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                                                                     EXHIBIT 4.5

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                            POOL ENERGY SERVICES CO.

                                       AND

                           THE GUARANTORS NAMED HEREIN

                              SERIES A AND SERIES B

                    8 5/8% SENIOR SUBORDINATED NOTES DUE 2008

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

                             SUPPLEMENTAL INDENTURE

                           DATED AS OF MARCH 31, 1998

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

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

                              MARINE MIDLAND BANK,

                                     TRUSTEE

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

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<PAGE>   2

         This SUPPLEMENTAL INDENTURE, dated as of March 31, 1998, is among Pool
Energy Services Co., a Texas corporation (the "Company"), each of the parties
identified under the caption "Guarantors" on the signature page hereto (the
"Guarantors") and Marine Midland Bank, as Trustee.

                                    RECITALS

         WHEREAS, the Company, the initial Guarantors and the Trustee entered
into an Indenture, dated as of March 31, 1998 (the "Indenture"), pursuant to
which the Company has originally issued $150,000,000 in principal amount of
8 5/8% Senior Subordinated Notes due 2008 (the "Notes"); and

         WHEREAS, Section 9.01 of the Indenture provides that the Company and
the Trustee may amend or supplement the Indenture in order to execute and
deliver a guarantee (a "Note Guarantee") to comply with Section 4.17 thereof
without the consent of the Holders of the Notes; and

         WHEREAS, all acts and things prescribed by the Indenture, by law and by
the charter and the bylaws (or comparable constituent documents) of the Company,
of the Guarantors and of the Trustee necessary to make this Supplemental
Indenture a valid instrument legally binding on the Company, the Guarantors and
the Trustee, in accordance with its terms, have been duly done and performed;

         NOW, THEREFORE, to comply with the provisions of the Indenture and in
consideration of the above premises, the Company, the Guarantors and the Trustee
covenant and agree for the equal and proportionate benefit of the respective
Holders of the Notes as follows:

                                    ARTICLE 1

         SECTION 1.01. This Supplemental Indenture is supplemental to the
Indenture and does and shall be deemed to form a part of, and shall be construed
in connection with and as part of, the Indenture for any and all purposes.

         SECTION 1.02. This Supplemental Indenture shall become effective
immediately upon its execution and delivery by each of the Company, the
Guarantors and the Trustee.

                                    ARTICLE 2

         From this date, in accordance with Section 4.17 and by executing this
Supplemental Indenture, the Guarantors whose signatures appear below are subject
to the provisions of the Indenture to the extent provided for in Article 11
thereunder.

                                    ARTICLE 3

         SECTION 3.01. Except as specifically modified herein, the Indenture and
the Notes are in all respects ratified and confirmed (mutatis mutandis) and
shall remain in full force and effect in accordance with their terms with all
capitalized terms used herein without definition having the same respective
meanings ascribed to them as in the Indenture.

<PAGE>   3

         SECTION 3.02. Except as otherwise expressly provided herein, no duties,
responsibilities or liabilities are assumed, or shall be construed to be
assumed, by the Trustee by reason of this Supplemental Indenture. This
Supplemental Indenture is executed and accepted by the Trustee subject to all
the terms and conditions set forth in the Indenture with the same force and
effect as if those terms and conditions were repeated at length herein and made
applicable to the Trustee with respect hereto.

         SECTION 3.03. THE LAW OF THE STATE OF NEW YORK SHALL GOVERN AND BE USED
TO CONSTRUE AND ENFORCE THIS SUPPLEMENTAL INDENTURE.

         SECTION 3.04. The parties may sign any number of copies of this
Supplemental Indenture. Each signed copy shall be an original, but all of such
executed copies together shall represent the same agreement.

                          [NEXT PAGE IS SIGNATURE PAGE]

<PAGE>   4

         IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture to be duly executed, all as of the date first written above.

                                     POOL ENERGY SERVICES CO.

