<PAGE>   1

                                                                   EXHIBIT 10.21

                     THIRD AMENDMENT TO DEPOSITORY AGREEMENT
                               FOR PURCHASE OPTION


     THIS THIRD AMENDMENT TO DEPOSITORY AGREEMENT FOR PURCHASE OPTION (this
"Third Amendment") is entered into as of February 22, 2001 by and between Grant
Geophysical Corp., a Texas corporation ("Grant"), and Elliott Associates, L.P.,
a Delaware limited partnership ("Elliott").

                                   WITNESSETH:

     WHEREAS, Grant and Elliott are the parties to that certain Depository
Agreement for Purchase Option dated as of December 1, 2000 (the "Original
Agreement"), as amended by that certain Amendment to Depository Agreement for
Purchase Option dated January 25, 2001 (the "First Amendment") and that certain
Second Amendment to Depository Agreement for Purchase Option dated February 20,
2001 (the "Second Amendment", the Original Agreement as amended by the First
Amendment and the Second Amendment is the "Depository Agreement"); and

     WHEREAS, Grant and Elliott deem it in their best interests to amend the
Depository Agreement to provide for a voluntary reduction in the amount of the
exercise price of the Option and the Amended Deposit at Grant's discretion.

     NOW, THEREFORE, the parties agree as follows:

     1.   Section 1(c) of the Depository Agreement is amended to add subsection
          (C) to Section 1(c)(iv) as follows:

          "(C) In the event Grant elects to voluntarily reduce the amount of the
               Amended Deposit with funds received from a source other than
               sales of licenses to the Survey it may do so by delivering a cash
               payment to Elliott. In that event, the cash payment will be
               applied in the same manner as a Cash Payment under Section
               1(c)(iv)(A) above."

     2. Except as specifically amended by this Third Amendment, all of the terms
and provisions of the Depository Agreement shall remain in full force and
effect.

     3. All capitalized terms used herein but not defined herein shall have the
meanings given to them in the Depository Agreement.

     4. This Third Amendment shall be governed by and construed in accordance
with the internal laws of the State of New York.

<PAGE>   2

     IN WITNESS WHEREOF, the parties hereto have executed this Third Amendment
as of the date first written above.

WITNESSES:                             GRANT GEOPHYSICAL CORP.

                                       By:
-----------------------------              --------------------------------
                                           Thomas Easley
                                           Executive Vice President-
-----------------------------              Finance and Administration

WITNESSES:                             ELLIOTT ASSOCIATES, L.P.

                                       By:
-----------------------------              --------------------------------
                                           Paul E. Singer
                                           General Partner
-----------------------------

                                       2