, (ii) the Company appoints, as of the date of execution of
the Resignation Agreement and this Supplemental Indenture by all parties thereto
and hereto, the Successor Trustee as Trustee under the Indenture; and (iii) the
Successor Trustee agrees to accept the appointment as Trustee under the
Indenture.

     D.  The parties hereto desire to execute this Supplemental Indenture to (i)
provide for the substitution of the Successor Trustee as Trustee under the
Indenture pursuant to the Resignation Agreement, (ii) provide for the
substitution of the Successor Trustee as Security Registrar and Paying Agent
under the Indenture, and (iii) amend certain provisions of the Indenture in
connection with such substitution as hereinafter set forth.

     NOW, THEREFORE, THIS SUPPLEMENTAL INDENTURE WITNESSETH, the Company,
Subsidiary Guarantor and Successor Trustee mutually covenant and agree for the
equal and proportionate benefit of all Holders as follows:

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                                  ARTICLE ONE

                            Amendment of Indenture

     Section 1.1  Amendment of Indenture.  The introductory paragraph of the
Indenture is hereby deleted in its entirety and substituted in lieu thereof with
the following:

          INDENTURE, dated as of October 30, 1995, among UNITED MERIDIAN
          CORPORATION, a Delaware corporation (hereinafter called the
          "Company"), UMC PETROLEUM CORPORATION, a Delaware corporation
          (hereinafter called the "Subsidiary Guarantor") and FIRST TRUST OF NEW
          YORK, NATIONAL ASSOCIATION, a national banking association, as Trustee
          (hereinafter called the "Trustee").

                                  ARTICLE TWO

     Section 2.1  Appointment and Acceptance. As of the close of business on the
date hereof, the Company hereby appoints the Successor Trustee as Trustee under
the Indenture with all of the rights, powers and duties heretofore vested in the
Resigning Trustee as Trustee under the Indenture, and the Successor Trustee
hereby acknowledges and accepts such appointment.

     Section 2.2  Confirmation. Pursuant to Section 6.10 of the Indenture, (i)
the Company and the Subsidiary Guarantor hereby confirm that the Successor
Trustee is vested with all rights, powers and trusts of the Trustee under the
Indenture, and (ii) upon the request of the Successor Trustee, the Company and
the Subsidiary Guarantor shall execute any and all instruments for more fully
and certainly vesting in and confirming to the Successor Trustee all such
rights, powers and trusts.

     Section 2.3  Notice. Pursuant to Section 6.9(f) of the Indenture, the
Successor Trustee, on behalf of the Company, shall give notice of the
resignation of the Resigning Trustee and the appointment of the Successor
Trustee to all Holders in the manner provided in Section 15.5 of the Indenture,
at the expense of the Successor Trustee.  Such notice shall include the name of
the Successor Trustee and the address of its Corporate Trust Office.

                                 ARTICLE THREE

     Section 3.1  Appointment and Acceptance. As of the close of business on the
date hereof, the Company hereby appoints the Successor Trustee as Security
Registrar for the purpose of registering Securities and transfers and exchanges
of Securities as provided in the Indenture, and as Paying Agent under the
Indenture, with all of the rights, powers and duties heretofore vested in the
Resigning Trustee, as Security Registrar and Paying Agent under the Indenture,
and the Successor Trustee hereby accepts such appointments.

     Section 3.2  Confirmation. The Company and the Subsidiary Guarantor hereby
confirm that (i) the Successor Trustee is vested with all rights, powers and
trusts of the Registrar and the 

                                       2
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Paying Agent under the Indenture, and (ii) upon the request of the Successor
Trustee, the Company and the Subsidiary Guarantor shall execute any and all
instruments fore more fully and certainly vesting in and confirming to the
Successor Trustee all such rights, powers and trusts.

                                 ARTICLE FOUR

                           Miscellaneous Provisions

     Section 4.1  Duplicate Originals.  The parties may sign any number of
copies or counterparts of this Supplemental Indenture.  Each signed copy shall
be an original, but all of them together represent the same agreement.

     Section 4.2  Separability Clause. In case any provision in this
Supplemental Indenture shall be invalid, illegal or unenforceable, the validity,
legality and enforceability of the remaining provisions shall not in any way be
affected or impaired thereby, and a Holder shall have no claim therefore against
any party hereto.

     Section 4.3  Effect of Headings. The Article and Section headings herein
are for convenience only and shall not affect the construction hereof.

     Section 4.4  Successors and Assigns. All covenants and agreements in this
Supplemental Indenture by the Company and the Subsidiary Guarantor shall bind
their respective successors and assigns, whether so expressed or not.  All
agreements of the Successor Trustee in this Supplemental Indenture shall bind
its successor.

     Section 4.5  Governing Law. THIS SUPPLEMENTAL INDENTURE SHALL BE GOVERNED
BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK, WITHOUT
REGARD TO PRINCIPLES OF CONFLICTS OF LAWS.

     Section 4.6  Effect of Supplemental Indenture. Except as amended by this
Supplemental Indenture, the terms and provisions of the Indenture shall remain
in full force and effect.


                            [SIGNATURE PAGE FOLLOWS]
                                        

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     IN WITNESS WHEREOF, the parties hereto have caused this agreement to be
duly executed and their respective corporate seals to be hereunto duly affixed
and attested by their respective officers thereunto duly authorized, all as of
the day and year first written above.

                              UNITED MERIDIAN CORPORATION


                              By:  /s/ Kevin McMillan
                                   ------------------
                              Name:  Kevin McMillan
                                   ------------------
                              Title:  Vice President and Treasurer
                                      ----------------------------              



                              UMC PETROLEUM CORPORATION


                              By:  /s/ Kevin McMillan
                                   ------------------
                              Name:  Kevin McMillan
                                    ------------------
                              Title:  Vice President and Treasurer
                                      ----------------------------              


                              FIRST TRUST OF NEW YORK, NATIONAL ASSOCIATION


                              By:  /s/ Gretchen L. Middents
                                  ------------------------
                              Name:  Gretchen L. Middents
                                     --------------------
                              Title:  Assistant Vice President
                                      ------------------------

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