<PAGE>   1
                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM 10-K

           [ X ] ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE

                       SECURITIES EXCHANGE ACT OF 1934

  FOR THE FISCAL YEAR ENDED SEPTEMBER 30, 1996      COMMISSION FILE NO. 0-10144

                           DAWSON GEOPHYSICAL COMPANY


  INCORPORATED IN THE STATE OF TEXAS                          75-0970548
                                                           (I.R.S. EMPLOYER
                                                          IDENTIFICATION NO.)


                  208 SOUTH MARIENFELD, MIDLAND, TEXAS 79701
                         (PRINCIPAL EXECUTIVE OFFICE)
                       TELEPHONE NUMBER: (915) 682-7356

                           ------------------------

        SECURITIES REGISTERED PURSUANT TO SECTION 12(B) OF THE ACT:NONE

          SECURITIES REGISTERED PURSUANT TO SECTION 12(G) OF THE ACT:

<TABLE>
<CAPTION>
        TITLE OF EACH CLASS                           NAME OF EACH EXCHANGE ON WHICH REGISTERED
        -------------------                           -----------------------------------------
 <S>                                                                 <C>
 COMMON STOCK, $.33 1/3 PAR VALUE                                        NONE
</TABLE>

    Indicate by check mark whether the Registrant (1)has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the 12 preceding months, and (2)has been subject to such filing
requirements for the past 90 days. Yes  X     No
                                      ------    ------

    Indicate by check mark if disclosure of delinquent filers pursuant to Item
405 of Regulation S-K (229.405 of this chapter) is not contained herein, and
will not be contained, to the best of registrant's knowledge, in definitive
proxy or information statements incorporated by reference in Part III of this
Form 10-K or any amendment to this Form 10-K. [ X ]

    The aggregate market value of the Common Stock of the Registrant based upon
the mean between the closing high and low price of the Common Stock as of
November 15, 1996 (as reported by Nasdaq), held by non-affiliates was
approximately $26,855,137 (See Item 12). On that date, there were 4,161,550
shares of Dawson Geophysical Company Common Stock, $.33 1/3 par value,
outstanding.


                     DOCUMENTS INCORPORATED BY REFERENCE

    The information required by Items 1, 5, 6, 7 and 8 of Parts I and II hereof
is incorporated by reference to the Registrant's 1996 Annual Report filed or to
be filed with the Commission no later than 120 days after the end of the fiscal
year covered by this Form 10-K.

    The information required by Items 4, 10, 11 and 12 of Parts I and III hereof
is incorporated by reference to the Registrant's definitive proxy statement
filed or to be filed with the Commission no later than 120 days after the end
of the fiscal year covered by this Form 10-K.
<PAGE>   2
                                     Part I

Item 1.       BUSINESS

       There are no patents, trademarks, franchises or concessions held by the
Registrant. Software licenses held by the Registrant are considered ordinary
and replaceable. Although the Registrant has individual customers that comprise
more than 10% of its total annual revenues, the Registrant does not consider
the loss of any individual customer to have a material adverse effect on the
Registrant due to the demand for the Registrant's services and for the services
of the industry in which the Registrant competes. Competitors of the Registrant
consist primarily of subsidiary companies of large corporations. Services
provided by competitor companies other than provided by the Registrant may
include marine geophysics, speculative acquisition of seismic data, a library
of seismic data, or a combination of these factors. The Registrant considers
price and quality of service to be its principal methods of competition.
Indicative of its level of commitment to the proprietary data of its customers,
the Registrant does not maintain a library of seismic data or participate in
speculative seismic data acquisition. Although the business of the Registrant
is not considered seasonal, it does depend on favorable weather.

       At September 30, 1996 the Company had 304 full-time employees. None of
the Company's employees are subject to a collective bargaining agreement. The
Company considers its relations with its employees to be good.

       Additional information required by this Item 1 is hereby incorporated by
reference to the Registrant's 1996 Annual Report (inside front cover, page 2
and page 18) filed or to be filed by the Registrant with the Securities and
Exchange Commission pursuant to Regulation 14A of the Securities and Exchange
Act of 1934 within 120 days after the end of the fiscal year covered by this
Form 10-K. (Exhibit 13 hereto.)

Item 2.       PROPERTIES

       The principal facilities of the Registrant are summarized in the table
below.

<TABLE>
<CAPTION>
                                                      Building Area
                 Fee or                                   Square
Location         Leased    Purpose                          Feet
--------         ------    -------                          ----
<S>              <C>       <C>                            <C>
Midland, TX      Fee       Executive offices and          10,400
                           data processing             
                                                       
Midland, TX      Fee       Field Office                   53,000
                           Equipment fabrication       
                           Maintenance and repairs        
</TABLE>

       The Registrant owns additional undeveloped real property consisting of
approximately 21,000 square feet in Midland, Texas, adjacent to the
headquarters office building.

       The Registrant operates only in one industry segment and only in the
United States.





