<PAGE>   1
                                    FORM 10-Q

                       SECURITIES AND EXCHANGE COMMISSION
                              WASHINGTON D.C. 20549

                                   (Mark One)

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

                For the quarterly period ended December 31, 1999
                                               -----------------

                                       OR

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

                  For the transition period from           to
                                                -----------   -----------

  For Quarter Ended December 31, 1999             Commission File number 2-71058
                    -----------------                                    -------

                           DAWSON GEOPHYSICAL COMPANY
              -----------------------------------------------------
             (Exact name of Registrant as specified in its Charter)

             TEXAS                                       75-0970548
         ------------                                 ----------------
(State or other jurisdiction of               (IRS Employer Identification No.)
incorporation or organization)

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

        (Registrant's telephone number, including area code) 915/684-3000
                                                             ------------

                                      NONE
                                      ----
 (Former Name, Former Address & Former Fiscal Year if changed since last report)

  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 preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days. Yes X . No   .
                                             ---    ---

  Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the latest practicable date.

                  CLASS                         Outstanding at December 31, 1999
    --------------------------------            --------------------------------
    Common Stock, $.33 1/3 par value                    5,428,294 shares





                                       -1-
<PAGE>   2
                           DAWSON GEOPHYSICAL COMPANY

                                      INDEX

<TABLE>
<CAPTION>

                                                                                       Page No.
                                                                                       --------

<S>               <C>                                                                <C>
Part I.           Financial Information:

     Item 1.      Financial Statements

                  Statements of Operations --
                        Three Months Ended December 31,
                        1999 and 1998                                                       3

                  Balance Sheets --
                        December 31, 1999 and September 30,
                        1999                                                                4

                  Statements of Cash Flows --
                        Three Months Ended December 31,
                        1999 and 1998                                                       5

                  Notes to Financial Statements                                             6

     Item 2.      Management's Discussion and Analysis of
                        Financial Condition and Results of
                        Operations                                                          8

     Item 3.      Quantitative and Qualitative Disclosures
                        About Market Risk                                                  11
</TABLE>





                                       -2-
<PAGE>   3



                          PART I. FINANCIAL INFORMATION

                          Item 1. Financial Statements


                           DAWSON GEOPHYSICAL COMPANY

                            STATEMENTS OF OPERATIONS
                                   (UNAUDITED)

<TABLE>
<CAPTION>

                                                        Three Months Ended
                                                           December 31
                                                -------------------------------

                                                   1999                 1998
                                                -----------         -----------

<S>                                             <C>                 <C>
Operating revenues                              $ 4,893,000         $ 8,018,000

Operating costs:
    Operating expenses                            5,530,000           6,433,000
    General and administrative                      763,000             546,000
    Depreciation                                  2,463,000           2,711,000
                                                -----------         -----------

                                                  8,756,000           9,690,000
                                                -----------         -----------

Loss from operations                             (3,863,000)         (1,672,000)
Other income (expense):
         Interest income                            228,000             186,000
         Other                                           --               6,000
         Gain on disposal of assets                      --              11,000
                                                -----------         -----------

Loss before income tax                           (3,635,000)         (1,469,000)

Income tax benefit:                               1,236,000             495,000
                                                -----------         -----------

Net loss                                        $(2,399,000)        $  (974,000)
                                                ===========         ===========


Net loss per common share                       $      (.44)        $      (.18)
                                                ===========         ===========


Weighted average equivalent common
         shares outstanding                       5,414,560           5,368,790
                                                ===========         ===========
</TABLE>



See accompanying notes to the financial statements.










                                       -3-



<PAGE>   4
                           DAWSON GEOPHYSICAL COMPANY

                                 BALANCE SHEETS

<TABLE>
<CAPTION>

                                            December 31, 1999   September 30,1999
                                            -----------------   -----------------
                                               (UNAUDITED)

<S>                                             <C>                <C>
ASSETS
Current assets:
   Cash and cash equivalents                    $ 3,847,000         $ 4,993,000
   Short-term investments                        13,537,000          13,547,000
   Accounts receivable, net of allowance
          for doubtful accounts of $313,000
          in 2000 and $133,000 in 1999            5,566,000           5,567,000
     Income taxes receivable                      2,395,000           1,668,000
   Prepaid expenses                                 588,000             466,000
                                                -----------         -----------

           Total current assets                  25,933,000          26,241,000
                                                -----------         -----------


Property, plant and equipment                    71,732,000          71,706,000
   Less accumulated depreciation                (39,086,000)        (36,529,000)
                                                -----------         -----------

         Net property, plant and equipment       32,646,000          35,177,000
                                                -----------         -----------

