<PAGE>   1
                                                                     EXHIBIT 4.2

                                                                          [FORM]


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


                           PETROLEUM GEO-SERVICES ASA,

                                   AS ISSUER,

                                       and

                              CHASE BANK OF TEXAS,
                              NATIONAL ASSOCIATION,

                                   AS TRUSTEE

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



                          FOURTH SUPPLEMENTAL INDENTURE

                           Dated as of March 20, 2000

                                       to

                       Indenture dated as of April 1, 1998


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


                                  $225,000,000

                          Floating Rate Notes due 2002


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





<PAGE>   2



                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                              Page
                                                                              ----
<S>           <C>            <C>                                              <C>
                                    ARTICLE I

                                   DEFINITIONS

SECTION 1.1  Terms Defined in the Original Indenture...........................2
SECTION 1.2  Certain Definitions...............................................2

                                   ARTICLE II

                                    THE NOTES

SECTION 2.1  Form..............................................................5
SECTION 2.2  Title and Amount..................................................5
SECTION 2.3  Registrar, Paying Agent and Calculation Agent.....................6
SECTION 2.4  No Additional Amounts.............................................6
SECTION 2.5  Legends...........................................................6

                                   ARTICLE III

                                   REDEMPTION

SECTION 3.1  Optional Redemption...............................................6

                                   ARTICLE IV

                              ADDITIONAL COVENANTS

SECTION 4.1  Limitation on Sale/Leaseback Transactions.........................6
SECTION 4.2  Limitation on Liens...............................................7
SECTION 4.3  Delivery of Information...........................................9
SECTION 4.4  Payment Currency..................................................9

                                    ARTICLE V

                          ADDITIONAL EVENTS OF DEFAULT

SECTION 5.1  Additional Events of Default.....................................10
</TABLE>




                                           i

<PAGE>   3



<TABLE>
<S>           <C>            <C>                                              <C>
                                   ARTICLE VI

                            MISCELLANEOUS PROVISIONS

SECTION 6.1  Table of Contents, Headings, etc.................................10
SECTION 6.2  Counterpart Originals............................................10
SECTION 6.3  Governing Law....................................................10
</TABLE>


Exhibit A         Form of Note


                                       ii

<PAGE>   4



                  FOURTH SUPPLEMENTAL INDENTURE dated as of March 20, 2000
between Petroleum Geo-Services ASA, a Norwegian public limited liability company
(the "Company"), and Chase Bank of Texas, National Association, a national
banking association, as trustee (the "Trustee").

                             RECITALS OF THE COMPANY

                  WHEREAS, the Company has executed and delivered to the Trustee
an Indenture, dated as of April 1, 1998 (the "Original Indenture" and, as
supplemented by the First Supplemental Indenture thereto dated as of April 1,
1998, the Second Supplemental Indenture thereto dated as of November 19, 1998,
the Third Supplemental Indenture thereto dated as of July 28, 1999, and this
Fourth Supplemental Indenture, the "Indenture"), providing for the issuance by
the Company from time to time of its unsecured debentures, notes or other
evidences of indebtedness (the "Securities"), issuable in one or more series;

                  WHEREAS, the Company has duly authorized and desires to cause
to be issued pursuant to the Original Indenture and this Fourth Supplemental
Indenture a series of Securities designated the "Floating Rate Notes due 2002"
(the "Notes");

                  WHEREAS, the Company desires to cause the issuance of the
Notes pursuant to Section 2.01 of the Original Indenture, which section permits
the execution of indentures supplemental thereto to establish the terms of
Securities of any series;

                  WHEREAS, Section 9.01 of the Original Indenture permits the
execution of supplemental indentures without the consent of any Holder (as
defined therein) (i) to add to the covenants of the Company for the benefit of
the Holders of all or any series of Securities (Section 9.01(6)), (ii) to add
any additional Events of Default with respect to all or any series of Securities
(Section 9.01(7)), (iii) to change or eliminate any provision of the Original
Indenture with respect to Securities of any series when there is no Security of
such series outstanding (Section 9.01(8)) and (iv) to establish the form or
terms of Securities of any series (Section 9.01(9));

                  WHEREAS, pursuant to Section 9.01 of the Original Indenture
the Company has requested that the Trustee join in the execution of this Fourth
Supplemental Indenture to establish the form and terms of the Notes;

                  WHEREAS, all things necessary have been done to make the
Notes, when executed by the Company and authenticated and delivered hereunder
and duly issued by the Company, the valid obligations of the Company, and to
make this Fourth Supplemental Indenture a valid agreement of the Company, in
accordance with their and its terms.

                  NOW, THEREFORE, the Company and the Trustee hereby agree that
the following provisions shall supplement the Original Indenture:



                                        1

<PAGE>   5



                                    ARTICLE I

                                   DEFINITIONS

         SECTION 1.1 Terms Defined in the Original Indenture.

                  Each capitalized term used but not defined in this Fourth
Supplemental Indenture shall have the meaning assigned to such term in the
Original Indenture.

         SECTION 1.2 Certain Definitions.

                  The following definitions are hereby added to, or, in the case
of the definitions of the terms "Business Day," "Issue Date" and "Subsidiary,"
substituted in lieu of, the definition contained in Section 1.01 of the Original
Indenture, but only with respect to the Notes:

                  "Attributable Indebtedness," when used with respect to any
Sale/Leaseback Transaction, means, as at the time of determination, the present
value (discounted at the rate set forth or implicit in the terms of the lease
included in such transaction) of the total obligations of the lessee for rental
payments (other than amounts required to be paid on account of property taxes,
maintenance, repairs, insurance, assessments, utilities, operating and labor
costs and other items that do not constitute payments for property rights)
during the remaining term of the lease included in such Sale/Leaseback
Transaction (including any period for which such lease has been extended).

                  "Business Day" means any day that is a London Business Day,
except a Saturday, a Sunday or a day on which banking institutions in The City
of New York, New York are authorized or obligated by law, regulation or
executive order to remain closed.

                  "Capitalized Lease Obligation" of any Person means any
obligation of such Person to pay rent or other amounts under a lease of
property, real or personal, that is required to be capitalized for financial
reporting purposes in accordance with GAAP; and the amount of such obligation
shall be the capitalized amount thereof determined in accordance with GAAP.

                  "Consolidated Net Tangible Assets" means, as of the date of
determination, Consolidated Total Assets after deducting therefrom, to the
extent included therein (with respect to clauses (a) and (b)), in each case
determined on a consolidated basis in accordance with GAAP (without
duplication): (a) unamortized debt discount and expenses; (b) goodwill, patents,
trademarks, service marks, trade names, copyrights and other items properly
classified as intangible assets in accordance with GAAP; and (c) all liabilities
properly classified as current liabilities in accordance with GAAP (except
liabilities that, by their terms, are extendable or renewable at the option of
the obligor to a date that is 12 months or more after the date on which such
current liabilities are determined).

