<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, 1999   COMMISSION FILE NO. 0-10144

                           DAWSON GEOPHYSICAL COMPANY

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

                 508 WEST WALL, SUITE 800, MIDLAND, TEXAS 79701
                          (PRINCIPAL EXECUTIVE OFFICE)
                         TELEPHONE NUMBER: 915-684-3000

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

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

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

        TITLE OF EACH CLASS          NAME OF EACH EXCHANGE ON WHICH REGISTERED
        -------------------          -----------------------------------------
 COMMON STOCK, $.33 1/3 PAR VALUE                      NONE

         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 Party 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 26, 1999 (as reported by NASDAQ), held by non-affiliates was
approximately $42,006,105 (See Item 12). On that date, there were 5,411,794
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 1999 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 services. 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, 1999, the Company had 260 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 1999 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>
                        Fee or                                              Building Area
Location                Leased       Purpose                                 Square  Feet
--------                ------       -------                                -------------

<S>                     <C>          <C>                                    <C>
Midland, TX             Leased       Executive offices and                      18,400
                                     data processing

Midland, TX             Fee          Field office                               53,000
                                     Equipment fabrication
                                     Maintenance and repairs
</TABLE>

         The Registrant owns additional undeveloped real property used for
employee parking consisting of approximately 21,000 square feet in Midland,
Texas, in the vicinity of the headquarters office building.

         The Registrant has placed for sale the office building consisting of
approximately 10,400 square feet previously occupied by the Registrant for
executive offices and data processing.



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<PAGE>   3

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

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 Registrant 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 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. The court has heard a motion for summary judgment in both
cases requesting that the Registrant be dismissed from such suit based upon
various legal theories. Such motion has not yet been ruled on by the court. 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 1999
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 26, 1999, 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 LLP as independent certified
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 25, 2000.



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<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 1999 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 1999 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 1999 Annual Report (pages 12 to 14) referred to in
Item 1.

ITEM 7A. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

         The primary sources of market risk include fluctuations in commodity
prices which effect demand for and pricing of the Company's services and
interest rate fluctuations. At September 30, 1999, the Company had no
indebtedness. The Company's short-term investments are fixed rate and the
Company does not necessarily intend to hold them to maturity, and therefore, the
short-term investments expose the Company to the risk of earnings or cash flow
loss due to changes in market interest rates. As of September 30, 1999, the
carrying value of the investments approximate fair value. The Company has not
entered into any hedge arrangements, commodity swap agreements, commodity
futures, options or other derivative financial instruments. The Company does not
currently conduct business internationally so it is generally not subject to
foreign currency exchange rate risk.

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 27 of Registrant's 1999
Annual Report for the year ended September 30, 1999, referred to above in Item
1, are incorporated herein by reference.

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

         None





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<PAGE>   5

                                    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 26, 1999 (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 6, "SECURITY OWNERSHIP OF CERTAIN
BENEFICIAL OWNERS AND MANAGEMENT") referred to above in Item 10.

         On July 13, 1999, the Board of Directors of the Company authorized and
declared a dividend to the holders of record on July 23, 1999 of one Right (a
"Right") for each outstanding share of the Company's common stock. When
exercisable, each Right will entitle the holder to purchase one one-hundredth of
a share of Series A Junior Participating Preferred Stock, par value $1.00 per
share, of the Company (the "Preferred Shares") at an exercise price of $50.00
per Right. The rights are not currently exercisable and will become exercisable
only if a person or group acquires beneficial ownership of 20% or more of the
Company's outstanding common stock or announces a tender offer or exchange
offer, the consummating of which would result in attaining the triggering
percentage. The Rights are subject to redemption by the Company for $.01 per
Right at any time prior to the tenth day after the first public announcement of
a triggering acquisition.

ITEM 13. CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS

         None




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<PAGE>   6

                                     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 27 of the Registrant's 1999 Annual Report to Shareholders for the
year ended September 30, 1999, and the Independent Auditors' Report on page 15
of such report, are incorporated herein by reference:

                                   DESCRIPTION

                   Balance Sheets, September 30, 1999 and 1998

                            Statements of Operations
                               For the Years Ended
                        September 30, 1999, 1998 and 1997

                            Statements of Cash Flows
                               For the Years Ended
                        September 30, 1999, 1998 and 1997

                       Statements of Stockholders' Equity
                               For the Years Ended
                        September 30, 1999, 1998 and 1997

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

         (9)    Voting Trust Agreement -- None; consequently, omitted.




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<PAGE>   7

         (10)     Material Contracts.

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

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

         (13)     1999 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 filed a report dated July 13, 1999 on Form 8-K
                  during the last quarter of the year ended September 30, 1999.

         (28)     Additional Exhibits -- None.

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






                                       6
<PAGE>   8

                                  EXHIBIT INDEX

<TABLE>
<CAPTION>
NUMBER            EXHIBIT                                                               PAGE
------            -------                                                               ----

<S>               <C>                                                                   <C>
(1)               *
(2)               *
(3)               Articles of Incorporation** and Bylaws                                E-2
(4)               Instruments defining the rights of security                           **
                  holders, including indentures--Shareholder Rights Plan                ***
(5)               *
(6)               *
(7)               *
(8)               *
(9)               Voting Trust Agreement                                                Omit
(10)              Material Contracts                                                    **
(11)              Statement re: computation of per share earnings                       Omit
(12)              Statement re: computation of ratios                                   Omit
(13)              1999 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).

*** Incorporation by reference to Registrant's Form 8-K, dated July 13, 1999
(Commission File No. 2-71058).




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<PAGE>   9

                                   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 26th day of November, 1999.

                                 DAWSON GEOPHYSICAL COMPANY

                                 By: /s/ L. Decker Dawson, President
                                     -------------------------------
                                     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                 11-26-99
--------------------------         Executive and Director
L. Decker Dawson

/s/ Howell W. Pardue               Executive Vice President             11-26-99
--------------------------         and Director
Howell W. Pardue

/s/ Paul H. Brown                  Director                             11-26-99
--------------------------
Paul H. Brown

/s/ Calvin J. Clements             Director                             11-26-99
--------------------------
Calvin J. Clements

/s/ Floyd B. Graham                Director                             11-26-99
--------------------------
Floyd B. Graham

/s/ Matthew P. Murphy              Director                             11-26-99
--------------------------
Matthew P. Murphy

/s/ Tim C. Thompson                Director                             11-26-99
--------------------------
Tim C. Thompson

/s/ Paula W. Henry                 Secretary                            11-26-99
--------------------------
Paula W. Henry

/s/ Christina W. Hagan             Vice President and                   11-26-99
--------------------------         Chief Financial Officer
Christina W. Hagan
</TABLE>



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<PAGE>   10


                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
EXHIBIT
NUMBER                        DESCRIPTION
-------                       -----------
<S>                      <C>
   3                     Articles of Incorporation and Bylaws

  13                     1999 Annual Report to Stockholders

  27                     Financial Data Schedule
</TABLE>