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<PAGE>   3
Item 3.       LEGAL PROCEEDINGS

       On July 1, 1995, an automobile accident claimed the lives of four
employees which involved an automobile owned by the Company. The Company is a
defendant in a lawsuit filed by the families of two of the employees whose
deaths resulted from the accident. The families filed suit against the Company
under the gross negligence provisions of the Texas Workers' Compensation Act.
Accordingly, the Company believes its exposure is limited to exemplary damages
of $36 million. The litigation is currently in the discovery stage. The Company
has approximately $12 million of insurance coverage available to provide
against an unfavorable outcome in this matter. Due to the uncertainties
inherent in litigation, no absolute assurance can be given as to the ultimate
outcome of this suit. However, the Company believes, based on knowledge of the
facts to date and consultation with its legal advisors, that liabilities, if
any, from this suit should not have a material adverse effect on the Company's
financial position.

       The Company is party to other legal actions arising in the ordinary
course of its business, none of which management believes will result in a
material adverse effect on the Company's financial position or results of
operations, as the Company believes it is adequately insured.

Item 4.       SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

       No matter has been submitted during the fourth quarter of the 1996 fiscal
year to a vote of security holders, through the solicitation of proxies or
otherwise. However, please refer to the Registrant's Proxy Statement dated
November 15, 1996, filed or to be filed with the Commission no later than 120
days after the end of the fiscal year covered by this Form 10-K, notifying as
to the election of Directors and selection of KPMG Peat Marwick LLP as
independent public accountants of the Company (requiring an affirmative vote of
a majority of shares present or represented by proxy), at the Annual Meeting to
be held on January 14, 1997.


                                    PART II

Item 5.       MARKET FOR REGISTRANT'S COMMON EQUITY AND RELATED
              STOCKHOLDER MATTERS

       The information required by this Item 5 is hereby incorporated by 
reference to the Registrant's 1996 Annual Report (page 28), "Common Stock
Information" referred to in Item 1 above.

Item 6.       SELECTED FINANCIAL DATA

       The information required by this Item 6 is hereby incorporated by 
reference to the Registrant's 1996 Annual Report (page 1, "Financial
Highlights") referred to above in Item 1.

Item 7.       MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
              CONDITION AND RESULTS OF OPERATIONS

       The information required by this Item 7 is hereby incorporated by 
reference to the Registrant's 1996 Annual Report (pages 24 to 27) referred to in
Item 1.





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<PAGE>   4
Item 8.       FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA

    The report of independent public accountants appearing on page 23 and the
financial statements appearing on pages 14 through 22 of Registrant's 1996
Annual Report for the year ended September 30, 1996, referred to above in Item
1, are incorporated herein by reference.

Item 9.       CHANGES IN AND DISAGREEMENTS ON ACCOUNTING AND
              FINANCIAL DISCLOSURES

    None


                                    PART III

Item 10.      DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT

    The information required by this Item 10 with respect to Directors and
Executive Officers is hereby incorporated by reference to the Registrant's
Proxy Statement dated November 15, 1996 (page 2) filed or to be filed by the
Registrant with the Securities and Exchange Commission pursuant to Regulation
14A of the Securities and Exchange Act of 1934 within 120 days after the end of
the fiscal year covered by this Form 10-K.

Item 11.      EXECUTIVE COMPENSATION

    The information required by this Item 11 is hereby incorporated by
reference to the Registrant's Proxy Statement (page 3) referred to above in Item
10.

Item 12.      SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND
              MANAGEMENT

    The information required by this Item 12 with respect to security ownership
of certain beneficial owners is hereby incorporated by reference to the
Registrant's Proxy Statement (page 5, "SECURITY OWNERSHIP OF CERTAIN BENEFICIAL
OWNERS") referred to above in Item 10.

    The information required by this Item 12 with respect to security ownership
of management is hereby incorporated by reference to the Registrant's Proxy
Statement (page 5, "SECURITY OWNERSHIP OF MANAGEMENT") referred to above in
Item 10.

Item 13.      CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS

    None






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<PAGE>   5
                                    PART IV

Item 14.      EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON
              FORM 8-K

   (a)  1.    Financial Statements

    The following financial statements of the Registrant, included in pages 14
through 22 of the Registrant's 1996 Annual Report to Shareholders for the year
ended September 30, 1996, and the Independent Auditors' Report on page 23 of
such report, are incorporated herein by reference:

                                  Description
                                  -----------

                  Balance Sheets, September 30, 1996 and 1995

                            Statements of Operations
                              For the Years Ended
                      September 30, 1996, 1995 and 1994

                           Statements of Cash Flows
                             For the Years Ended
                      September 30, 1996, 1995 and 1994

                      Statements of Stockholders' Equity
                             For the Years Ended
                      September 30, 1996, 1995 and 1994

                        Notes to Financial Statements

                         Independent Auditors' Report

   (a)  2.    All schedules are omitted because they are not applicable, not
required or because the required information is included in the financial
statements or notes thereof.

   (a)  3.    Exhibits

   The exhibits and financial statements filed as a part of this report are
listed below according to the number assigned to it in the exhibit table of
Item 601 of Regulation S-K:

        (3)   Restated Articles of Incorporation and Bylaws.

        (4)   Instruments defining the rights of security holders, including
              indentures.





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<PAGE>   6
        (9)   Voting Trust Agreement -- None; consequently, omitted.

        (10)  Material Contracts.

        (11)  Statement re: computation of per share earnings -- Not
              Applicable.

        (12)  Statement re:Computation of ratios -- Not Applicable.

        (13)  1996 Annual Report.

        (18)  Letter re: change in accounting principles -- Not Applicable.

        (19)  Previously unfiled documents -- No documents have been executed
              or in effect during the reporting period which should have been
              filed; consequently, this exhibit has been omitted.

        (22)  Subsidiaries of the Registrant -- There are no subsidiaries of
              the Registrant; consequently, this exhibit has been omitted.

        (23)  Published  report regarding matters submitted to vote of security
              holders -- None; consequently, omitted.

        (24)  Consent of experts and counsel -- Not Applicable.

        (25)  Power of Attorney -- There are no signatures contained within
              this report pursuant to a power of attorney; consequently, this
              exhibit has been omitted.

        (b)   Reports on Form 8-K

              The Registrant has not filed any reports on Form 8-K during the
              last quarter of the year ended September 30, 1996.

        (28)  Additional Exhibits -- None.

        (29)  Information from reports furnished to state insurance regulatory
              authorities -- None.





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<PAGE>   7
                                 EXHIBIT INDEX


<TABLE>
<CAPTION>
Number            Exhibit                                                   Page
------            -------                                                   ----
<S>               <C>                                                       <C>
(1)               *                                                         
(2)               *                                                         
(3)               Articles of Incorporation and Bylaws                      **
(4)               Instruments defining the rights of security               **
                                                                            
                  holders, including indentures                             
(5)               *                                                         
(6)               *                                                         
(7)               *                                                         
(8)               *                                                         
(9)               Voting Trust Agreement                                    Omit
(10)              Material Contracts                                        **
(11)              Statement re: computation of per share                    Omit
                  earnings                                                  
(12)              Statement re: computation of ratios                       Omit
(13)              1996 Annual Report to Stockholders                        E-1
(14)              *                                                         
(15)              *                                                         
                                                                            
(16)              *                                                         
(17)              *                                                         
(18)              Letter re: change in accounting principles                Omit
(19)              Previously unfiled documents                              Omit
(20)              *                                                         
(21)              *                                                         
(22)              Subsidiaries of the Registrant                            Omit
(23)              Published report regarding matters submitted              Omit
                  to vote of security holders                               
(24)              Consent of experts                                        
(25)              Power of Attorney                                         Omit
(26)              *                                                         
                                                                            
(27)              Financial Data Schedule                                   
(28)              Additional Exhibits                                       Omit
(29)              Information from reports furnished to state               Omit
                  insurance regulatory authorities                          
</TABLE>

                  *This exhibit is not required to be filed in accordance with
Item 601 of Regulation S-K.

                  **Incorporated by reference to Registrant's Form 10-Q, dated
March 31, 1996 (Commission File No. 0-10144).





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<PAGE>   8
                                   SIGNATURES

Pursuant to the requirements of Section 13 or 15(d) of the Securities Exchange
Act of 1934, the Registrant has duly caused this report to be signed on its
behalf by the undersigned, thereunto duly authorized, in the City of Midland,

and the State of Texas, on the 15th day of November, 1996.



                                          DAWSON GEOPHYSICAL COMPANY


                                          By:  /s/ L. Decker Dawson            
                                               --------------------------------
                                               L. Decker Dawson, President


Pursuant to the requirements of the Securities Exchange Act of 1934, this
report has been signed below by the following persons in the capacities and on
the date indicated.


<TABLE>
<CAPTION>
SIGNATURE                              TITLE                        DATE
---------                              -----                        ----
<S>                                    <C>                          <C>
/s/ L. Decker Dawson                   President, Principal         11-15-96
---------------------------            Executive and Financial      
L. Decker Dawson                       Officer and Director         
                                                                    
/s/ Floyd B.Graham                     Vice President and           11-15-96
---------------------------            Director                     
Floyd B. Graham                                                     
                                                                    
/s/ Howell W. Pardue                   Vice President and           11-15-96
---------------------------            Director                     
Howell W. Pardue                                                    
                                                                    
/s/ Calvin J. Clements                 Director                     11-15-96
---------------------------                                         
Calvin J. Clements                                                  
                                                                    
/s/ Matthew P. Murphy                  Director                     11-15-96
---------------------------                                         
Matthew P. Murphy                                                   
                                                                    
/s/ Tim C. Thompson                    Director                     11-15-96
---------------------------                                         
Tim C. Thompson                                                     
                                                                    
/s/ Paula W. Henry                     Secretary                    11-15-96
---------------------------                                         
Paula W. Henry                                                      
                                                                    
/s/ Christina W. Hagan                 Treasurer                    11-15-96
---------------------------                                         
Christina W. Hagan
</TABLE>







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