                  "Consolidated Total Assets" means, as of any date, the total
assets of the Company and its Subsidiaries that would be shown as assets on a
consolidated balance sheet of the Company and its Subsidiaries as of such date
prepared in accordance with GAAP.



                                        2

<PAGE>   6



                  "Global Notes" shall have the meaning set forth in Section
2.1.

                  "Indebtedness" of any Person at any date means, without
duplication, (a) all indebtedness or obligations of such Person for borrowed
money (whether or not the recourse of the lender is to the whole of the assets
of such Person or only to a portion thereof), (b) all obligations of such Person
evidenced by bonds, debentures, notes or other similar instruments, (c) all
obligations of such Person in respect of letters of credit or other similar
instruments (or reimbursement obligations with respect thereto), other than
standby letters of credit and bid or performance bonds issued by such Person in
the ordinary course of business, to the extent not drawn or, to the extent
drawn, if such drawing is reimbursed not later than 30 Business Days following
demand for reimbursement, (d) all obligations of such Person to pay the deferred
and unpaid purchase price of property or services, except trade payables and
accrued expenses incurred in the ordinary course of business, (e) all
Capitalized Lease Obligations of such Person, (f) all Indebtedness of others
secured by a Lien on any asset of such Person, whether or not such Indebtedness
is assumed by such Person, and (g) all Indebtedness of others guaranteed by such
Person to the extent of such guarantee.

                  "Issue Date" means the first date on which the Notes are
originally issued under the Indenture.

                  "Lien" means, with respect to any property or asset, any
mortgage, lien, pledge, charge, security interest or encumbrance of any kind in
respect of such property or asset, whether or not filed, recorded or otherwise
perfected under applicable law, but excluding agreements to refrain from
granting Liens. The Company or any Subsidiary of the Company shall be deemed to
own subject to a Lien any property or asset that it has acquired or holds
subject to the interest of a vendor or lessor under any conditional sale
agreement, Capitalized Lease Obligation or other title retention agreement
relating to such asset; provided, however, that "Lien" shall not include a trust
or similar arrangement established for the purpose of defeasing any Indebtedness
pursuant to the terms evidencing or providing for the issuance of such
Indebtedness.

                  "London Business Day" means any day on which dealings in U.S.
dollars are transacted in the London interbank market.

                  "Net Proceeds" means, with respect to any Sale/Leaseback
Transaction entered into by the Company or any Subsidiary of the Company, the
aggregate net proceeds received by the Company or such Subsidiary from such
Sale/Leaseback Transaction after payment of expenses, taxes, commissions and
similar amounts incurred in connection therewith, whether such proceeds are in
cash or in property (valued at the fair market value thereof at the time of
receipt, as determined by the Board of Directors).

                  "Non-Recourse Indebtedness" means, at any date, the aggregate
amount at such date of Indebtedness of the Company or any Subsidiary of the
Company in respect of which the recourse of the holder of such Indebtedness,
whether direct or indirect and whether contingent or otherwise, is effectively
limited to specified assets, and with respect to which neither the Company nor
any of its Subsidiaries provides any credit support other than the grant of a
Lien on such assets.

                  "Notes" shall have the meaning set forth in the recitals
hereof.


                                        3

<PAGE>   7



                  "Original Indenture" shall have the meaning set forth in the
recitals hereof.

                  "Pari Passu Indebtedness" means any Indebtedness of the
Company, whether outstanding on the Issue Date for the Notes or thereafter
created, incurred or assumed, unless, in the case of any particular
Indebtedness, the instrument creating or evidencing the same or pursuant to
which the same is outstanding expressly provides that such Indebtedness shall be
subordinated in right of payment to the Notes.

                  "Project Finance Debt" means Indebtedness of a Project Finance
Subsidiary (a) as to which neither the Company nor any Subsidiary of the Company
is directly or indirectly liable (by virtue of the Company's or such
Subsidiary's being the primary obligor, or guarantor of (by way of guarantee,
statute, common law or otherwise), or otherwise contractually liable in any
respect on, such Indebtedness) and (b) that is not secured by any assets of the
Company or of any Subsidiary of the Company.

                  "Project Finance Subsidiary" means any Person acquired or
organized after the Issue Date for the Notes in which the Company or one or more
of its Subsidiaries, or the Company and one or more of its Subsidiaries, have an
equity ownership interest and that is designated as a Project Finance Subsidiary
by a resolution of the Board of Directors in accordance with the requirements of
the following sentence. The Company may designate any entity that satisfies the
requirements of the previous sentence to be a Project Finance Subsidiary by a
resolution of the Board of Directors, if after giving effect to such designation
(a) such entity does not own or hold any Capital Stock of, or any Lien on any
property or assets of, the Company or any Subsidiary of the Company and (b) such
entity is not liable, directly or indirectly, with respect to any Indebtedness
other than Project Finance Debt.

                  "Sale/Leaseback Transaction" means any arrangement with any
Person providing for the leasing by the Company or any Subsidiary of the
Company, for a period of more than five years, of any real or tangible personal
property, which property has been or is to be sold or transferred by the Company
or such Subsidiary to such Person in contemplation of such leasing.

                  "Subsidiary" means, as to any Person, any corporation,
association or other business entity, other than a Project Finance Subsidiary,
in which such Person or one or more of its Subsidiaries or such Person and one
or more of its Subsidiaries own more than 50% of the total combined voting power
of all Common Equity, and any partnership or joint venture if more than a 50%
interest in the profits or capital thereof is owned by such Person or one or
more of its Subsidiaries or such Person and one or more of its Subsidiaries
(unless such partnership or joint venture can and does ordinarily take major
business actions without the prior approval of such Person or one or more of its
Subsidiaries).

                  For greater certainty, a Project Finance Subsidiary of a
Person shall not be a Subsidiary of such Person regardless of whether such
Person owns more than 50% of the total combined voting power of all Common
Equity of the Project Finance Subsidiary or more than a 50% interest in the
profits or capital of any Project Finance Subsidiary organized as a partnership
or joint venture. If the Company or one or more of its Subsidiaries or the
Company and one or more of its Subsidiaries own more than 50% of the total
combined voting power of all Common Equity or more


                                        4

<PAGE>   8



than a 50% interest in the profits or capital of a Project Finance Subsidiary,
the Board of Directors, by resolution, may designate such Project Finance
Subsidiary to be a Subsidiary of the Company, provided that immediately after
giving effect to such designation, no Default or Event of Default shall have
occurred and be continuing.


