<PAGE>
                                                                     EXHIBIT 2.6

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

                           PETROLEUM GEO-SERVICES ASA,

                                   AS ISSUER,

                       EACH OF THE GUARANTORS NAMED HEREIN

                                       AND

                    LAW DEBENTURE TRUST COMPANY OF NEW YORK,

                                   AS TRUSTEE

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

                          SECOND SUPPLEMENTAL INDENTURE

                            DATED AS OF JUNE 4, 2004

                                       TO

                     INDENTURE DATED AS OF NOVEMBER 5, 2003

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


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         This Second Supplemental Indenture, dated as of June 4, 2004 (this
"Supplemental Indenture"), among Petroleum Geo-Services ASA, a Norwegian public
limited liability company (the "Company"), the guarantors named on the signature
page hereof (the "Guarantors") and Law Debenture Trust Company of New York (the
"Trustee"). Capitalized terms used but not defined in this Supplemental
Indenture shall have the meanings assigned to them in the Indenture (as defined
below).

                              W I T N E S S E T H:

         WHEREAS, the Company, the Guarantors and Trustee are parties to an
Indenture, dated as of November 5, 2003 (the "Base Indenture"), as amended and
supplemented by the First Supplemental Indenture dated as of November 5, 2003
(the "First Supplemental Indenture" and, together with the Base Indenture, the
"Indenture"), relating to the 10% Senior Notes due 2010 (the "Notes due 2010")
and the 8% Senior Notes due 2006 (the "Notes due 2006" and, together with the
Notes due 2010, the "Notes").

         WHEREAS, covenants set forth in Section 4.03 of the Base Indenture and
Section 4.3 of the First Supplemental Indenture require the Company, among other
things, (i) to prepare and file with the Trustee audited consolidated financial
statements prepared in accordance GAAP for each fiscal year within 180 days
after the end of the fiscal year and unaudited GAAP consolidated financial
statements for each of the first three financial quarters of each of its fiscal
years within 60 days after the applicable financial quarter; and (ii) to comply
with the provisions of TIA Section 314(a).

         WHEREAS, Section 9.02 of the Indenture provides that the Company, the
Guarantors and the Trustee may enter into a supplemental indenture to the
Indenture, with the prior written consent of the Holders of a majority in
principal amount of each of the then outstanding Notes due 2010 and Notes due
2006, to, among other things, change the provisions of the Indenture in certain
respects and modify the rights of the holders of the Notes due 2010 and the
Notes due 2006, respectively.

         WHEREAS, Holders of a majority in principal amount of each of the
outstanding Notes due 2010 and the Notes due 2006 have consented to the
amendments to the Indenture to provide that, until June 30, 2005, the Company
may prepare and file with Trustee audited and unaudited consolidated financial
statements prepared in accordance with Norwegian generally accepted accounting
principles ("NGAAP") (which NGAAP audited financial statements may include a
qualified opinion from the Company's independent auditors) in lieu of financial
statements prepared in accordance with GAAP.

         WHEREAS, Holders of a majority in principal amount of each of the
outstanding Notes due 2010 and the Notes due 2006 have waived (i) any and all
Defaults and Events of Default relating to any failure on the part of the
Company to observe or perform its obligations under Section 4.03 of the Base
Indenture and Section 4.3 of the First Supplemental Indenture, and any other
Defaults or Events of Default related to the provision of financial statements
and other financial information to the Trustee, in each case in this clause (i)
with respect to financial statements and other financial information prepared in
accordance with GAAP; and (ii) any and all Defaults or Events of Default related
to the notification to the Trustee or any other Person by the Company or the
Guarantors of any failure to provide such statements and information



                                       1
<PAGE>

(collectively, the "Covenant Defaults"); in each case during the period
beginning on May 30, 2004 and ending on (a) with respect to Covenant Defaults
related to obligations under Section 4.03 of the Base Indenture, June 30, 2005,
or (b) with respect to Covenant Defaults related to obligations under Section
4.3 of the First Supplemental Indenture, the date hereof.

         WHEREAS, the Company has determined that this Supplemental Indenture
complies with Section 9.02 of the Indenture.

         NOW, THEREFORE, for and in consideration of the premises and the mutual
covenants herein contained, it is mutually covenanted and agreed, for the equal
and ratable benefit of the Holders of the Notes, as follows:

         1.     Amendments of Indenture.


         (i)     The following definition is hereby added to Section 1.1
of the Indenture:

         "NGAAP" means generally accepted accounting principles of the Kingdom
         of Norway.