                                                $58,579,000         $61,418,000
                                                ===========         ===========

LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
   Accounts payable                             $   968,000         $   778,000
   Accrued liabilities:
      Payroll costs and other taxes                 271,000             506,000
      Other                                           4,000              21,000
                                                -----------         -----------

           Total current liabilities              1,243,000           1,305,000
                                                -----------         -----------


Deferred income taxes                               136,000             645,000

Stockholders' equity:
   Preferred stock - par value $1.00 per share;
       5,000,000 shares authorized, none
     outstanding                                         --                  --
   Common stock - par value $.33 1/3 per share;
     10,000,000 shares authorized, 5,428,294
       and 5,406,794 shares issued and
       outstanding respectively                   1,809,000           1,802,000
   Additional paid-in capital                    38,621,000          38,497,000
   Retained earnings                             16,770,000          19,169,000
                                                -----------         -----------

           Total stockholders' equity            57,200,000          59,468,000
                                                -----------         -----------


Contingencies (See Note 2)
                                                $58,579,000         $61,418,000
                                                ===========         ===========
</TABLE>


See accompanying notes to the financial statements.



                                       -4-
<PAGE>   5
                           DAWSON GEOPHYSICAL COMPANY

                            STATEMENTS OF CASH FLOWS

                                   (UNAUDITED)

<TABLE>
<CAPTION>

                                                                   Three Months Ended
                                                                       December 31
                                                              -----------------------------

                                                                 1999               1998
                                                              -----------       -----------


<S>                                                           <C>               <C>
Cash flows from operating activities:
         Net loss                                             $(2,399,000)      $  (974,000)
         Adjustments to reconcile net loss to net cash
             provided by (used in) operating activities:
         Depreciation                                           2,463,000         2,711,000
         Gain on disposal of assets                                    --           (11,000)
         Non-cash compensation                                     99,000           251,000
         Deferred income taxes                                   (509,000)          120,000
         Other                                                    103,000            68,000
         Change in current assets and liabilities:
         Decrease in accounts receivable                            1,000         3,728,000
         Increase in income taxes receivable                     (727,000)         (651,000)
         Decrease (increase) in prepaid expenses                 (122,000)           56,000
         Increase (decrease) in accounts payable                  190,000        (1,133,000)
         Decrease in accrued liabilities                         (254,000)       (1,136,000)
                                                              -----------       -----------
Net cash provided by (used in) operating activities            (1,155,000)        3,029,000
                                                              -----------       -----------

Cash flows from investing activities:
         Proceeds from disposal of assets                              --            11,000
         Capital expenditures                                     (25,000)          (50,000)
         Proceeds from maturity of short-term investments       1,000,000         1,000,000
         Investment in short-term investments                    (998,000)         (978,000)
                                                              -----------       -----------

Net cash used in investing activities                             (23,000)          (17,000)
                                                              -----------       -----------

Cash flows from financing activities:
         Proceeds from exercise of stock options                   32,000                --
                                                              -----------       -----------


Net cash provided by financing activities                          32,000                --
                                                              -----------       -----------

Net increase (decrease) in cash and cash equivalents           (1,146,000)        3,012,000

Cash and cash equivalents at beginning of period                4,993,000         5,745,000
                                                              -----------       -----------

Cash and cash equivalents at end of period                    $ 3,847,000       $ 8,757,000
                                                              ===========       ===========
</TABLE>



See accompanying notes to the financial statements.








                                       -5-




<PAGE>   6



                           DAWSON GEOPHYSICAL COMPANY

                          NOTES TO FINANCIAL STATEMENTS


1.       OPINION OF MANAGEMENT

         Although the information furnished is unaudited, in the opinion of
management of the Registrant, the accompanying financial statements reflect all
adjustments (consisting only of normal recurring accruals) necessary for a fair
presentation of the financial condition and results of operations for the
periods presented. The results of operations for the three months ended December
31, 1999, are not necessarily indicative of the results to be expected for the
fiscal year.


2.       CONTINGENCIES

         The Company 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 Company which was used to
transport employees to various job sites and a non-Company owned vehicle. The
accident resulted in the deaths of four Company employees who were passengers in
such van. The Company 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 Company, the driver of such non-Company owned vehicle, who
was then an employee of the Company, the owner of such vehicle, and Ford Motor
Company, the manufacturer of the Company van involved in such accident. In
general, the claims against the Company include allegations of negligence, gross
negligence and/or intentional tort as a result of, among other things, the
Company'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, prejudgment 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 Company
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 Company 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
Company 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 Company's liability insurance to
cover any such damages, if any, which may be assessed against the Company in
such suits. A judgment awarding plaintiffs an amount significantly exceeding the
Company's available insurance coverage could have a material adverse effect on
the Company's financial condition, results of operations and liquidity.