                                   ARTICLE II

                                    THE NOTES

         SECTION 2.1 Form.

                  The Notes and the Trustee's certificate of authentication
shall be substantially in the form of Exhibit A to this Fourth Supplemental
Indenture, which is hereby incorporated into this Indenture. The terms and
provisions contained in the Notes shall constitute, and are hereby expressly
made, a part of this Fourth Supplemental Indenture and to the extent applicable,
the Company and the Trustee, by their execution and delivery of this Fourth
Supplemental Indenture, expressly agree to such terms and provisions and to be
bound thereby.

                  The Notes will initially be issued in permanent global form,
substantially in the form of Exhibit A attached hereto (the "Global Notes").
Each Global Note shall represent such of the outstanding Notes as shall be
specified therein and shall provide that it shall represent the aggregate amount
of outstanding Notes from time to time endorsed thereon and that the aggregate
amount of outstanding Notes represented thereby may from time to time be reduced
or increased, as appropriate, to reflect exchanges and redemptions. Any
endorsement of a Global Note to reflect the amount, or any increase or decrease
in the amount, of outstanding Notes represented thereby shall be made by the
Trustee in accordance with written instructions or such other written form of
instructions as is customary for the Depositary, from the Depositary or its
nominee on behalf of any Person having a beneficial interest in the Global Note.

                  The Company initially appoints The Depository Trust Company
and the Trustee to act as Depositary and Securities Custodian, respectively,
with respect to the Global Notes.

         SECTION 2.2 Title and Amount.

                  The Notes shall be entitled the "Floating Rate Notes due
2002." The aggregate principal amount of Notes that may be authenticated and
delivered under this Fourth Supplemental Indenture is unlimited (except for
Notes authenticated and delivered upon registration of transfer of, or in
exchange for, or in lieu of, other Notes of this series pursuant to Section
2.08, 2.09, 2.12, 2.17, 3.07 or 9.05 of the Original Indenture). The Trustee
shall authenticate and deliver (i) Notes for original issue on the Issue Date
in the aggregate principal amount of $225,000,000 and (ii) additional Notes
for original issue from time to time after the Issue Date in such principal
amounts as may be set forth in an order of the Company described in this
sentence, in each case upon a Company Order for the authentication and
delivery thereof and satisfaction of Sections 2.01 and 2.04 of the Indenture.
Such order shall specify the principal amount of the Notes to be authenticated,
the date on which the original issue of Notes is to be authenticated and the
name or names of the initial Holder or Holders.


                                        5

<PAGE>   9



         SECTION 2.3 Registrar, Paying Agent and Calculation Agent.

                  The Company initially appoints the Trustee as Registrar,
Paying Agent and Calculation Agent with respect to the Notes. The office where
Notes may be presented for registration of transfer or exchange  and the Place
of Payment for the Notes shall initially be the Corporate Trust Office of the
Trustee in the Borough of Manhattan, The City of New York and at 1201 Main
Street, 18th Floor, Dallas, Texas 75202.

         SECTION 2.4 No Additional Amounts.

                  No Additional Amounts shall be payable with respect to the
Notes.

         SECTION 2.5 Legends.

                  Each certificate evidencing the Global Notes shall bear the
paragraph referred to in the footnote on page A-1 of the form of Note attached
hereto as Exhibit A.


                                   ARTICLE III

                                   REDEMPTION

         SECTION 3.1 Optional Redemption.

                  There shall be no sinking fund for the retirement of Notes.
The Company, at its option, may redeem the Notes in accordance with the
provisions of paragraph 6 of the Notes and Article III of the Original
Indenture.


                                   ARTICLE IV

                              ADDITIONAL COVENANTS

                  The following covenants are hereby added to the covenants of
the Company for the benefit of the Holders of the Notes, and such covenants are
expressly being included solely for the benefit of such Notes:

         SECTION 4.1 Limitation on Sale/Leaseback Transactions.

                  The Company shall not, and shall not permit any of its
Subsidiaries to, enter into any Sale/Leaseback Transaction with any Person
(other than the Company or a Subsidiary of the Company) unless:

                  (a) the Company or such Subsidiary would be entitled to incur
         Indebtedness, in a principal amount equal to the Attributable
         Indebtedness with respect to such Sale/Lease-


                                       6
<PAGE>   10


         back Transaction, secured by a Lien on the property subject to such
         Sale/Leaseback Transaction pursuant to Section 4.2 of this Fourth
         Supplemental Indenture without equally and ratably securing the Notes
         pursuant to such covenant;

                  (b) after the Issue Date for the Notes and within a period
         commencing 12 months prior to the consummation of such Sale/Leaseback
         Transaction and ending 12 months after the consummation thereof, the
         Company or such Subsidiary shall have expended for property used or to
         be used in the business of the Company and its Subsidiaries an amount
         equal to all or a portion of the Net Proceeds from such Sale/Leaseback
         Transaction and the Company shall have elected to designate such amount
         as a credit against such Sale/Leaseback Transaction (with any such
         amount not being so designated to be applied as set forth in clause (c)
         below); or

                  (c) the Company, during the 12-month period after the
         effective date of such Sale/Leaseback Transaction, shall have applied
         to the voluntary defeasance or retirement of Notes or any Pari Passu
         Indebtedness an amount equal to the greater of the Net Proceeds of the
         sale or transfer of the property leased in such Sale/Leaseback
         Transaction and the fair value, as determined by the Board of
         Directors, of such property at the time of entering into such
         Sale/Leaseback Transaction (in either case adjusted to reflect the
         remaining term of the lease and any amount expended by the Company as
         set forth in clause (b) above), less an amount equal to the principal
         amount of Notes and Pari Passu Indebtedness voluntarily defeased or
         retired by the Company within such 12-month period and not designated
         as a credit against any other Sale/Leaseback Transaction entered into
         by the Company or any Subsidiary of the Company during such period.

         SECTION 4.2 Limitation on Liens.

