<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, 1997         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 21, 1997 (as reported by Nasdaq), held by non-affiliates was
approximately $91,245,880 (See Item 12). On that date, there were 5,350,000
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 1997 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. The Registrant does not have individual customers
that comprise more than 10% of its total annual revenues and 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, 1997 the Company had 360 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 1997 Annual Report (inside front cover, page 2
and page 20) 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 operates only in one industry segment and only in the
United States.





                                       1
<PAGE>   3
ITEM 3.  LEGAL PROCEEDINGS

         The Registrant is a defendant in two lawsuits pending in the 112th and
83rd District Courts of Pecos County, Texas (respectively, Cause No. 8812,
Ernestine Bernal, et al. vs. Javier Antonio Orona, et al.; and Cause No.
P5565-83-CV, Carla Jaquez, et al. vs. Javier Antonio Orona, et al.) relating
to a July 1995 accident involving a van owned by the Registrant which was used
to transport employees to various job sites and a non-Registrant owned vehicle.
The accident resulted in the deaths of four of the Registrant's employees who
were passengers in such van. The Registrant is one of several named defendants
in such suits. Other named defendants include the estate of the deceased driver
of such van, who was an employee of the Registrant, the driver of such
non-Registrant owned vehicle, who was then an employee of the Registrant, the
owner of such vehicle, and Ford Motor Company, the manufacturer of the
Registrant's van involved in such accident. In general, the claims against the
Registrant include allegations of negligence, gross negligence and/or
intentional tort as a result of, among other things, the Registrant's alleged
failure to provide safe transportation for its employees and to properly
select, train and supervise the deceased driver of such van. The plaintiffs in
such suits are seeking actual damages from the defendants of $15.5 million,
additional unspecified actual damages, pre-judgment and post-judgment interest
and costs of suit as well as exemplary and punitive damages in an amount not to
exceed four times the amount of actual damages. The Registrant believes that it
has meritorious defenses to the claims asserted against it in such suits and it
intends to continue to vigorously defend itself against such claims. In
addition, the Registrant believes that it has approximately $11 million of
liability insurance coverage to provide against an unfavorable outcome. Such
suits are currently in the discovery stage and the Registrant currently has
pending before the court a motion for summary judgment in Cause No. 8812
requesting that the Registrant be dismissed from such suit based upon various
legal theories. A trial date of July 20, 1998 has been set in Cause No. 8812.
No trial date has yet been set for Cause No. P5565-83-CV. A motion to
consolidate such suits into a single proceeding is currently pending before the
courts. Due to the uncertainties inherent in litigation, no assurance can be
given as to the ultimate outcome of such suits or the adequacy or availability
of the Registrant's liability insurance to cover the damages, if any, which may
be assessed against the Registrant in such suits. A judgment awarding
plaintiffs an amount significantly exceeding the Registrant's available
insurance coverage could have a material adverse effect on the Registrant's
financial condition, results of operations and liquidity.

         In addition to the foregoing, from time to time the Registrant is a
party to various legal proceedings arising in the ordinary course of business.
Although the Registrant cannot predict the outcomes of any such legal
proceedings, the Registrant's management believes that the resolution of
pending legal actions will not have a material adverse effect on the
Registrant's financial condition, results of operations or liquidity.

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

         No matter has been submitted during the fourth quarter of the 1997
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 21, 1997, 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 certified public accountants of the Registrant (requiring an
affirmative vote of a majority of shares present or represented by proxy), at
the Annual Meeting to be held on January 13, 1998.





                                       2
<PAGE>   4

                                    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 1997 Annual Report (page 25, "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 1997 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 1997 Annual Report (pages 12 to 14) referred to
in Item 1.

ITEM 8.  FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA

         The report of independent public accountants appearing on page 15 and
the financial statements appearing on pages 16 through 21 of Registrant's 1997
Annual Report for the year ended September 30, 1997, 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 21, 1997 (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.





                                       3
<PAGE>   5
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 6, "SECURITY OWNERSHIP OF CERTAIN
BENEFICIAL OWNERS AND MANAGEMENT") referred to above in Item 10.

ITEM 13. CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS

         None

                                    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 16 through 24 of the Registrant's 1997 Annual Report to Shareholders for
the year ended September 30, 1997, and the Independent Auditors' Report on page
15 of such report, are incorporated herein by reference:

                                  DESCRIPTION

                  Balance Sheets, September 30, 1997 and 1996

                            Statements of Operations
                              For the Years Ended
                       September 30, 1997, 1996 and 1995

                            Statements of Cash Flows
                              For the Years Ended
                       September 30, 1997, 1996 and 1995

                       Statements of Stockholders' Equity
                              For the Years Ended
                       September 30, 1997, 1996 and 1995

                         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 statement schedules 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
<PAGE>   6
         (4)     Instruments defining the rights of security holders, including
                 indentures.

         (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)    1997 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, 1997.

         (28)    Additional Exhibits -- None.

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





                                       5
<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)              1997 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)              *
(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 June 30,
1997 (Commission File No. 0-10144) and Registrant's Form S-1, dated October 21,
1997 (Registrant No. 333-38393).





                                       6
<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 21st day of November, 1997.

                                       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                  11-21-97
-----------------------------------               Executive and Financial
L. Decker Dawson                                  Officer and Director   
                                                  

/s/ Floyd B. Graham                               Executive Vice President and          11-21-97
-----------------------------------               Director
Floyd B. Graham                                   

/s/ Howell W. Pardue                              Executive Vice President and          11-21-97
-----------------------------------               Director
Howell W. Pardue                                  

/s/ Christina W. Hagan                            Vice President and                    11-21-97
-----------------------------------               Chief Financial Officer
Christina W. Hagan                                

/s/ Calvin J. Clements                            Director                              11-21-97
-----------------------------------
Calvin J. Clements

/s/ Matthew P. Murphy                             Director                              11-21-97
-----------------------------------
Matthew P. Murphy

/s/ Tim C. Thompson                               Director                              11-21-97
-----------------------------------
Tim C. Thompson

/s/ Paula W. Henry                                Secretary                             11-21-97
-----------------------------------
Paula W. Henry

</TABLE>




                                       7
<PAGE>   9

                                 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)              1997 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)              *
(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 June 30,
1997 (Commission File No. 0-10144) and Registrant's Form S-1, dated October 21,
1997 (Registrant No. 333-38393).