<PAGE>
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                   FORM 10-K/A
                                 AMENDMENT NO. 1

[X]             ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF
              THE SECURITIES EXCHANGE ACT OF 1934 (NO FEE REQUIRED)

                   FOR THE FISCAL YEAR ENDED DECEMBER 31, 2001

[ ]           TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF
              THE SECURITIES EXCHANGE ACT OF 1934 (NO FEE REQUIRED)

           FOR THE TRANSITION PERIOD FROM             TO
                                          -----------    -------------

                        COMMISSION FILE NUMBER: 0-13857

                                NOBLE CORPORATION
             (Exact name of registrant as specified in its charter)

<Table>
<S>                                                                    <C>
                         CAYMAN ISLANDS                                               98-0366361
         --------------------------------------------                  ---------------------------------------
 (State or other jurisdiction of incorporation or organization)        (I.R.S. employer identification number)

</Table>
          13135 SOUTH DAIRY ASHFORD, SUITE 800, SUGAR LAND, TEXAS 77478
          -------------------------------------------------------------
               (Address of principal executive offices) (Zip Code)

       REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE: (281) 276-6100

           Securities registered pursuant to Section 12(b) of the Act:

<Table>
<Caption>
 ORDINARY SHARES, PAR VALUE $.10 PER SHARE              NEW YORK STOCK EXCHANGE
 PREFERRED SHARE PURCHASE RIGHTS                        NEW YORK STOCK EXCHANGE
 -----------------------------------------    -----------------------------------------
<S>                                           <C>
              Title of each class             Name of each exchange on which registered
</Table>

           Securities registered pursuant to Section 12(g) of the Act:
                                      NONE

         Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days. Yes [X] No [ ]

         Indicate by check mark if disclosure of delinquent filers pursuant to
Item 405 of Regulation S-K is not contained herein, and will not be contained,
to the best of registrant's knowledge, in definitive proxy or information
statements incorporated by reference in Part III of this Form 10-K or any
amendment to this Form 10-K. [X]

         Aggregate market value of Common Stock of Noble Drilling Corporation
         held by nonaffiliates as of January 31, 2002: $4,200,000,000

         Number of shares of Common Stock of Noble Drilling Corporation
         outstanding as of January 31, 2001: 132,083,096

                       DOCUMENTS INCORPORATED BY REFERENCE

         Listed below are documents parts of which are incorporated herein by
reference and the part of this report into which the document is incorporated:

         (1) Proxy statement for the 2002 annual meeting of stockholders of
Noble Drilling Corporation - Part III


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<PAGE>


EXPLANATORY NOTE

         This Amendment No. 1 to Annual Report on Form 10-K is being filed by
Noble Corporation, a Cayman Islands exempted company limited by shares
("Noble-Cayman"), as successor issuer to Noble Drilling Corporation, a Delaware
corporation ("Noble-Delaware"), pursuant to Rule 15d-5 promulgated under the
United States Securities Exchange Act of 1934. Pursuant to a corporate
reorganization (the "Reorganization") that became effective on April 30, 2002,
Noble-Delaware became an indirect, wholly owned subsidiary of Noble-Cayman. In
the merger, each person holding shares of Noble-Delaware common stock (and
related preferred stock purchase rights) immediately before the merger received
one ordinary share, par value US$.10 per share ("Ordinary Shares"), of
Noble-Cayman (and related preferred share purchase right) for each share of
Noble-Delaware common stock (and related preferred stock purchase right) held by
such person.

         This Amendment No. 1 to Annual Report on Form 10-K for the year ended
December 31, 2001 (the "2001 Form 10-K") is being filed for the following
purposes:

         (1) To file the financial statements required by Form 11-K for the
             fiscal year ended December 31, 2001 with respect to the Noble
             Drilling Corporation 401(k) Savings Plan (formerly the Noble
             Drilling Corporation Thrift Plan) as Exhibit 99.1.

         (2) To amend Item 14 of the 2001 Form 10-K to reflect the filing
             herewith of new Exhibit 99.1. Item 14 is restated as set forth
             below.

         (3) To restate in its entirety the Index to Exhibits to the 2001 Form
             10-K as set forth following the signature page, in order to reflect
             the inclusion therein, and the filing herewith, of new Exhibit
             99.1.