                  The Company shall not, and shall not permit any Subsidiary of
the Company to, issue, assume or guarantee any Indebtedness for borrowed money
secured by any Lien on any property or asset now owned or hereafter acquired by
the Company or such Subsidiary without making effective provision whereby any
and all Notes then or thereafter outstanding will be secured by a Lien equally
and ratably with any and all other obligations thereby secured for so long as
any such obligations shall be so secured. Notwithstanding the foregoing, the
Company or any Subsidiary of the Company may, without so securing the Notes,
issue, assume or guarantee Indebtedness for borrowed money secured by the
following Liens:

                  (a) Liens existing on the Issue Date for the Notes or provided
         for under the terms of agreements existing on such date securing
         Indebtedness (i) existing on such date (including, without limitation,
         the Lien provided for pursuant to Section 7.07 of the Original
         Indenture) or (ii) to be incurred under agreements existing on such
         date;

                  (b) Liens on property or assets securing (i) all or any
         portion of the cost of acquiring, constructing, altering, improving or
         repairing such property or assets, real or personal, or improvements
         used or to be used in connection with such property or assets, (ii)
         Indebtedness incurred by the Company or any Subsidiary of the Company
         prior to or within 24 months after the later of the acquisition, the
         completion of construction, alteration,


                                       7
<PAGE>   11


         improvement or repair or the commencement of commercial operation
         thereof, which Indebtedness is incurred for the purpose of financing
         all or any part of the purchase price thereof or construction,
         alteration, improvement or repair thereof or (iii) Indebtedness in
         excess of such purchase price or cost of acquisition, construction,
         alteration, improvement or repair, provided that recourse for payment
         of such excess Indebtedness is limited to such property or assets;

                  (c) Liens securing Indebtedness owed by a Subsidiary of the
         Company to the Company or to any other Subsidiary of the Company;

                  (d) Liens on the property, assets or Capital Stock of any
         Person existing at the time such Person becomes a Subsidiary of the
         Company and not incurred as a result of (or in connection with or in
         anticipation of) such Person's becoming a Subsidiary of the Company,
         provided that such Liens do not extend to or cover any property, assets
         or Capital Stock of the Company or any of its Subsidiaries other than
         the property, assets or Capital Stock encumbered at the time such
         Person becomes a Subsidiary of the Company;

                  (e) Liens on any property or assets securing Indebtedness
         issued or guaranteed by the United States or any State thereof or any
         department, agency or instrumentality of either;

                  (f) Liens affecting property or assets existing at the time
         such property or assets become property or assets of the Company or a
         Subsidiary of the Company;

                  (g) Liens on Capital Stock, debt securities or other
         securities of a Person that is not a Subsidiary of the Company;

                  (h) Liens relating to accounts receivable of the Company or
         any Subsidiary of the Company that have been sold, assigned or
         otherwise transferred to a Person other than the Company or a
         Subsidiary of the Company;

                  (i) Liens created pursuant to applications or reimbursement
         agreements pertaining to commercial letters of credit;

                  (j) Liens relating to accounts receivable or inventory that
         secure working capital loans that are part of a credit facility with a
         term not exceeding five years;

                  (k) any Lien extending, renewing or replacing (or successive
         extensions, renewals or replacements of) any Lien of any type permitted
         under clauses (a) through (j) above, provided that such Lien extends to
         or covers only the property or asset that is subject to the Lien being
         extended, renewed or replaced and that the principal amount of the
         Indebtedness secured thereby shall not exceed the sum of (i) the
         principal amount of Indebtedness so secured at the time of such
         extension, renewal or replacement, (ii) any additional Indebtedness
         incurred to pay the cost of altering, improving or repairing such
         property or asset and (iii) any expenses of the Company and its
         Subsidiaries (including any premium) incurred in connection with any
         such extension, renewal or replacement; and


                                       8
<PAGE>   12


                  (l) other Liens (exclusive of any Lien of any type otherwise
         permitted under clauses (a) through (k) above) securing Indebtedness
         for borrowed money of the Company or any Subsidiary of the Company in
         an aggregate principal amount that, together with the aggregate amount
         of Attributable Indebtedness deemed to be outstanding in respect of all
         Sale/Leaseback Transactions entered into pursuant to clause (a) of
         Section 4.1 hereof (exclusive of any such Sale/Leaseback Transactions
         otherwise permitted under clauses (a) through (j) above), does not at
         the time such Indebtedness is incurred exceed 15% of Consolidated Net
         Tangible Assets of the Company (as shown in the most recent audited
         consolidated balance sheet of the Company and its Subsidiaries).

         SECTION 4.3 Delivery of Information.

                  If the Company is required to furnish annual or quarterly
reports to its shareholders pursuant to the Exchange Act, the Company shall
cause any annual report furnished to its shareholders generally and any
quarterly or other financial reports furnished by it to its shareholders
generally to be filed with the Trustee and mailed to the Holders at their
addresses appearing in the register of Securities maintained by the Registrar.
If the Company is not required to furnish annual or quarterly reports to its
shareholders pursuant to the Exchange Act, the Company shall cause its financial
statements referred to in Section 4.03(a) of the Original Indenture, including
any notes thereto (and with respect to annual reports, an auditors' report by a
firm of established national reputation), and a "Management's Discussion and
Analysis of Financial Condition and Results of Operations" to be so mailed to
the Holders within 90 days after the end of each of the Company's fiscal years
and within 60 days after the end of each of the Company's first three fiscal
quarters.

         SECTION 4.4 Payment Currency.

                  All payments due under the Notes shall be made in Dollars. To
the fullest extent permitted by applicable law, the obligation of the Company in
respect of any amount due under the Notes shall, notwithstanding any payment in
any other currency (whether pursuant to a judgment or otherwise), be discharged
only to the extent of the amount in Dollars that the party entitled to receive
such payment may, in accordance with normal banking procedures, purchase with
the sum paid in such other currency (after any premium and costs of exchange) in
the city of receipt on the Business Day immediately following the day on which
such party receives such payment. If the amount in Dollars that may be so
purchased for any reason falls short of the amount originally due, the Company
shall pay such additional amounts, in Dollars, as may be necessary to compensate
for the shortfall. Any obligation of the Company not discharged by such
additional payment shall, to the fullest extent permitted by applicable law, be
due as a separate and independent obligation and, until discharged as provided
herein, shall continue in full force and effect. The provisions of the last
paragraph of Section 6.10 of the Original Indenture shall not apply to the
Notes.


                                       9
<PAGE>   13


                                    ARTICLE V

                          ADDITIONAL EVENTS OF DEFAULT

         SECTION 5.1 Additional Events of Default.

                  The following Events of Default are hereby added to the Events
of Default with respect to the Notes, and such additional Events of Default
apply only to the Notes:

                  (a) any default shall occur which results in the acceleration
         of the maturity of any Indebtedness (other than the Notes or any
         Non-Recourse Indebtedness) of the Company or any Subsidiary of the
         Company having an outstanding principal amount of $20 million or more
         individually or, taken together with all other such Indebtedness that
         has been so accelerated, in the aggregate; and

                  (b) a judgment or order for the payment of money in excess of
         $20 million (net of applicable insurance coverage) shall be rendered
         against the Company or any Subsidiary of the Company and such judgment
         or order shall continue unsatisfied and unstayed for a period of 30
         days.

                                   ARTICLE VI

                            MISCELLANEOUS PROVISIONS

         SECTION 6.1 Table of Contents, Headings, etc.

                  The table of contents and headings of the Articles and
Sections of this Fourth Supplemental Indenture have been inserted for
convenience of reference only, are not to be considered a part hereof and shall
in no way modify or restrict any of the terms or provisions hereof.

         SECTION 6.2 Counterpart Originals.

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

         SECTION 6.3 Governing Law.

                  THIS FOURTH SUPPLEMENTAL INDENTURE AND THE NOTES SHALL BE
GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK.


                                       10
<PAGE>   14


                  IN WITNESS WHEREOF, the parties hereto have caused this Fourth
Supplemental Indenture to be duly executed as of the day and year first above
written.

                                          PETROLEUM GEO-SERVICES ASA



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


                                          CHASE BANK OF TEXAS,
                                          NATIONAL ASSOCIATION,
                                               as Trustee


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



<PAGE>   15



                                                                       EXHIBIT A

                             [FORM OF FACE OF NOTE]

[THIS NOTE IS A GLOBAL NOTE WITHIN THE MEANING OF THE INDENTURE HEREINAFTER
REFERRED TO AND IS REGISTERED IN THE NAME OF THE DEPOSITORY OR A NOMINEE
THEREOF. THIS NOTE MAY NOT BE EXCHANGED IN WHOLE OR IN PART FOR A NOTE
REGISTERED, AND NO TRANSFER OF THIS NOTE IN WHOLE OR IN PART MAY BE REGISTERED,
IN THE NAME OF ANY PERSON OTHER THAN SUCH DEPOSITARY OR A NOMINEE THEREOF,
EXCEPT IN THE LIMITED CIRCUMSTANCES DESCRIBED IN THE INDENTURE. UNLESS AND UNTIL
IT IS EXCHANGED IN WHOLE OR IN PART FOR NOTES IN DEFINITIVE FORM, THIS NOTE MAY
NOT BE TRANSFERRED EXCEPT AS A WHOLE BY THE DEPOSITARY TO A NOMINEE OF THE
DEPOSITARY OR BY A NOMINEE OF THE DEPOSITARY TO THE DEPOSITARY OR ANOTHER
NOMINEE OF THE DEPOSITARY OR BY THE DEPOSITARY OR ANY SUCH NOMINEE TO A
SUCCESSOR DEPOSITARY OR A NOMINEE OF SUCH SUCCESSOR DEPOSITARY. THE DEPOSITORY
TRUST COMPANY, A NEW YORK CORPORATION ("DTC"), SHALL ACT AS THE DEPOSITARY UNTIL
A SUCCESSOR SHALL BE APPOINTED BY THE COMPANY AND THE REGISTRAR. UNLESS THIS
CERTIFICATE IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF DTC TO THE ISSUER OR
ITS AGENT FOR REGISTRATION OF TRANSFER, EXCHANGE OR PAYMENT, AND ANY CERTIFICATE
ISSUED IS REGISTERED IN THE NAME OF CEDE & CO. OR IN SUCH OTHER NAME AS IS
REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC (AND ANY PAYMENT IS MADE TO
CEDE & CO. OR TO SUCH OTHER ENTITY AS IS REQUESTED BY AN AUTHORIZED
REPRESENTATIVE OF DTC), ANY TRANSFER, PLEDGE OR OTHER USE HEREOF FOR VALUE OR
OTHERWISE BY OR TO ANY PERSON IS WRONGFUL INASMUCH AS THE REGISTERED OWNER
HEREOF, CEDE & CO., HAS AN INTEREST HEREIN.]*

                           PETROLEUM GEO-SERVICES ASA

                           FLOATING RATE NOTE DUE 2002

                                CUSIP 716597 BF 5

No.___________                                                      $___________

                  Petroleum Geo-Services ASA, a Norwegian public limited
liability company (the "Company," which term includes any successor Person under
the Indenture hereinafter referred to), for value received, promises to pay to
___________________ or registered assigns the principal sum of ____________
Dollars [or such greater or lesser amount as indicated in the Schedule of
Exchanges of Notes],* on March 20, 2002.

                  Interest Payment Dates:  March 20, June 20, September 20 and
                                           December 20

                  Record Dates:            March 5, June 5, September 5 and
                                           December 5

                  Reference is hereby made to the further provisions of this
Note set forth on the reverse hereof, which further provisions shall for all
purposes have the same effect as if set forth at this place.

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

* To be included in Global Note


                                       A-1

<PAGE>   16



                  IN WITNESS WHEREOF, the Company has caused this Note to be
signed manually or by facsimile by its duly authorized officers.

Dated:

                                          PETROLEUM GEO-SERVICES ASA

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

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


Certificate of Authentication:

                  This is one of the Securities of the series designated therein
referred to in the within- mentioned Indenture.

                                               CHASE BANK OF TEXAS,
                                               NATIONAL ASSOCIATION, as Trustee



                                               By:
                                                  -----------------------------
                                                       Authorized Signatory






                                       A-2

<PAGE>   17



                            [FORM OF REVERSE OF NOTE]

                           PETROLEUM GEO-SERVICES ASA

                           FLOATING RATE NOTE DUE 2002

                  This Note is one of a duly authorized issue of Floating Rate
Notes due 2002 (the "Notes") of Petroleum Geo-Services ASA, a Norwegian public
limited liability company (the "Company").

                  1. Interest. The Company promises to pay interest on the
principal amount of this Note as set forth below from March 20, 2000 until
maturity. The Company will pay interest quarterly in arrears on March 20, June
20, September 20 and December 20 of each year (each an "Interest Payment Date").
Interest on the Notes will accrue from, and including, the most recent Interest
Payment Date on which interest has been paid or, if no interest has been paid,
from, and including, the Issue Date for the Notes; provided that if there is no
existing Default in the payment of interest, and if this Note is authenticated
between the 15th calendar day next preceding each Interest Payment Date (each, a
"Record Date") and such Interest Payment Date, interest shall accrue from, and
including, such next succeeding Interest Payment Date; provided, further, that
the first Interest Payment Date shall be June 20, 2000. The Company shall pay
interest on overdue principal and premium (if any) from time to time on demand
at a rate equal to the interest rate then in effect; it shall pay interest on
overdue installments of interest (without regard to any applicable grace
periods) from time to time to Holders as of a special record date set by the
Trustee at the same rate to the extent lawful. If any Interest Payment Date
(other than an Interest Payment Date at maturity) falls on a day that is not a
Business Day, such Interest Payment Date will be postponed until the next
succeeding Business Day unless such Business Day falls in the next calendar
month, in which case such Interest Payment Date will be the next preceding
Business Day. If the maturity date of the Notes is a day that is not a Business
Day, all payments to be made on such day will be made on the next succeeding
Business Day with the same force and effect as if made on the due date, and no
additional interest will be payable as a result of such delay in payment. The
period beginning on, and including, March 20, 2000, and ending on, but
excluding, the next Interest Payment Date thereafter, and each successive
three-month period beginning on, and including, an Interest Payment Date and
ending on, but excluding, the next succeeding Interest Payment Date is herein
called an "Interest Period."

