EXHIBIT 31.1
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                                  CERTIFICATION

I, L. Decker Dawson, certify that:

1.   I have reviewed this periodic report on Form 10-Q of Dawson Geophysical
     Company;

2.   Based on my knowledge, this periodic report does not contain any untrue
     statement of a material fact or omit to state a material fact necessary to
     make the statements made, in light of the circumstances under which such
     statements were made, not misleading with respect to the period covered by
     this periodic report;

3.   Based on my knowledge, the financial statements, and other financial
     information included in this periodic report, fairly present in all
     material respects the financial condition, results of operations and cash
     flows of the registrant as of, and for, the periods presented in this
     periodic report;

4.   The registrant's other certifying officers and I are responsible for
     establishing and maintaining disclosure controls and procedures (as defined
     in Exchange Act Rules 13a-14 and 15d-14) for the registrant and have:

     a)  designed such disclosure controls and procedures to ensure that
         material information relating to the registrant, including its
         consolidated subsidiaries, is made known to us by others within those
         entities, particularly during the period in which this periodic report
         is being prepared;

     b)  evaluated the effectiveness of the registrant's disclosure controls and
         procedures as of a date within 90 days prior to the filing date of this
         periodic report (the "Evaluation Date"); and

     c)  presented in this periodic report our conclusions about the
         effectiveness of the disclosure controls and procedures based on our
         evaluation as of the Evaluation date;

5.   The registrant's other certifying officer and I have disclosed, based on
     our most recent evaluation, to the registrant's auditors and the audit
     committee of registrant's board of directors (or persons performing the
     equivalent functions):

     a)  all significant deficiencies in the design or operation of internal
         controls which could adversely affect the registrant's ability to
         record, process, summarize and report financial data and have
         identified for the registrant's auditors any material weaknesses in
         internal controls; and

     b)  any fraud, whether or not material, that involves management or other
         employees who have a significant role in the registrant's internal
         controls; and

6.   The registrant's other certifying officer and I have indicated in this
     periodic report whether there were significant changes in internal controls
     or in other factors that could significantly affect internal controls
     subsequent to the date of our most recent evaluation, including any
     corrective actions with regard to significant deficiencies and material
     weaknesses.

Dated: August 5, 2004                        Signature: /s/ L. Decker Dawson
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                                                        L. Decker Dawson
                                                        Chairman of the Board
                                                        Chief Executive Officer