         Pursuant to the Reorganization, Ordinary Shares will henceforth be
issuable under the Noble Drilling Corporation 401(k) Savings Plan in lieu of
common stock of Noble-Delaware, but Noble-Delaware will continue to sponsor the
Plan. The 2001 Form 10-K is not being updated by this Amendment No. 1, except as
specifically enumerated above. All references in this Amendment No. 1 to "the
Registrant" in connection with dates preceding the Reorganization are references
to Noble-Delaware.

ITEM 14.  EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM 8-K

(a)      The following documents are filed as part of this report:

         (1) A list of the financial statements filed as a part of this report
             is set forth in Item 8 on page 23 of the 2001 Form 10-K and is
             incorporated herein by reference.

         (2) Financial Statement Schedules:

             All schedules are omitted because they are either not applicable or
             required information is shown in the financial statements or notes
             thereto.

         (3) Exhibits:

             The information required by this Item 14(a)(3) is set forth in the
             Index to Exhibits accompanying this Annual Report on Form 10-K and
             is incorporated herein by reference.

         (4) Financial Statements required by Form 11-K for the fiscal year
             ended December 31, 2001, with respect to the Noble Drilling
             Corporation 401(k) Savings Plan are filed as Exhibit 99.1 hereto.

(b)      Reports on Form 8-K:

         The Registrant furnished a Form 8-K on October 25, 2001, which included
         its press release dated October 25, 2001 as Exhibit 99.1, announcing
         financial results for the quarter ended September 30, 2001.

         The Registrant furnished a Form 8-K on December 19, 2001, which
         included its Fleet Status Update as of December 19, 2001 as Exhibit
         99.1.


                                       2
<PAGE>


                                   SIGNATURES


         Pursuant to the requirements of Section 13 or 15(d) of the Securities
Exchange Act of 1934, the Registrant has duly caused this report to be signed on
its behalf by the undersigned, thereunto duly authorized.


                                            NOBLE CORPORATION


Date:  June 26, 2002                        By: /s/ ROBERT D. CAMPBELL
                                                -------------------------------
                                                Robert D. Campbell, President


                                       3
<PAGE>
                                INDEX TO EXHIBITS

<Table>
<Caption>
EXHIBIT
NUMBER                                 EXHIBIT
-------                                -------
<S>      <C>
2.1      Agreement of Sale and Purchase dated as of April 25, 1996 between the
         Registrant and Royal Nedlloyd N.V. and Neddrill Holding B.V. (filed as
         Exhibit 2.1 to the Registrant's Registration Statement on Form S-3 (No.
         333-2927) and incorporated herein by reference).

3.1      Restated Certificate of Incorporation of the Registrant dated August
         29, 1985 (filed as Exhibit 3.7 to the Registrant's Registration
         Statement on Form 10 (No. 0-13857) and incorporated herein by
         reference).

3.2      Certificate of Amendment of Restated Certificate of Incorporation of
         the Registrant dated May 5, 1987 (filed as Exhibit 4.2 to the
         Registrant's Registration Statement on Form S-3 (No. 33-67130) and
         incorporated herein by reference).

3.3      Certificate of Amendment of Certificate of Incorporation of the
         Registrant dated July 31, 1991 (filed as Exhibit 3.16 to the
         Registrant's Annual Report on Form 10-K for the year ended December 31,
         1991 and incorporated herein by reference).

3.4      Certificate of Amendment of Certificate of Incorporation of the
         Registrant dated September 15, 1994 (filed as Exhibit 3.1 to the
         Registrant's Quarterly Report on Form 10-Q for the three-month period
         ended March 31, 1995 and incorporated herein by reference).

3.5      Certificate of Designations of Series A Junior Participating Preferred
         Stock, par value $1.00 per share, of the Registrant dated as of June
         29, 1995 (filed as Exhibit 3.2 to the Registrant's Quarterly Report on
         Form 10-Q for the three-month period ended June 30, 1995 and
         incorporated herein by reference).

3.6      Certificate of Amendment of Certificate of Designations of Series A
         Junior Participating Preferred Stock of Registrant dated September 5,
         1997 (filed as Exhibit 3.6 to the Registrant's Annual Report on Form
         10-K for the year ended December 31, 1997 and incorporated herein by
         reference).