                                     By: /s/ E. J. SPILLARD
                                        --------------------------------------
                                     Name:   E. J. Spillard
                                     Title:  Senior Vice President, Finance

                                     GUARANTORS:

                                     ASSOCIATED PETROLEUM SERVICES, INC.
                                     BIG 10 FISHING TOOL COMPANY, INC.
                                     INTERNATIONAL AIR DRILLING COMPANY
                                     KUUKPIK/POOL ARCTIC ALASKA
                                         By: Pool Alaska, Inc., d/b/a Pool
                                             Arctic Alaska
                                     PCNV, INC.
                                     POOL ALASKA, INC.
                                     POOL AMERICAS, INC.
                                     POOL-AUSTRALIA, INC.
                                     POOL CALIFORNIA ENERGY SERVICES, INC.
                                     POOL COMPANY
                                     POOL COMPANY HOUSTON LTD.
                                         By:  Pool Company, General Partner
                                     POOL COMPANY TEXAS, LTD.
                                         By:  Pool Company, General Partner
                                     POOL INTERNATIONAL, INC.
                                     POOL PRODUCTION SERVICES, INC.
                                     PTX, INC.
                                     SEA MAR, INC.
                                     SEA MAR MANAGEMENT, INC.

                                     By: /s/ E. J. SPILLARD
                                        --------------------------------------
                                     Name:   E. J. Spillard
                                     Title:  Senior Vice President, Finance

                                     MARINE MIDLAND BANK,
                                           as Trustee

                                     By: /s/ FRANK J. GODINO
                                        --------------------------------------
                                     Name:   FRANK J. GODINO
                                     Title:  Vice President<PAGE>   1
                                                                     EXHIBIT 4.6

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                             NABORS HOLDING COMPANY
                  (formerly known as POOL ENERGY SERVICES CO.)

                                       and

                           THE GUARANTORS NAMED HEREIN

                                  $150,000,000

                    8 5/8% Senior Subordinated Notes due 2008

                          SECOND SUPPLEMENTAL INDENTURE

                          Dated as of December 1, 1999

                                 HSBC BANK USA,

                                   AS TRUSTEE

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         This SECOND SUPPLEMENTAL INDENTURE, dated as of December 1 1999, is
among Nabors Holding Company, a Delaware corporation (formerly known as Pool
Energy Services Co., a Texas corporation) ("NHC" or the "Company"), Associated
Petroleum Services, Inc., International Air Drilling Company, Kuukpik-Pool
Arctic Alaska, Pool Alaska, Inc. (the successor by merger of Pool Alaska, Inc.,
a Texas corporation), Pool Americas, Inc., Pool-Australia, Inc., Pool Company,
Pool Company Texas, Ltd. (the successor by merger of Pool Production Services,
Inc.), Pool International, Inc., Pool Well Services Co. (the successor by merger
of Pool California Energy Services, Inc. and Big 10 Fishing Tool Company), PCNV,
Inc., PTX, Inc., Sea Mar, Inc. and Sea Mar Management, Inc. (collectively
referred to herein as the "Guarantors") and HSBC Bank USA (formerly known as
Marine Midland Bank), as trustee (the "Trustee").

                                    RECITALS

         WHEREAS, Pool Energy Services Co., a Texas corporation ("PESC"), the
subsidiary guarantors referred to therein and the Trustee entered into an
Indenture, dated as of March 31, 1998, as amended by the First Supplemental
Indenture, dated as of March 31, 1998 (as amended, the "Indenture"), pursuant to
which PESC issued $150,000,000 in aggregate principal amount of 8 5/8% Senior
Subordinated Notes due 2008 (the "Notes"), the payment of which was guaranteed
by such subsidiary guarantors.

         WHEREAS, as of November 24, 1999 (i) Starry Acquisition Corp. merged
with and into PESC, and as a result PESC became a wholly-owned subsidiary of
Nabors Industries, Inc. ("Nabors") and (ii) PESC changed its state of
incorporation and name through a merger with and into NHC (such transactions are
collectively referred to as the "Acquisition"), in each case in accordance with
Section 5.01 of the Indenture.