                (ii)   The last sentence of Section 4.3(a) of the First
Supplemental Indenture is hereby amended and restated in its entirety to provide
as follows:

         "Each set of financial statements delivered by the Company hereunder
         shall be prepared in accordance with GAAP or, prior to June 30, 2005,
         at the Company's option, NGAAP; provided that any such financial
         statements prepared in accordance with NGAAP may include a qualified
         opinion from the Company's independent auditors. Each set of financial
         statements delivered by the Company shall be certified by an Officer of
         the Company as fairly representing its consolidated financial condition
         and operations as at the end of and for the period in relation to which
         those financial statements were prepared."

         2.     Incorporation of Indenture. All the provisions of this
Supplemental Indenture shall be deemed to be incorporated in, and made a part
of, the Indenture; and the Indenture, as supplemented and amended by this
Supplemental Indenture, shall be read, taken and construed as one and the same
instrument.

         3.     Headings and Recitals. The headings of the Sections of this
Supplemental Indenture are inserted for convenience of reference and shall not
be deemed to be a part thereof. The Trustee shall not be responsible in any
manner whatsoever for or in respect of the validity or sufficiency of this
Supplemental Indenture or for or in respect of the recitals contained herein,
all of which are made solely by the Company and the Guarantors.

         4.     Counterparts. This Supplemental Indenture may be executed in any
number of counterparts, and by different parties hereto on separate
counterparts, each of which, when so executed and delivered shall be deemed to
be an original, but all such counterparts shall together constitute but one and
the same instrument.



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<PAGE>

         5.     Conflict with Trust Indenture Act. If any provision of this
Supplemental Indenture limits, qualifies or conflicts with another provision
hereof that is required to be included in this Supplemental Indenture by any of
the provisions of the Trust Indenture Act, such required provision shall
control.

         6.     Successors. All covenants and agreements in this Supplemental
Indenture by the Company shall be binding upon and accrue to the benefit of its
successors. All covenants and agreements in this Supplemental Indenture by the
Trustee shall be binding upon and accrue to the benefit of its successors.

         7.     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.

         8.     Benefits of Supplement. Nothing in this Supplemental Indenture,
express or implied, shall give to any person, other than the parties hereto and
their successors hereunder and the Holders of the Notes, any benefit or any
legal or equitable right, remedy or claim under this Supplemental Indenture.


                                       3
<PAGE>


         IN WITNESS WHEREOF, the parties hereto have caused their duly
authorized officers to execute and deliver this Supplemental Indenture, as of
the date first above written.

                     PETROLEUM GEO-SERVICES ASA


                     By:      /s/  Sam R. Morrow
                         -------------------------------------------------
                           Sam R. Morrow
                           Senior Vice President - Finance and Treasurer

                     GUARANTORS:

                     MULTIKLIENT INVEST AS


                     By:      /s/  Sam R. Morrow
                         -------------------------------------------------
                           Sam R. Morrow
                           Authorized Signatory

                     PGS EXPLORATION (UK) LTD.


                     By:      /s/  Sam R. Morrow
                         -------------------------------------------------
                           Sam R. Morrow
                           Authorized Signatory

                     PGS GEOPHYSICAL AS


                     By:      /s/  Sam R. Morrow
                         -------------------------------------------------
                           Sam R. Morrow
                           Authorized Signatory

                     PGS SHIPPING (IOM) LTD.


                     By:      /s/  Sam R. Morrow
                         -------------------------------------------------
                           Sam R. Morrow
                           Authorized Signatory

                     PGS RIO BONITO SA


                     By:      /s/  Sam R. Morrow
                         -------------------------------------------------
                           Sam R. Morrow
                           Authorized Signatory

                     By:      /s/  Alexander Holst
                         -------------------------------------------------
                           Alexander Holst
                           Authorized Signatory



                                       4
<PAGE>


                     PGS INVETIGACAO PETROLIFERA LTD


                     By:      /s/  Sam R. Morrow
                         -------------------------------------------------
                           Sam R. Morrow
                           Authorized Signatory

                     PGS ONSHORE, INC.


                     By:      /s/  Sam R. Morrow
                         -------------------------------------------------
                           Sam R. Morrow
                           Authorized Signatory



                     LAW DEBENTURE TRUST COMPANY OF NEW YORK, as Trustee


                     By:      /s/  Patrick J. Healy
                         -------------------------------------------------
                           Name:  Patrick J. Healy
                           Title:  Vice President








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