3.7      Composite copy of the Bylaws of the Registrant as currently in effect
         (filed as Exhibit 3.7 to the Registrant's Annual Report on Form 10-K
         for the year ended December 31, 1998 and incorporated herein by
         reference).

4.1      Indenture dated as of March 1, 1999, between Noble Drilling Corporation
         and Chase Bank of Texas, National Association, as trustee (filed as
         Exhibit 4.1 to the Registrant's Form 8-K dated March 22, 1999 (date of
         event: March 1, 1999) and incorporated herein by reference).

4.2      Supplemental Indenture dated as of March 16, 1999, between Noble
         Drilling Corporation and Chase Bank of Texas, National Association, as
         trustee (filed as Exhibit 4.2 to the Registrant's Form 8-K dated March
         22, 1999 (date of event: March 1, 1999) and incorporated herein by
         reference).

4.3      Rights Agreement dated as of June 28, 1995 between the Registrant and
         Liberty Bank and Trust Company of Oklahoma City, N.A. (filed as Exhibit
         4 to the Registrant's Form 8-K dated June 29, 1995 (date of event: June
         28, 1995) and incorporated herein by reference).

4.4      Amendment No. 1 to Rights Agreement, dated September 3, 1997, between
         Noble Drilling Corporation and Liberty Bank and Trust Company of
         Oklahoma City, N.A. (filed as Exhibit 4.2 to the Registrant's Form
         8-A/A (Amendment No. 1) dated September 3, 1997 and incorporated herein
         by reference).
</Table>


                                       4
<PAGE>


<Table>
<S>      <C>
4.5+     Amendment No. 2 to Rights Agreement, dated February 5, 2002, between
         Noble Drilling Corporation and Bank One Trust Company, N.A., as
         successor to Liberty Bank and Trust Company of Oklahoma City, N.A.

4.6+     Consent and Agreement dated December 20, 2001 by and among Noble
         Drilling (Paul Romano) Inc., Noble Drilling Corporation and the
         Noteholders a party hereto.

4.7      Note Purchase Agreement dated as of September 24, 1998, by and among
         Noble Drilling (Paul Romano) Inc. and each of the note purchasers
         thereunder. Each note purchaser has entered into a separate Note
         Purchase Agreement, which agreements are substantially identical in all
         material respects, except for the principal amount of notes to be
         purchased. A schedule identifying each of the note purchasers that
         entered into a Note Purchase Agreement with Noble Drilling (Paul
         Romano) Inc. and the principal amount of notes to be purchased by each
         such note purchaser is included as Schedule A to the Note Purchase
         Agreement (filed as Exhibit 4.1 to the Registrant's Quarterly Report on
         Form 10-Q for the three-month period ended September 30, 1998 and
         incorporated herein by reference).

4.8      Trust Indenture and Security Agreement dated as of November 24, 1998,
         between Noble Drilling (Paul Romano) Inc. and Chase Bank of Texas,
         National Association, as Trustee (filed as Exhibit 4.18 to the
         Registrant's Registration Statement on Form S-3 (No. 333-72059) and
         incorporated herein by reference).

4.9      First Naval Mortgage covering the Noble Paul Romano dated as of
         November 24, 1998, made by Noble Drilling (Paul Romano) Inc. in favor
         of Chase Bank of Texas, National Association, as Indenture Trustee
         (filed as Exhibit 4.19 to the Registrant's Registration Statement on
         Form S-3 (No. 333-72059) and incorporated herein by reference).

4.10     Note Purchase Agreement dated as of July 1, 1998, by and among Noble
         Drilling (Paul Wolff) Ltd., Chase Bank of Texas, National Association,
         as Trustee, and each of the note purchasers thereunder. Each note
         purchaser has entered into a separate Note Purchase Agreement, which
         agreements are substantially identical in all material respects, except
         for the principal amount of notes purchased. A schedule identifying
         each of the note purchasers that entered into a Note Purchase Agreement
         with Noble Drilling (Paul Wolff) Ltd. and the principal amount of notes
         purchased by each such note purchaser is included in Annex I to the
         Note Purchase Agreement (filed as Exhibit 4.4 to the Registrant's
         Quarterly Report on Form 10-Q for the three-month period ended
         September 30, 1998 and incorporated herein by reference).

