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EXHIBIT 31.1

CERTIFICATION

I, L. Decker Dawson, certify that:



| | 1. | I have reviewed this annual report on Form 10-K/A of Dawson Geophysical Company;                                                                                                                                                                                                                          
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| | 2. | Based on my knowledge, this 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 report;
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| | 3. | Based on my knowledge, the financial statements, and other financial information
included in this 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 report;                   
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| | 4. | The registrants other certifying officer and I are responsible for establishing and
maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e)
and 15d-15(e)) for the registrant and have:                                                                               



| | (a) | Designed such disclosure controls and procedures, or caused such disclosure
controls and procedures to be designed under our supervision, 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 report is being prepared;         
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| | (b) | Evaluated the effectiveness of the registrants disclosure controls and
procedures and presented in this report our conclusions about the effectiveness of the
disclosure controls and procedures, as of the end of the period covered by this report
based on such evaluation; and                                                                                                    
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| | (c) | Disclosed in this report any change in the registrants internal control over
financial reporting that occurred during the registrants most recent fiscal quarter
(the registrants fourth fiscal quarter in the case of an annual report) that has
materially affected, or is reasonably likely to materially affect, the registrants
internal control over financial reporting; and



| | 5. | The registrants other certifying officer and I have disclosed, based on our most
recent evaluation of internal control over financial reporting, to the registrants
auditors and the audit committee of the registrants board of directors (or persons
performing the equivalent functions):
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| | (a) | All significant deficiencies and material weaknesses in the design or operation
of internal control over financial reporting which are reasonably likely to adversely
affect the registrants ability to record, process, summarize and report financial
information; and
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| | (b) | Any fraud, whether or not material, that involves management or other employees
who have a significant role in the registrants internal control over financial
reporting.                                                                                               

Date: February 28, 2005

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| | /s/ L. Decker Dawson                                                            | 
| | L. Decker Dawson                                                                | 
| | Chief Executive Officer and Chairman of the
Board (principal executive officer) | 
|