<PAGE>

                                  EXHIBIT 4(c)

================================================================================


                      TUBOSCOPE VETCO INTERNATIONAL INC.,

                                   as Issuer,


                   TUBOSCOPE VETCO INTERNATIONAL CORPORATION,

                                  as Guarantor


                                      and

                 NORWEST BANK MINNESOTA, NATIONAL ASSOCIATION,

                                   as Trustee



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



                          FIRST SUPPLEMENTAL INDENTURE


                         Dated as of December 13, 1996



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


                                  $75,000,000


                   10 3/4% Senior Subordinated Notes due 2003


================================================================================
<PAGE>

       FIRST SUPPLEMENTAL INDENTURE dated as of December 17, 1996, between
TUBOSCOPE VETCO INTERNATIONAL INC., a Texas corporation, as issuer (the
"Company"), TUBOSCOPE VETCO INTERNATIONAL CORPORATION, a Delaware corporation,
as guarantor (the "Guarantor"), and NORWEST BANK MINNESOTA, NATIONAL
ASSOCIATION, a national banking association, as trustee (the "Trustee").

                                    RECITALS
                                    --------

          WHEREAS, the Company, the Guarantor and the Trustee are parties to
that certain Indenture dated as of April 1, 1993 (the "Indenture"), regarding
the Company's 10 3/4% Senior Subordinated Notes due 2003 (the "Notes");

          WHEREAS, the Company has commenced an offer to purchase (the "Offer")
for cash all of its outstanding Notes from all registered holders thereof (the
"Holders"), upon the terms and subject to the conditions set forth in the Offer
to Purchase and Consent Solicitation Statement dated as of November 20, 1996 and
in the related Consent and Letter of Transmittal, as amended by the terms set
forth in the Company's press release dated December 4, 1996;

          WHEREAS, in connection with the Offer and forming a part thereof, the
Company has solicited consents (the "Consents") of the Holders of the Notes to
effect certain amendments (the "Amendments") to the Indenture (the
"Solicitation");

          WHEREAS, there have been validly delivered Consents of Holders of a
majority in aggregate principal amount of the Notes outstanding that are owned
by Holders other than the Company, any subsidiary or any person directly or
indirectly controlling or controlled by, or under direct or indirect common
control with, the Company or any subsidiary;

          WHEREAS, Section 9.2 of the Indenture permits the Company, the
Guarantor and the Trustee to enter into a Supplemental Indenture; and

          WHEREAS, in accordance with the terms of the Offer and Solicitation,
the Company has determined that it is necessary or required to supplement the
Indenture to reflect the Amendments.

                                   AGREEMENT
                                   ---------

          NOW, THEREFORE, in consideration of the foregoing and the mutual
premises contained herein and for other good and valuable consideration, the
receipt and adequacy of which are hereby acknowledged, the parties hereto agree
as follows:

          1.   Section 4.3 Covenant Defeasance of the Indenture is hereby
amended by deleting the first sentence of the Section in its entirety and
inserting the following sentence in lieu thereof:

          "Upon the Company's exercise under Section 4.1 of the option
          applicable to this Section 4.3, the Company shall be released from its
          obligations under any covenant contained in Section 8.1(a)(v), and in
          Sections 10.13, 10.16 and 10.18, with respect to the Outstanding Notes
          on and after the date the conditions set forth below are satisfied
          (hereinafter, "covenant defeasance"), and Notes shall thereafter be
          deemed to be not "Outstanding" for the purposes of any direction,
          waiver, consent or declaration or Act of Holders (and the consequences
          of any thereof) in connection with such covenants but shall continue
          to be deemed "Outstanding" for all other purposes hereunder."

          2.   Section 10.7 Limitation on Company and Subsidiary Indebtedness of
the Indenture is hereby deleted in its entirety.

          3.   Section 10.8 Limitation on Indebtedness and Preferred Stock of
Subsidiaries of the Indenture is hereby deleted in its entirety.

          4.   Section 10.9 Limitation on Payment Restrictions Affecting
Subsidiaries of the Indenture is hereby deleted in its entirety.

          5.   Section 10.10 Limitation on Restricted Payments of the Indenture
is hereby deleted in its entirety.

          6.   Section 10.11 Provision of Financial Reports of the Indenture is
hereby deleted in its entirety.

          7.   Section 10.12 Transactions with Related Persons of the Indenture
is hereby deleted in its entirety.
<PAGE>

          8.   Section 10.14 Restriction on Senior Subordinated Indebtedness of
the Indenture is hereby deleted in its entirety.

          9.   Section 10.15 Restriction on Lien of the Indenture is hereby
deleted in its entirety.

          10.  Section 10.17 Limitation on Sale-Leaseback Transactions of the
Indenture is hereby deleted in its entirety.

          11.  This First Supplemental Indenture will become effective upon the
date on which the Company has accepted for purchase all Notes validly tendered
(and not withdrawn) pursuant to the terms and conditions of the Offer.

          12.  Capitalized terms used herein without definition shall have the
meanings set forth in the Indenture.

          13.  This First Supplemental Indenture may be executed in any number
of counterparts with the same effect as if the signatures to each counterpart
were upon a single instrument, and all such counterparts together will be deemed
an original of this First Supplemental Indenture.
<PAGE>

          IN WITNESS WHEREOF, the parties hereto have caused this First
Supplemental Indenture to be duly executed, and their respective corporate seals
to be hereunto affixed and attested, all as of the date first written above.


                              TUBOSCOPE VETCO INTERNATIONAL INC.



                              By:          /s/ JAMES F. MARONEY, III
                                 -----------------------------------------------
                                    James F. Maroney, III
                                    Vice President, General Counsel
                                    and Secretary

Attest: /s/ VINCE GILLESPIE
        -------------------
        Vince Gillespie
        Assistant Secretary


                              TUBOSCOPE VETCO INTERNATIONAL INC.
                               CORPORATION


                              By:          /s/ JAMES F. MARONEY, III
                                 -----------------------------------------------
                                    James F. Maroney, III
                                    Vice President, General Counsel
                                    and Secretary

Attest: /s/ VINCE GILLESPIE
        -------------------
        Vince Gillespie
        Assistant Secretary


                              NORWEST BANK MINNESOTA,
                               NATIONAL ASSOCIATION



                              By:
                                 -----------------------------------------------
                              Name:
                                   ---------------------------------------------
                              Title:
                                    --------------------------------------------
Attest:
       ---------------------
Name:
     -----------------------
Title:
      ----------------------