4.11     Indenture of First Naval Mortgage, dated as of July 1, 1998, made by
         Noble Drilling (Paul Wolff) Ltd. in favor of Chase Bank of Texas,
         National Association, as Trustee (filed as Exhibit 4.5 to the
         Registrant's Quarterly Report on Form 10-Q for the three-month period
         ended September 30, 1998 and incorporated herein by reference).

4.12     Parent Guaranty, dated as of July 1, 1998, by Noble Drilling
         Corporation in favor of Chase Bank of Texas, National Association, as
         Trustee (filed as Exhibit 4.6 to the Registrant's Quarterly Report on
         Form 10-Q for the three-month period ended September 30, 1998 and
         incorporated herein by reference).

4.13     Note Purchase Agreement dated as of December 21, 1998, by and among
         Noble Drilling (Jim Thompson) Inc., Chase Bank of Texas, National
         Association, as Trustee, and each of the note purchasers hereunder.
         Each note purchaser has entered into a separate Note Purchase
         Agreement, which agreements are substantially identical in all material
         respects, except for the principal amount of notes purchased. A
         schedule identifying each of the note purchasers that entered into a
         Note Purchase Agreement with Noble Drilling (Jim Thompson) Inc. and the
         principal amount of notes purchased by each such note purchaser is
         included as Annex I to the Note Purchase Agreement (filed as Exhibit
         4.24 to the Registrant's Registration Statement on Form S-3 (No.
         333-72059) and incorporated herein by reference).
</Table>


                                       5
<PAGE>

<Table>
<S>      <C>
4.14     Indenture of First Naval Mortgage, dated as of December 21, 1998, made
         by Noble Drilling (Jim Thompson) Inc. in favor of Chase Bank of Texas,
         National Association, as Trustee (filed as Exhibit 4.25 to the
         Registrant's Registration Statement on Form S-3 (No. 333-72059) and
         incorporated herein by reference).

4.15     Parent Guaranty, dated as of December 21, 1998, by Noble Drilling
         Corporation in favor of Chase Bank of Texas, National Association, as
         Trustee (filed as Exhibit 4.26 to the Registrant's Registration
         Statement on Form S-3 (No. 333-72059) and incorporated herein by
         reference).

4.16     Credit Agreement dated May 30, 2001, among Noble Drilling Corporation,
         Christiania Bank og Kreditkasse ASA, New York Branch, as Administrative
         Agent, and the lenders named therein (filed as Exhibit 4 to the
         Registrant's Quarterly Report on Form 10-Q for the three-month period
         ended June 30, 2001 and incorporated herein by reference).

4.17+    Irrevocable Letter of Credit, dated December 20, 2001, by Nordea Bank
         Norge ASA, New York Branch, and issued to JP Morgan Chase Bank, as
         Trustee of the Trust Indenture and Security Agreement, dated as of
         November 24, 1998, between Noble Drilling (Paul Romano) Inc. and the
         Trustee, for the benefit of the note holders thereunder.

10.1*    Noble Drilling Corporation 1991 Stock Option and Restricted Stock Plan
         (filed as Exhibit 4.1 to the Registrant's Registration Statement on
         Form S-8 (No. 333-80511) and incorporated herein by reference).

10.2*    Noble Drilling Corporation 1992 Nonqualified Stock Option Plan for
         Non-Employee Directors (filed as Exhibit 4.1 to the Registrant's
         Registration Statement on Form S-8 (No. 33-62394) and incorporated
         herein by reference).

10.3*    Amendment No. 1 to the Noble Drilling Corporation 1992 Nonqualified
         Stock Option Plan for Non-Employee Directors dated as of July 28, 1994
         (filed as Exhibit 10.44 to the Registrant's Annual Report on Form 10-K
         for the year ended December 31, 1994 and incorporated herein by
         reference).

10.4*    Noble Drilling Corporation Equity Compensation Plan for Non-Employee
         Directors (filed as Exhibit 10.1 to the Registrant's Quarterly Report
         on Form 10-Q for the three-month period ended September 30, 1996 and
         incorporated herein by reference).

10.5*    Noble Drilling Corporation Short Term Incentive Plan (revised April
         2001) (filed as Exhibit 10 to the Registrant's Quarterly Report on Form
         10-Q for the three-month period ended September 30, 2001 and
         incorporated herein by reference).