         WHEREAS, as of November 24, 1999 and in connection with the
Acquisition: (i) Pool California Energy Services, Inc. ("PCESI") merged with and
into Pool Well Services Co. ("PWSC"), a newly-formed wholly-owned subsidiary of
PCESI incorporated under the laws of Delaware; (ii) PoolCo transferred certain
assets and stock to Pool Production Services, Inc. ("PPS"); (iii) PPS merged
with and into Pool Company Texas Ltd. ("PCT"); (iv) Pool Alaska, Inc., a Texas
corporation ("PAI") merged with and into Pool Alaska, Inc., a newly formed
subsidiary of NHC incorporated in Delaware ("New Pool Alaska") and (v) Big 10
Fishing Tool Company, Inc. ("Big 10") merged with and into PWSC (such
transactions are collectively referred to as the "Mergers"). Upon consummating
of all of the Mergers: (a) PWSC became the successor by merger of PCESI and Big
10; (b) PCT became the successor by merger of PPS; and (c) New Pool Alaska
became the successor by merger of PAI.

         WHEREAS, in connection with the Acquisition, Pool Company Houston Ltd.
("PCH Ltd.") has or will dissolve and distribute its assets to its limited and
general partners, PCNV and PWSC (such transaction is referred to as the
"Dissolution," together with the Mergers, the "Transactions").

         WHEREAS, Section 9.01 of the Indenture permits PESC, the subsidiary
guarantors, parties thereto and the Trustee to amend or supplement the Indenture
or the Notes without the consent of any Holders to, among other things, provide
for the assumption of the obligations to the Holders of PESC or such subsidiary
guarantors, as the case may be, in the event of a merger or consolidation and to
make any change that (1) would provide any additional rights or benefits to
Holders or (2) does not adversely affect the legal rights under this Indenture
of any Holder.

         WHEREAS, the Company desires to and has requested that the Trustee
enter into this Second Supplemental Indenture to, among other things, (i)
provide for the Acquisition and the change of the name of the issuer of the
Notes to "Nabors Holding Company" and a change of its jurisdiction of
incorporation to Delaware, (ii) provide for the assumption or reaffirmation of
the obligations of PESC to the Holders by the Company, and (iii) provide for the
Transactions and the assumption and/or ratification of the obligations of the
applicable subsidiary guarantors by the applicable surviving entities.

         WHEREAS, the execution and delivery of this Second Supplemental
Indenture has been duly authorized by the appropriate resolutions of the Board
of Directors (or other applicable governing body) of the Company and each of the
guarantors listed on the signature pages hereto.

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         WHEREAS, the Board of Directors of the Company has determined that the
preservation of the existence of PCESI, PPS, PAI, Big 10 and PCH Ltd. is no
longer desirable in the conduct of the business of the Company and its
subsidiaries taken as a whole, and that the loss thereof is not adverse in any
material respect to the Holders.

         WHEREAS, all conditions and requirements necessary to make this Second
Supplemental Indenture a valid, binding and legal instrument enforceable in
accordance with its terms have been performed and fulfilled by the parties
hereto and the execution and delivery thereof have been in all respects duly
authorized by the parties hereto.

         NOW, THEREFORE, in consideration of the above recitals, each party
hereto agrees, for the benefit of the other and for the equal and ratable
benefit of the Holders of the Notes, as follows:

                                    ARTICLE I
                ASSUMPTION OF OBLIGATIONS; ADDITION OF GUARANTEES

         Section 1.1. Assumption and Reaffirmation by the Company. In accordance
with Section 5.01 of the Indenture, the Company hereby assumes and reaffirms the
obligations of PESC under the Indenture and the Notes in accordance with the
provisions thereof.

         Section 1.2. Reaffirmation of Guarantees by Surviving Original
Subsidiary Guarantors. In accordance with Section 5.01 of the Indenture, each of
Associated Petroleum Services, Inc., International Air Drilling Company,
Kuukpik-Pool Arctic Alaska, Pool Americas, Inc., Pool-Australia, Inc., Pool
Company, PCT, Pool International, Inc., PCNV, PTX, Inc., Sea Mar, Inc. and Sea
Mar Management, Inc. hereby assumes and reaffirms the obligations of a Guarantor
under the Indenture and the Notes in accordance with the provisions thereof and
is subject to the provisions of the Indenture in accordance with Article 11
thereunder.

