Exhibit 10.3

SCHLUMBERGER 1998 STOCK OPTION PLAN

(As Established Effective January 21, 1998)

Second Amendment

Schlumberger Limited, a Netherlands Antilles corporation, having heretofore adopted the Schlumberger 1998 Stock Option Plan, as established effective January 21, 1998, and having reserved the right under Section 12 thereof to amend the Plan, does hereby amend the Plan, generally effective January 17, 2008, or as otherwise specified below, as follows:

1. The last sentence of Section 3(b) of the Plan is hereby amended to read as follows:

“Except in the case of death or disability (as described in Section 5(c)(iv)(B) or 5(c)(v)(B)), no Stock Option shall vest or become exercisable with respect to any portion of the shares of Common Stock thereunder unless and until the recipient remains in the employment of the Company or a subsidiary for a period of at least one (1) year from the date of grant of the option (which provision shall not be construed to impair in any way the right of the Company or subsidiary to terminate such employment).”

2. Section 5(c)(i) of the Plan is hereby amended in its entirety to read as follows:

“(i) Subject to the requirements of Section 3(b), each Stock Option granted hereunder shall be exercisable in one or more installments (annual or other) on such date or dates as the Committee may in its sole discretion determine and communicate to the optionee in communicating the grant of the option, provided that no Stock Option may be exercised after the expiration of ten (10) years from the date such option is granted (the maximum term established by the Committee with respect to a particular Stock Option is hereinafter referred to as the ‘Option Period’).”

3. Section 5(c)(iv) of the Plan is hereby amended in its entirely to read as follows:

“(iv) Termination of Employment and Subsequent Events.

(A) If the optionee’s employment with the Company is terminated with the consent of the Company and provided such employment is not terminated for cause (of which the Committee shall be the sole judge), the Committee may permit such Stock Option to be exercised by such optionee at any time during the period of three (3) months after such termination or the remainder of the Option Period whichever is less, provided that such option may be exercised only to the extent it was exercisable on the date of such termination.

(B) In the event an optionee dies while in the employ of the Company, any outstanding Stock Option shall automatically become fully vested and exercisable by the person or persons entitled thereto under the optionee’s will or the laws of descent and distribution during the ‘Post-Death Exercise Period.’ The Post-Death Exercise Period shall commence on the date of the optionee’s death and shall end sixty (60) months thereafter or the remainder of the Option Period whichever is less.

(C) In the event an optionee dies after termination of employment but prior to the exercise in full of any Stock Option which was exercisable on the date of such termination, such option may be exercised before expiration of its term by the person or persons entitled thereto under the optionee’s will or the laws of descent and distribution during the Post-Death Exercise Period to the extent exercisable by the optionee at the date of death. For purposes of this Section 5(c)(iv)(C), the Post-Death Exercise Period shall commence on the date of the optionee’s termination of employment and shall end sixty (60) months thereafter or the remainder of the Option Period whichever is less.

(D) If the optionee’s employment with the Company is terminated without the consent of the Company for any reason other than the death of the optionee, or if the optionee’s employment with the Company is terminated for cause, his or her rights under any then outstanding Stock Option shall terminate immediately. The Committee shall be the sole judge of whether the optionee’s employment is terminated without the consent of the Company or for cause.

(E) Notwithstanding the foregoing, if the optionee engages in ‘detrimental activity’ (as hereinafter defined) within one year after termination of employment for any reason other than retirement or disability, the Committee, in its discretion, may cause the optionee’s right to exercise such option to be forfeited. Such forfeiture may occur at any time after the Committee determines that the optionee has engaged in detrimental activity and prior to the actual delivery of all shares of Common Stock subject to the option pursuant to the exercise of such option. If an allegation of detrimental activity by an optionee is made to the Committee, the Committee, in its discretion, may suspend the exercisability of the optionee’s options for up to two months to permit the investigation of such allegation. In addition, if the optionee engages in detrimental activity within one year following termination of employment for any reason other than retirement or disability, the Committee, in its discretion, may rescind any option exercise made within the period commencing six months preceding the date of the optionee’s termination of employment and ending three months following such termination. For purposes of this Section 5, ‘detrimental activity’ means activity that is determined by the Committee in its sole and absolute discretion to be detrimental to the interests of the Company or any of its subsidiaries, including but not limited to situations where such optionee: (1) divulges trade secrets of the Company, proprietary data or other confidential information relating to the Company or to the business of the Company and any subsidiaries, (2) enters into employment with a competitor under circumstances suggesting that such optionee will be using unique or special knowledge gained as a Company employee to compete with the Company, (3) uses information obtained during the course of his or her prior employment for his or her own purposes, such as for the solicitation of business, (4) is determined to have engaged (whether or not prior to termination) in either gross misconduct or criminal activity harmful to the Company, or (5) takes any action that harms the business interests, reputation, or goodwill of the Company and/or its subsidiaries.”

4. Section 5(c)(v) of the Plan is hereby amended in its entirety to read as follows:

“(v) Retirement, Disability and Subsequent Events.

(A) If the optionee’s employment with the Company is terminated due to retirement (within the meaning of any prevailing pension plan in which such optionee is a participant), such Stock Option shall be exercisable by such optionee at any time during the period of sixty (60) months after such termination or the remainder of the Option Period, whichever is less (the ‘Retirement Exercise Period’), provided that such option may be exercised after such termination and before expiration only to the extent that it is exercisable on the date of such termination.

(B) If the optionee’s employment with the Company is terminated due to disability, such Stock Option shall automatically become fully vested and exercisable. Such optionee may exercise the outstanding Stock Option at any time during (1) in the case of Stock Options intended to be incentive stock options within the meaning of Section 422 of the Code and granted prior to January 17, 2008, the period of three (3) months after such termination or the remainder of the Option Period, whichever is less, or (2) in the case of all other Stock Options, the period of sixty (60) months after such termination or the remainder of the Option Period, whichever is less (the ‘Disability Exercise Period’). For purposes of this Section 5(c)(v), ‘disability’ shall mean such disability (whether through physical or mental impairment) which totally and permanently incapacitates the optionee from any gainful employment in any field which the optionee is suited by education, training, or experience, as determined by the Committee in its sole and absolute discretion.

(C) In the event an optionee dies during the Retirement Exercise Period or the Disability Exercise Period, such Stock Option may be exercised by the person or persons entitled thereto under the optionee’s will or the laws of descent and distribution to the extent exercisable by the optionee at the date of death and to the extent the term of the Option Period has not expired within such Retirement Exercise Period or Disability Exercise Period.

(D) Notwithstanding the foregoing, if the optionee engages in ‘detrimental activity’ (as defined in Section 5(c)(iv)(E)) within five years after termination of employment by reason of retirement or disability, the Committee, in its discretion, may cause the optionee’s right to exercise such option to be forfeited. Such forfeiture may occur at any time after the Committee determines that the optionee has engaged in detrimental activity and prior to the actual delivery of all shares of Common Stock subject to the option

pursuant to the exercise of such option. If an allegation of detrimental activity by an optionee is made to the Committee, the Committee, in its discretion, may suspend the exercisability of the optionee’s options for up to two months to permit the investigation of such allegation. In addition, if the optionee engages in detrimental activity within five years following termination of employment by reason of retirement or disability, the Committee, in its discretion, may rescind any option exercise made within the period commencing six months preceding the date of the optionee’s termination of employment by retirement or disability and ending one year following such termination.”

5. For the avoidance of doubt, in no event shall the provisions of this Amendment apply to any Stock Option held by an optionee whose employment terminated due to death or disability prior to January 17, 2008.