10.6*    Noble Drilling Corporation Amended and Restated Thrift Restoration Plan
         (filed as Exhibit 10.46 to the Registrant's Annual Report on Form 10-K
         for the year ended December 31, 1994 and incorporated herein by
         reference).

10.7*    Amendment No. 1 to the Noble Drilling Corporation Amended and Restated
         Thrift Restoration Plan dated January 29, 1998 (filed as Exhibit 10.18
         to the Registrant's Annual Report on Form 10-K for the year ended
         December 31, 1997 and incorporated herein by reference).

10.8*    Noble Drilling Corporation Retirement Restoration Plan dated April 27,
         1995 (filed as Exhibit 10.2 to the Registrant's Quarterly Report on
         Form 10-Q for the three-month period ended March 31, 1995 and
         incorporated herein by reference).

10.9*    Amendment No. 1 to the Noble Drilling Corporation Retirement
         Restoration Plan dated January 29, 1998 (filed as Exhibit 10.18 to the
         Registrant's Annual Report on Form 10-K for the year ended December 31,
         1997 and incorporated herein by reference).
</Table>


                                       6
<PAGE>


<Table>
<S>      <C>
10.10*   Form of Indemnity Agreement entered into between the Registrant and
         each of the Registrant's directors and bylaw officers (filed as Exhibit
         10.46 to the Registrant's Annual Report on Form 10-K for the year ended
         December 31, 1995 and incorporated herein by reference).

10.11    Guarantee dated August 26, 1994 between the Registrant and Hibernia
         Management and Development Company Ltd. (filed as Exhibit 10.45 to the
         Registrant's Annual Report on Form 10-K for the year ended December 31,
         1994 and incorporated herein by reference).

10.12*   Employment Agreement, dated as of October 22, 1998, by and between
         Noble Drilling Corporation and James C. Day (filed as Exhibit 10.1 to
         the Registrant's Quarterly Report on Form 10-Q for the three-month
         period ended September 30, 1998 and incorporated herein by reference).

10.13*   Employment Agreement dated as of October 22, 1998, by and between the
         Company and Julie J. Robertson (filed as Exhibit 10.3 to the
         Registrant's Quarterly Report on Form 10-Q for the three-month period
         ended September 30, 1998 and incorporated herein by reference).

10.14*   Employment Agreement dated as of January 1, 1999 by and between Noble
         Drilling Corporation and Robert D. Campbell (filed as Exhibit 10.22 to
         the Registrant's Annual Report on Form 10-K for the year ended December
         31, 1998 and incorporated herein by reference).

10.15*   Employment Agreement dated as of October 22, 1998 by and between Noble
         Drilling Corporation and Danny W. Adkins (filed as Exhibit 10.21 to the
         Registrant's Annual Report on Form 10-K for the year ended December 31,
         2000 and incorporated herein by reference).

10.16*   Employment Agreement dated as of September 1, 2000 by and between Noble
         Drilling Corporation and Mark A. Jackson (filed as Exhibit 10.22 to the
         Registrant's Annual Report on Form 10-K for the year ended December 31,
         2000 and incorporated herein by reference).

10.17*   Amendment to the Noble Drilling Corporation 1991 Stock Option and
         Restricted Stock Plan, dated October 28, 1999 (filed as Exhibit 10.21
         to the Registrant's Annual Report on Form 10-K for the year ended
         December 31, 1999 and incorporated herein by reference).

10.18*   Noble Drilling Corporation 401(k) Savings Restoration Plan (filed as
         Exhibit 10.1 to the Registrant's Registration Statement on Form S-8
         dated January 18, 2001 (No. 333-53912) and incorporated herein by
         reference).

21.1+    Subsidiaries of the Registrant.

23.1+    Consent of PricewaterhouseCoopers LLP.

99.1**   Financial Statements required by Form 11-K for the fiscal year ended
         December 31, 2001 with respect to the Noble Drilling Corporation 401(k)
         Savings Plan (including consent of PricewaterhouseCoopers LLP regarding
         the incorporation by reference thereof).
</Table>

----------
*        Management contract or compensatory plan or arrangement required to be
         filed as an exhibit hereto.

**       Filed with this Amendment No. 1.

+        This exhibit was previously filed as part of, and is hereby
         incorporated by reference to the same numbered exhibit filed with, the
         Registrant's Annual Report on Form 10-K for the fiscal year ended
         December 31, 2001.


                                       7