         Section 1.3. Assumption and Reaffirmation of Guarantees by Surviving
Subsidiary Guarantors. Each of New Pool Alaska, PWSC and PCT (in each case,
without duplication of any applicable obligations under Section 1.2 hereof)
hereby assumes and reaffirms the obligation of a Guarantor under the Indenture
and the Notes in accordance with the provision thereof and is subject to the
provisions of the Indenture in accordance with Article 11 thereunder.

                                   ARTICLE II
                           AMENDMENTS TO THE INDENTURE

         Section 2.1. Change of Name and Jurisdiction of Organization. For all
purposes of the Indenture and the Notes, the Indenture and the Notes are amended
by deleting all references to "Pool Energy Services Co." and "Pool Energy
Services Co., a Texas corporation" (or substantially similar phrases) and
replacing them with "Nabors Holding Company" and "Nabors Holding Company, a
Delaware corporation" (or substantially similar phrases), respectively, as the
context requires.

         Section 2.2. References to Subsidiary Guarantors. For all purposes of
the Indenture and the Notes, all references to "Subsidiary Guarantors" or
"Subsidiary Guarantor" are amended to refer to the guarantors listed on the
signature pages hereof or any one of them, respectively, as the context
requires.

         Section 2.3. Change of Address. The Company hereby designates that the
address listed below be the address set forth for the Company or the Guarantors
for all purposes of the Indenture, including without limitation, Section 12.02
thereof:

                      Nabors Holding Company
                      515 West Greens Road
                      Suite 1200
                      Houston, Texas 77067-4525
                      Telecopier:  (281) 775-8431
                      Attention:  Legal Department.

                                  Page 3
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                                   ARTICLE III
                                NOTATION OF NOTES

         Notes authenticated and delivered for transfer or exchange of
outstanding Notes after the Effective Time (as defined below), and all Notes
presented or delivered to the Trustee on after such date for the purpose of
being stamped, shall be stamped (unless textually revised as hereinafter
provided) by the Trustee with a notation substantially in the form as follows:

                  "THE INDENTURE DATED AS OF MARCH 31, 1998 REFERRED TO IN THIS
                  NOTE HAS BEEN AMENDED BY A FIRST SUPPLEMENTAL INDENTURE DATED
                  AS OF MARCH 31, 1998 AND A SECOND SUPPLEMENTAL INDENTURE DATED
                  AS OF DECEMBER 1, 1999, PURSUANT TO WHICH CERTAIN PROVISIONS
                  OF THE INDENTURE HAVE BEEN AMENDED, ELIMINATED OR OTHERWISE
                  MODIFIED AS SET FORTH IN SUCH FIRST AND SECOND SUPPLEMENTAL
                  INDENTURES. COPIES OF THE FIRST AND SECOND SUPPLEMENTAL
                  INDENTURES ARE ON FILE WITH, AND AVAILABLE ON REQUEST FROM,
                  THE TRUSTEE AND THE COMPANY."

Any Notes hereafter authenticated or delivered may be textually revised, making
changes in phraseology and form (but not in substance) as may be appropriate so
as to conform, in the opinion of the Trustee and the Company, to modifications
made by this Second Supplemental Indenture.

                                   ARTICLE IV
                                  MISCELLANEOUS

         Section 4.1. Capitalized Terms. Capitalized terms used herein and not
otherwise defined have the meaning set forth in the Indenture.

         Section 4.2. Operation of Second Supplemental Indenture. This Second
Supplemental Indenture will become effective as of the date hereof.

         Section 4.3. Conflict with the Trust Indenture Act. If any provision of
this Second Supplemental Indenture modifies or excludes any provision of the
Trust Indenture Act that is required under such Act to be part of and govern
this Second Supplemental Indenture, the latter provision of the Trust Indenture
Act shall control. If any provision hereof modifies or excludes any provision of
the Trust Indenture Act that may be so modified or excluded, the latter
provision of the Trust Indenture Act shall be deemed to apply to this Second
Supplemental Indenture, as so modified or excluded, as the case may be.

         Section 4.4. Notes Deemed Conformed. As of the Effective Time, the
provisions of each Note then outstanding shall be deemed to be conformed,
without the necessity for any reissuance or exchange of such Note or any other
action on the part of the Holders, the Company, the Guarantors or the Trustee,
so as to reflect this Second Supplemental Indenture.