                  2.       Calculation of Interest.

                  (a) The rate of interest payable from time to time in respect
of this Note (the "Rate of Interest") shall be a floating rate subject to
adjustment once for each Interest Period and determined by reference to LIBOR,
determined as described below, plus a spread of 0.65% per annum. All percentages
resulting from any calculation of the Rate of Interest on the Notes shall be
rounded to the nearest one hundred-thousandth of a percentage point, with five
one millionths of a percentage point rounded upwards (e.g., 9.876545% (or
 .09876545) would be rounded to 9.87655% (or .0987655)), and all dollar amounts
used in or resulting from such calculation on the Notes shall be rounded to the
nearest cent (with one-half cent being rounded upward).



                                       A-3

<PAGE>   18



                  The Rate of Interest in effect on each day that is not an
Interest Reset Date (as defined below) shall be the Rate of Interest determined
as of the Interest Determination Date (as defined below) in respect of the next
preceding Interest Reset Date. The Rate of Interest in effect on each day that
is an Interest Reset Date shall be the Rate of Interest determined as of the
Interest Determination Date in respect of such Interest Reset Date.

                  (b) The Calculation Agent shall reset the Rate of Interest on
each Interest Payment Date and on March 20, 2000 (each, an "Interest Reset
Date"). At approximately 11:00 a.m., London time, on the second London Business
Day (or, for purposes of the third sentence of paragraph (c) below, the Business
Day) next preceding each Interest Reset Date (each, an "Interest Determination
Date"), Chase Bank of Texas, National Association, or its successor in this
capacity (the "Calculation Agent"), shall calculate the Rate of Interest for the
following Interest Period as, subject to the provisions described below, the
rate per annum equal to 0.65% above the rate for deposits in United States
dollars having a maturity of three months commencing on the first day of such
Interest Period that appears on the Telerate Page (as defined below) on such
Interest Determination Date.

                  (c) If no such rate appears on the Telerate Page as specified
in paragraph (b) above, the Calculation Agent shall request the principal London
offices of each of four major reference banks in the London interbank market, as
selected by the Calculation Agent, to provide the Calculation Agent with its
offered quotation for deposits in United States dollars for the period of three
months, commencing on the first day of the applicable Interest Period, to prime
banks in the London interbank market at approximately 11:00 a.m., London time,
on such Interest Determination Date and in a principal amount that is
representative for a single transaction in United States dollars in that market
at that time. If at least two quotations are provided, then LIBOR on such
Interest Determination Date shall be the arithmetic mean of such quotations. If
fewer than two quotations are provided, then LIBOR on such Interest
Determination Date shall be the arithmetic mean of the rates quoted at
approximately 11:00 a.m., in The City of New York, on the Interest Determination
Date by three major banks in The City of New York selected by the Calculation
Agent for loans in United States dollars to leading European banks, having a
three-month maturity and in a principal amount that is representative for a
single transaction in United States dollars in that market at that time. If,
however, the banks selected by the Calculation Agent are not providing
quotations in the manner described by the previous sentence, LIBOR determined as
of such Interest Determination Date shall be LIBOR in effect on such Interest
Determination Date.

                  "Telerate Page" means the display designated as "Page 3750" on
Bridge Telerate, Inc., or any successor service, for the purpose of displaying
the London interbank rates of major banks for United States dollars.

                  (d) The Calculation Agent shall, as soon as practicable after
11:00 a.m. (London time) on each Interest Determination Date, determine the Rate
of Interest and calculate the amount of interest payable in respect of the
following Interest Period (the "Interest Amount"). The Interest Amount shall be
calculated by applying the Rate of Interest to the principal amount of each Note
outstanding at the commencement of the Interest Period, multiplying each such
amount by the actual number of days in the Interest Period concerned (which
actual number of days shall include the first day but exclude the last day of
such Interest Period) divided by 360 and rounding the resultant figure upwards
to the nearest cent (half a cent being rounded upwards). The determination of
the Rate of


                                       A-4

<PAGE>   19



Interest and the Interest Amount by the Calculation Agent shall (in the absence
of manifest error) be final and binding on all parties.

                  The Calculation Agent has determined that the Rate of Interest
for the initial Interest Period is 6.84125%.

                  (e) Notwithstanding anything herein to the contrary, the Rate
of Interest shall in no event be higher than the maximum rate permitted by New
York law, as the same may be modified by United States law of general
application.

                  (f) Interest shall cease to accrue on this Note on the
maturity date unless, upon presentation of this Note, payment of principal is
improperly withheld or refused, in which case, interest shall continue to
accrue.

                  3. Calculation Agent. So long as any of the Notes remain
outstanding, the Company shall maintain under appointment a Calculation Agent,
which shall initially be the Trustee, for the purpose of the Notes. If the
Trustee shall be unable or unwilling to continue to act as Calculation Agent
or if the Calculation Agent fails to calculate properly the Rate of Interest
for any Interest Period, the Company shall appoint another leading commercial
or investment bank engaged in the London interbank market to act as the
Calculation Agent. The Company may change the Calculation Agent without notice.
The Calculation Agent may not resign in its duties, and the Company may not
change the Calculation Agent, without a successor Calculation Agent having
been appointed that meets the requirements of this paragraph.

                  All certificates, communications, opinions, determinations,
calculations, quotations and decisions given, expressed, made or obtained for
the purposes of the provisions hereof relating to the payment and calculation of
interest on the Notes, whether by the reference banks referred to in paragraph
2(c) above (or any of them) or the Calculation Agent, shall (in the absence of
manifest error) be binding on the Company, the Calculation Agent and all of the
holders and owners of beneficial interests in this Note, and no liability shall
(in the absence of manifest error) attach to the Calculation Agent in connection
with the exercise or non-exercise by it of its powers, duties and discretions.

                  4. Method of Payment. The Company will pay interest on the
Notes (except defaulted interest) to the Persons who are registered Holders of
Notes at the close of business on the Record Date next preceding the Interest
Payment Date, even if such Notes are canceled after such Record Date and on or
before such Interest Payment Date. The Holder must surrender this Note to a
Paying Agent to collect principal payments. The Company will pay the principal
of and interest on the Notes in money of the United States of America that at
the time of payment is legal tender for payment of public and private debts. The
Company, however, may pay such amounts (i) by wire transfer with respect to
Notes held in book-entry form or (ii) by check payable in such money mailed to a
Holder's registered address with respect to any Notes.

