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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
                                                         -----------------------
                                                         Chief Financial Officer


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                                  EXHIBIT INDEX

Exhibit No.   Subject Matter

   99.1     - Press Release dated June 3, 2004

                                                                    Exhibit 99.1
                Dawson Geophysical Announces Planned Expansion@

    MIDLAND, Texas, June 3 /PRNewswire-FirstCall/ -- The following was
released by Dawson Geophysical Company (Nasdaq: DWSN):

    Dawson Geophysical Company today announced its intention to field an
additional seismic data acquisition crew in response to continuing demand for
its high resolution surveys.  This expansion will bring the crew complement to
eight.  Improved market conditions are a direct result of more favorable
prices for crude oil and natural gas obtained by the Company's client base.
    Founded in 1952, Dawson Geophysical Company acquires and processes 2-D,
3-D and multi-component seismic data used in analyzing subsurface geologic
conditions for the potential of oil and natural gas accumulation.  Dawson's
clients -- major and intermediate-sized oil and gas companies and independent
oil operators -- retain exclusive rights to the information obtained.
    The Company operates highly mobile, land-based acquisition crews
throughout the lower 48 states.  Data processing is performed by geophysicists
at Dawson's computer center in the Midland, Texas headquarters.  The Company
also provides data processing services through the Houston, Texas office.
    In accordance with the Safe Harbor provisions of the Private Securities
Litigation Reform Act of 1995, Dawson Geophysical Company cautions that
statements in this press release which are forward-looking and which provide
other than historical information involve risks and uncertainties that may
impact the Company's actual results of operations.  Please see the Company's
Form 10-K for the fiscal year ended September 30, 2003 for a more complete
discussion of such risk factors.

SOURCE  Dawson Geophysical Company
    -0-                             06/03/2004
    /CONTACT:  L. Decker Dawson or Christina Hagan, both of Dawson Geophysical
Company, +1-432-684-3000/
    /Web site:  http://www.dawson3d.com /
    (DWSN)
CO:  Dawson Geophysical Company
ST:  Texas
IN:  OIL
SU: