Exhibit 10.2

ATWOOD OCEANICS, INC. SALARY CONTINUATION PLAN

(Formerly the Restated Executive Life Insurance Plan)

FIRST AMENDMENT

WHEREAS, Atwood Oceanics, Inc., a Texas corporation (the “Company”), has adopted and maintains the Atwood Oceanics, Inc. Restated Executive Life Insurance Plan (the “Plan”) for the benefit of the Company’s executive officers and other designated key employees; and

WHEREAS, pursuant to Section 4.1 of the Plan, the Company has reserved the right to change, modify, amend or terminate the Plan at any time; and

WHEREAS, the Company desires to rename the Plan, to prospectively modify the terms of the Plan regarding participation in the Plan and to update the definition of “Change of Control” for purposes of the Plan.

NOW, THEREFORE, the Company hereby amends the Plan, effective as of May 24, 2012, as follows:

1. The Plan is hereby amended to change the name of the Plan to the “Atwood Oceanics, Inc. Salary Continuation Plan”.

2. Section 2.1 of the Plan is hereby amended in its entirety to read as follows:

“2.1 Eligibility and Benefits. Individuals who are eligible to participate in the Plan are those listed on Exhibit A attached hereto. The Board of Directors of the Company (the ‘Board’) may, from time to time, designate additional full-time key employees as eligible participants in the Plan by delivery of written notice to such employees and amendment of Exhibit A. Such individuals are eligible for benefits pursuant to the Plan and are referred to as ‘Executives’ for purposes of the Plan. Benefits shall be payable only in event of the death of the Executive while the Executive is engaged in ‘active employment’ with the Company. For purposes of the Plan, ‘active employment’ means the Executive must be working for the Company or a subsidiary of the Company at the time of death on a full-time basis and paid regular earnings.”

3. Section 2.5 of the Plan is hereby amended in its entirety to read as follows:

“2.5 Change in Control. In the event of a termination of any Executive’s Employment with the Company during the two and one-half year period immediately following a Change in Control, then any Salary Continuation Agreement between the Company and such Executive shall remain in effect, and the Company and/or its successor shall be obligated to consider such Executive as having remained in active employment with the Company, and such Executive shall be deemed to remain in active employment with the Company for purposes of determining eligibility for benefits under the Plan, until the earlier of (i) the death of such Executive (at which time the right of the estate or the designated beneficiaries of such Executive under the Plan and the related Salary Continuation Agreement shall have been established), or (ii) the expiration of the two and one-half year period following the Change in Control. For purposes of this Plan, ‘Change in Control’ means each of the following:

a. the acquisition after the Effective Date by any ‘person’ (within the meaning of Section 13(d)(3) or 14(d)(2) of the Securities Exchange Act of 1934, as amended (the ‘Exchange Act’)) (a ‘Person’) of beneficial ownership (within the meaning of Rule 13d-3 promulgated under the Exchange Act) of 20% or more of the combined voting power of the then outstanding capital stock of the Company entitled to vote generally in the election of directors (the ‘Outstanding Company Voting Securities’); provided, however, that the following acquisitions shall not constitute a Change in Control: (i) any acquisition directly from the Company, (ii) any acquisition by the Company, (iii) any acquisition by any employee benefit plan (or related trust) sponsored or maintained by the Company or any entity controlled by the Company, (iv) any acquisition approved by at least a majority of the members of the Incumbent Board (as such term is hereinafter defined) either prior to such acquisition or within five business days after the Company has notice of such acquisition, provided that, after such acquisition, such Person does not beneficial own more than 50% of the combined voting power of the Outstanding Company Voting Securities, or (v) any acquisition by any Person pursuant to a transaction which complies with clauses (A), (B) and (C) of subsection (c) of this Section 2.5;

b. the first day on which individuals who, as of May 1, 2012, constitute the Board (the ‘Incumbent Board’) cease for any reason to constitute at least a majority of the Board; provided, however, that any individual becoming a director subsequent to May 1, 2012 whose election or appointment, or whose nomination for election by the Company’s shareholders, was approved by at least a majority of the directors then comprising the Incumbent Board shall be considered as though such individual were a member of the Incumbent Board, but excluding, for purposes of this definition, any such individual whose initial assumption of office occurs as a result of an actual or threatened election contest with respect to the election or removal of directors or other actual or threatened solicitation of proxies or consents by or on behalf of a Person other than the Board;

c. the consummation of (x) a reorganization, share exchange or merger involving the Company or (y) a sale of all or substantially all of the assets of the Company and its subsidiaries taken as a whole (other than by way of reorganization, share exchange or merger) to any Person other than a subsidiary of the Company (a transaction referred to in clause (x) or (y) is referred to as a ‘Business Combination’), in each case, unless, following such Business Combination, (A) all or substantially all of the individuals and entities who were the beneficial owners, respectively, of the outstanding shares of common stock of the Company (the ‘Outstanding Company Common Stock’) and Outstanding Company Voting Securities immediately prior to such Business Combination

beneficially own, directly or indirectly, more than 50% of the combined voting power of the then outstanding capital stock entitled to vote generally in the election of directors (or comparable governing persons) of the Company or an entity that, as a result of such Business Combination, owns, directly or indirectly through one or more wholly owned subsidiaries, the Company or all or substantially all of its assets (the ‘Resulting Entity’; such capital stock is referred to as the ‘Outstanding Successor Voting Securities’), (B) no Person (excluding any employee benefit plan (or related trust) of the Company or the Resulting Entity and excluding any Person that beneficially owns 20% or more of the combined voting power of the Outstanding Company Voting Securities prior to such Business Combination, provided that such Person’s percentage ownership of the combined voting power of the Outstanding Successor Voting Securities does not increase as a result of such Business Combination) will beneficially own, directly or indirectly, 20% or more of the combined voting power of the then Outstanding Successor Voting Securities, and (C) at least a majority of the members of the board of directors (or comparable governing body) of the Resulting Entity were members of the Incumbent Board immediately prior to consummation of such Business Combination; or

d. the adoption of a plan relating to the complete liquidation or dissolution of the Company.”

4. Section 4.1 of the Plan is hereby amended by deleting the parenthetical therein.

5. The Plan is hereby amended to add a new Exhibit A to the Plan in the form attached hereto as Addendum 1 to this First Amendment.

6. All other provisions of the Plan shall remain the same and are hereby ratified.

IN WITNESS WHEREOF, Atwood Oceanics, Inc. has executed this First Amendment to the Atwood Oceanics, Inc. Restated Executive Life Insurance Plan this 29th day of May, 2012, to be effective May 24, 2012.