                  5. Ranking. The Notes are senior unsecured obligations of the
Company and rank pari passu with all other unsecured and unsubordinated
indebtedness of the Company.



                                       A-5

<PAGE>   20



                  6. Optional Redemption. The Notes are subject to redemption,
at the option of the Company, in whole or in part, in principal amounts of
$1,000 or any integral multiple thereof, on March 20, 2001 and on each Interest
Payment Date thereafter, upon not less than 30 nor more than 60 days' prior
notice as provided in the Indenture (as hereinafter defined), at a Redemption
Price equal to 100% of the principal amount of the Notes to be redeemed plus
accrued and unpaid interest to the date of redemption.

                  7. Paying Agent and Registrar. Initially, Chase Bank of Texas,
National Association (the "Trustee"), the trustee under the Indenture, will act
as Paying Agent and Registrar. The Company may change any Paying Agent,
Registrar, co-registrar or additional paying agent without notice to any Holder.
The Company may act in any such capacity.

                  8. Indenture. The Company issued the Notes under an Indenture
dated as of April 1, 1998 (the "Original Indenture") between the Company and the
Trustee, as supplemented by the First Supplemental Indenture thereto dated as of
April 1, 1998, the Second Supplemental Indenture thereto dated as of November
19, 1998, the Third Supplemental Indenture thereto dated as of July 28, 1999,
and the Fourth Supplemental Indenture thereto dated as of March 20, 2000 (as so
supplemented, the "Indenture") between the Company and the Trustee. The terms of
the Notes include those stated in the Indenture and those made part of the
Indenture by reference to the Trust Indenture Act of 1939, as amended (15 U.S.
Code Sections 77aaa-77bbbb) (the "TIA"), as in effect on the date of execution
of the Original Indenture. The Notes are subject to all such terms, and Holders
are referred to the Indenture and the TIA for a statement of such terms and for
the definitions of capitalized terms used but not defined herein. The Notes are
unsecured general obligations of the Company. The aggregate principal amount of
the Notes that may be outstanding at any time is unlimited. The Original
Indenture provides for the issuance of other series of debt securities
(including the Notes, the "Debt Securities") thereunder.

                  9. Denominations, Transfer, Exchange. The Notes are in
registered form without coupons in denominations of $1,000 and integral
multiples of $1,000. The transfer of Notes may be registered and Notes may be
exchanged as provided in the Indenture. The Registrar and the Trustee may
require a Holder, among other things, to furnish appropriate endorsements and
transfer documents and to pay any taxes and fees required by law or permitted by
the Indenture. The Registrar shall not be required to exchange or register the
transfer of any Notes during the period between a record date and the
corresponding Interest Payment Date, nor shall the Registrar be required to
register the transfer or exchange of (a) any Note selected for redemption in
whole or in part, except the unredeemed portion of any Note being redeemed in
part, or (b) any Note during the period beginning 15 Business Days before the
mailing of notice of redemption of Notes to be redeemed and ending at the close
of business on the date of mailing.

                  10. Persons Deemed Owners. The registered Holder of a Note
shall be treated as its owner for all purposes.

                  11. Amendments and Waivers. Subject to certain exceptions and
limitations, (a) the Indenture may be amended or supplemented with the consent
of the Holders of at least a majority in principal amount of the then
outstanding Debt Securities of all series affected by such amendment or
supplement (acting as one class), and (b) compliance by the Company with any


                                       A-6

<PAGE>   21



provision of the Indenture with respect to the Notes (other than any continuing
Default or Event of Default in the payment of the principal of or premium (if
any) or interest on the Notes) may be waived by the Holders of at least a
majority in principal amount of the Notes then outstanding in accordance with
the terms of the Indenture. Without the consent of any Holder, the Company and
the Trustee may amend or supplement the Notes or the Indenture with respect to
the Notes (i) to cure any ambiguity, omission, defect or inconsistency; (ii) to
provide for the assumption of the obligations of the Company under the Indenture
to Holders in the case of the merger, consolidation or sale, lease, conveyance,
transfer or other disposition of all or substantially all of the assets of the
Company; (iii) to provide for uncertificated Notes in addition to or in place of
certificated Notes, or to provide for the issuance of bearer Notes (with or
without coupons); (iv) to provide any security for the Notes; (v) to comply with
any requirement in order to effect or maintain the qualification of the
Indenture under the TIA; (vi) to add to the covenants of the Company for the
benefit of the Holders of Notes, or to surrender any right or power conferred
upon the Company pursuant to the Indenture; (vii) to add any additional Events
of Default with respect to the Notes; (viii) to change or eliminate any of the
provisions of the Indenture, provided that any such change or elimination shall
become effective only when there is no outstanding Debt Security of any series
created prior to the execution of such amendment or supplemental indenture that
is adversely affected in any material respect by such change in or elimination
of such provision; (ix) to supplement any of the provisions of the Indenture to
such extent as shall be necessary to permit or facilitate the defeasance and
discharge of the Notes, provided, however, that any such action shall not
adversely affect the interest of the Holders of Notes or any other series of
Debt Securities in any material respect; or (x) to evidence and provide for the
acceptance of appointment under the Indenture by a successor Trustee with
respect to the Notes and to add to or change any of the provisions of the
Indenture as shall be necessary to provide for or facilitate the administration
of the trusts thereunder by more than one Trustee, pursuant to the requirements
of the Indenture.

                  The right of any Holder to participate in any consent required
or sought pursuant to any provision of the Indenture (and the obligation of the
Company to obtain any such consent otherwise required from such Holder) may be
subject to the requirement that such Holder shall have been the Holder of record
of any Notes with respect to which such consent is required or sought as of a
date identified by the Trustee in a notice furnished to Holders in accordance
with the terms of the Indenture.

                  Without the consent of each Holder affected, an amendment,
supplement or waiver under the Indenture may not (i) reduce the amount of Notes
whose Holders must consent to an amendment, supplement or waiver; (ii) reduce
the rate of or change the time for payment of interest, including default
interest, on any Note; (iii) reduce the principal of or premium on, or change
the Stated Maturity of, any Note; (iv) reduce the premium, if any, payable upon
the redemption of any Note or change the time at which any Note may or shall be
redeemed; (v) change the coin or currency or currencies in which any Note or any
premium or interest thereon is payable; (vi) impair the right to institute suit
for the enforcement of any payment of principal of or premium (if any) or
interest on any Note; (vii) make any change in the percentage of principal
amount of Notes necessary to waive compliance with certain provisions of the
Indenture or (viii) waive a continuing Default or Event of Default in the
payment of principal of or premium (if any) or interest on the Notes.



