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                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM 8-K

                                 CURRENT REPORT
                     PURSUANT TO SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

Date of Report  June 3, 2003
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                           Dawson Geophysical Company
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             (Exact name of registrant as specified in its charter)

           Texas                         2-71058                 75-0970548
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(State or other jurisdiction        (Commission File            (IRS Employer
     of incorporation)                   Number)             Identification No.)

508 W. Wall, Suite 800   Midland, Texas                            79701
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(Address of principal executive offices)                         (Zip Code)

Registrant's telephone number, including area code     432/684-3000
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          (Former name or former address if changed since last report)

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Item. 5     The Registrant has issued a press release announcing its intention
            to field an additional seismic data acquisition crew.

Item. 7     Financial Statements, Pro Forma Financial Information and Exhibits

            (c)   Exhibits
                  99.1 - Press Release dated June 3, 2004

                                   SIGNATURES

      Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.

                                                     DAWSON GEOPHYSICAL COMPANY

                             Date: June 3, 2004      By: /s/ L. Decker Dawson
                                                         -----------------------
                                                         Chief Executive Officer

                                                         /s/ Christina W. Hagan
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                                                         Chief Financial Officer


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                                  EXHIBIT INDEX

Exhibit No.   Subject Matter

   99.1     - Press Release dated June 3, 2004