         Section 4.5. Mutatis Mutandis. Except as specifically modified herein,
the Indenture and the Notes are in all respects ratified and confirmed (mutatis
mutandis) and shall remain in full force and effect in accordance with their
terms with all capitalized terms used herein without definition having the same
definition ascribed to them as in the Indenture. The Indenture shall be deemed
to have such other changes as to grammar, tense, syntax and like concepts as
shall be necessary to effect the changes contemplated herein.

                                 Page 4
<PAGE>   5

         Section 4.6. No Additional Trustee Obligations. Except as otherwise
expressly provided herein, no duties, responsibilities or liabilities are
assumed, or shall be construed to be assumed, by the Trustee by reason of this
Second Supplemental Indenture. This Second Supplemental Indenture is executed
and accepted by the Trustee subject to all the terms and conditions set forth in
the Indenture with the same force and effect as if those terms and conditions
were repeated at length herein and made applicable to the Trustee with respect
hereto.

         Section 4.7. Successors. All agreements of the Company, the Guarantors
and the Trustee in this Second Supplemental Indenture and in the Indenture shall
bind their respective successors.

         Section 4.8. Benefits of Second Supplemental Indenture. Nothing in this
Second Supplemental Indenture, express or implied, shall give to any person,
other than the parties hereto and their successors hereunder and the Holders,
any benefit or any legal or equitable right, remedy or claim under this Second
Supplemental Indenture or the Indenture.

         Section 4.9. Severability. In case any provision in this Second
Supplemental Indenture, or in the 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, it being
intended that all of the provisions hereof shall be enforceable to the full
extent permitted by law.

         Section 4.10. Headings. The Section headings of this Second
Supplemental Indenture have been inserted for convenience of reference only, are
not to be considered a part of this Second Supplemental Indenture and shall not
modify or restrict any of the terms or provisions hereof.

         Section 4.11. Multiple Originals. The parties may sign any number of
copies of this Second Supplemental Indenture. Each signed copy shall be an
original, but all of them together represent the same agreement.

         Section 4.12. The Trustee. The Trustee is not responsible in any manner
whatsoever for or in respect of the validity or sufficiency of this Second
Supplemental Indenture or for or in respect of the recitals contained herein,
all of which are made solely by the Company.

         Section 4.13. Governing Law. THE LAW OF THE STATE OF NEW YORK SHALL
GOVERN AND BE USED TO CONSTURE AND ENFORCE THIS SECOND SUPPLEMENTAL INDENTURE.

                            [Signature Pages Follows]

                                 Page 5
<PAGE>   6

IN WITNESS WHEREOF, the parties hereto have caused this Second Supplemental
Indenture to be duly executed as of the date first above written.

                                   COMPANY:
                                   NABORS HOLDING COMPANY (formerly known as
                                   POOL ENERGY SERVICES CO.)

                                   By: /s/ Daniel McLachlin

                                      Name: Daniel McLachlin
                                      Title: Secretary

                                   GUARANTORS:
                                   ASSOCIATED PETROLEUM SERVICES, INC.
                                   INTERNATIONAL AIR DRILLING COMPANY
                                   KUUKPIK - POOL ARCTIC ALASKA
                                        By: Pool Alaska, Inc., d/b/a Pool Arctic
                                            Alaska
                                   POOL ALASKA, INC.
                                   POOL AMERICAS, INC.
                                   POOL-AUSTRALIA, INC.
                                   POOL COMPANY
                                   POOL COMPANY TEXAS, LTD.
                                        By: Pool Well Services Co., General
                                            Partner
                                   POOL INTERNATIONAL, INC.
                                   POOL WELL SERVICES CO.
                                   PTX, INC.
                                   SEA MAR, INC.
                                   SEA MAR MANAGEMENT, INC.

                                   By:  /s/ Daniel McLachlin
                                      Name: Daniel McLachlin
                                      Title: Secretary

                                   PCNV, INC.

                                   By:  /s/ Jay Weidenbach
                                      Name: Jay Weidenbach
                                      Title: Secretary

                                   TRUSTEE:
                                   HSBC BANK USA, as Trustee

                                   By:  /s/ Frank J. Godino
                                      Name: Frank J. Godino
                                      Title: Vice President

                                 Page 6

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