                                       A-7

<PAGE>   22



                  A supplemental indenture that changes or eliminates any
covenant or other provision of the Indenture that has expressly been included
solely for the benefit of one or more particular series of Debt Securities, or
that modifies the rights of the Holders of Debt Securities of such series with
respect to such covenant or other provision, shall be deemed not to affect the
rights under the Indenture of the Holders of Debt Securities of any other
series.

                  12. Defaults and Remedies. Events of Default are defined in
the Indenture and generally include: (i) default by the Company for 30 days in
payment of any interest on the Notes; (ii) default by the Company in any payment
of principal of or premium (if any) on the Notes at maturity; (iii) default by
the Company in compliance with any of its other covenants or agreements in, or
provisions of, the Notes or in the Indenture which shall not have been remedied
within 90 days after written notice by the Trustee or by the Holders of at least
25% in principal amount of the Notes then outstanding (or, in the event that
other Debt Securities issued under the Indenture are also affected by the
default, then 25% in principal amount of the outstanding Debt Securities so
affected); (iv) the acceleration of the maturity of any Indebtedness (other than
the Notes or any Non-Recourse Indebtedness) of the Company or any Subsidiary of
the Company having an outstanding principal amount of $20 million or more,
individually or in the aggregate; (v) a judgment or order for the payment of
money in excess of $20 million (net of applicable insurance coverage) having
been rendered against the Company or any Subsidiary of the Company and such
judgment or order shall continue unsatisfied and unstayed for a period of 30
days; or (vi) certain events involving bankruptcy, insolvency or reorganization
of the Company or any Significant Subsidiary. If an Event of Default with
respect to the Notes occurs and is continuing, the Trustee or the Holders of at
least 25% in principal amount of the then outstanding Notes may declare the
principal of and interest on the Notes to be immediately due and payable, except
that in the case of an Event of Default arising from certain events of
bankruptcy, insolvency or reorganization of the Company or any Significant
Subsidiary, all outstanding Debt Securities under the Indenture become due and
payable immediately without further action or notice. The amount due and payable
upon the acceleration of any Note is equal to 100% of the principal amount
thereof plus accrued interest to the date of payment. Holders may not enforce
the Indenture or the Notes except as provided in the Indenture. The Trustee may
require indemnity reasonably satisfactory to it before it enforces the Indenture
or the Notes. Subject to certain limitations, Holders of a majority in principal
amount of the then outstanding Notes may direct the Trustee in its exercise of
any trust or power. The Trustee may withhold from Holders notice of any
continuing default (except a default in payment of principal or interest) if it
determines that withholding notice is in their interests. The Company must
furnish an annual compliance certificate to the Trustee.

                  13. Discharge Prior to Maturity. The Indenture with respect to
the Notes shall be discharged and canceled upon the payment of all of the Notes
and shall be discharged except for certain obligations upon the irrevocable
deposit with the Trustee of funds or U.S. Government Obligations sufficient for
such payment.

                  14. Trustee Dealings with Company. The Trustee, in its
individual or any other capacity, may make loans to, accept deposits from, and
perform services for the Company or its Affiliates, and may otherwise deal with
the Company or its Affiliates, as if it were not Trustee.



                                       A-8

<PAGE>   23



                  15. No Recourse Against Others. A director, officer, employee
or stockholder, as such, of the Company shall not have any liability for any
obligations of the Company under the Notes or the Indenture or for any claim
based on, in respect of or by reason of such obligations or their creation. Each
Holder by accepting a Note waives and releases all such liability. The waiver
and release are part of the consideration for the issuance of the Notes.

                  16. Authentication. This Note shall not be valid until
authenticated by the manual signature of the Trustee or an authenticating agent.

                  17. CUSIP Numbers. Pursuant to a recommendation promulgated by
the Committee on Uniform Security Identification Procedures, the Company has
caused CUSIP numbers to be printed on the Notes as a convenience to the Holders
of the Notes. No representation is made as to the accuracy of such numbers as
printed on the Securities and reliance may be placed only on the other
identification numbers printed thereon.

                  18. Abbreviations. Customary abbreviations may be used in the
name of a Holder or an assignee, such as: TEN COM (= tenants in common), TEN ENT
(= tenants by the entireties), JT TEN (= joint tenants with right of
survivorship and not as tenants in common), CUST (= Custodian), and U/G/M/A (=
Uniform Gifts to Minors Act).

                  19. Restrictions on Transfer. By its acceptance of any Note
bearing a legend restricting transfer, each Holder of such a Note acknowledges
the restrictions on transfer of such Note set forth in the Indenture and such
legend and agrees that it will transfer such Note only as provided in the
Indenture.

                  THE COMPANY WILL FURNISH TO ANY HOLDER, UPON WRITTEN REQUEST
AND WITHOUT CHARGE, A COPY OF THE INDENTURE. UNLESS NOTICE DESIGNATING A
DIFFERENT ADDRESS IS TRANSMITTED TO HOLDERS, REQUEST MAY BE MADE TO:

                  PETROLEUM GEO-SERVICES ASA
                  STRANDVEIEN 50E
                  P.O. BOX 89
                  N-1325 LYSAKER
                  NORWAY
                  ATTENTION: GENERAL COUNSEL

                  or to

                  PETROLEUM GEO-SERVICES ASA
                  16010 BARKER'S POINT LANE
                  HOUSTON, TEXAS 77079
                  ATTENTION: CHIEF FINANCIAL OFFICER


                                       A-9

<PAGE>   24



                                                  ASSIGNMENT FORM

         To assign this Note, fill in the form below: (I) or (we) assign and
transfer this Note to _________________________________________________________
                       (Insert assignee's social security or tax I.D. number)

_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
              (Print or type assignee's name, address and zip code)

and irrevocably appoint _______________________________________________________
as agent to transfer this Note on the books of the Company. The agent may
substitute another to act for him.


Date:                               Your Signature:
      -------------------------                    ----------------------------
                                         (Sign exactly as your name appears on
                                                 the face of this Note)

Signature Guarantee:
                    -----------------------------------------------------------
                             (Participant in a Recognized Signature
                                  Guaranty Medallion Program)



                                      A-10

<PAGE>   25


                         SCHEDULE OF EXCHANGES OF NOTES*

     The following exchanges of a part of this Global Note for other Notes have
been made:



<TABLE>
<CAPTION>
                                                                                Principal Amount
                               Amount of                  Amount of              of this Global              Signature of
                              Decrease in                Increase in             Note following           Authorized Officer
                           Principal Amount           Principal Amount            such decrease              of Trustee or
  Date of Exchange        of this Global Note        of this Global Note          (or increase)           Security Custodian
  ----------------        -------------------        -------------------     -----------------------      ------------------
<S>                       <C>                        <C>                     <C>                          <C>
</TABLE>






----------------
* To be included in Global Note.



                                      A-11