         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
operation, as the Company believes it is adequately insured.



                                       -6-


<PAGE>   7
3.       NET INCOME PER COMMON SHARE

         The following table sets forth the computation of basic and diluted net
income per common share:

<TABLE>
<CAPTION>

                                              Three Months Ended
                                                 December 31
                                        -----------------------------
                                            1999              1998
                                        -----------       -----------

<S>                                     <C>              <C>
Numerator:
  Net loss and numerator for basic
    and diluted net loss per
    common share-income available
    to common stockholders              $(2,399,000)      $  (974,000)
                                        -----------       -----------

Denominator:
  Denominator for basic net loss
    per common share-weighted
    average common shares                 5,414,560         5,368,790
  Effect of dilutive securities-
    employee stock options                       --                --
                                        -----------       -----------
  Denominator for diluted net
    loss per common share-
    adjusted weighted average
    common shares and assumed
    conversions                           5,414,560         5,368,790
                                        -----------       -----------

Net loss per common share               $      (.44)      $      (.18)
                                        ===========       ===========

Net loss per common
  share--assuming dilution              $      (.44)      $      (.18)
                                        ===========       ===========
</TABLE>

     Employee stock options to purchase shares of common stock were outstanding
during fiscal year 2000 and 1999 but were not included in the computation of
diluted net loss per share because either (i) the employee stock options'
exercise price was greater than the average market price of the common stock of
the Company, or (ii) the Company had a net loss from continuing operations and,
therefore, the effect would be antidilutive.


                                       -7-




<PAGE>   8

                     MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS


The following discussion should be read in conjunction with the Company's
financial statements. In addition, in reviewing the Company's financial
statements it should be noted that the Company's revenues relate to oil and gas
exploration and production activity and fluctuations in the Company's results of
operations may occur due to commodity prices, weather, land use permitting and
other factors.

FORWARD LOOKING STATEMENTS

All statements other than statements of historical fact included in this report,
including without limitation, statements under "Management's Discussion and
Analysis of Financial Condition and Results of Operations" regarding the
Company's financial position, business strategy and plans and objectives of
management of the Company for future operations, are forward-looking statements
within the meaning of Section 27A of the Securities Act of 1933 and Section 21E
of the Securities Exchange Act of 1934. When used in this report, words such as
"anticipate", "believe", "estimate", "expect", "intend", and similar
expressions, as they relate to the Company or its management, identify
forward-looking statements. Such forward-looking statements are based on the
beliefs of the Company's management as well as assumptions made by and
information currently available to the Company's management. Actual results
could differ materially from those contemplated by the forward-looking
statements as a result of certain factors, including but not limited to
dependence upon energy industry spending, weather problems, inability to obtain
land use permits, the volatility of oil and gas prices, and the availability of
capital resources. Such statements reflect the current views of the Company with
respect to future events and are subject to these and other risks, uncertainties
and assumptions relating to the operations, results of operations, growth
strategy and liquidity of the Company. All subsequent written and oral
forward-looking statements attributable to the Company or persons acting on its
behalf are expressly qualified in their entirety by this paragraph. The Company
assumes no obligation to update any such forward-looking statements.

OVERVIEW

The revenues of the Company continue to be severely impacted although crude oil
prices have recovered relative to last year. Demand for the Company's services
is expected to be related to crude oil and natural gas prices; however, the
Company is prepared for some delay in demand for its services as its clients and
potential clients recover from their losses.


RESULTS OF OPERATIONS

The Company's operating revenues for the first quarter of fiscal 2000 decreased
39% from $8,018,000 to $4,893,000. Demand for the Company's services continues
to be negatively impacted by the drop in crude oil prices, which occurred in
late 1998. During the quarter ended December 31, 1998, the Company reduced the
number of operating crews from six to three. The Company is currently operating
four crews. In addition to

                                      -8-


<PAGE>   9


the decrease in the number of operating crews, the decrease in revenues reflects
severe price competition.

Operating expenses decreased 14% in the first quarter of fiscal 2000 as compared
to the same period of fiscal 1999 as a result of decreased demand for the
Company's services. The Company reduced the number of employees and enacted
other cost saving measures in January 1999; however, the Company has retained
key field personnel in anticipation of increased demand.

General and administrative expenses for the quarter ended December 31, 1999
totaled $763,000, an increase of $217,000 from the same period of fiscal 1999.
The increase primarily consists of a provision for doubtful accounts of $180,000
recognized during the quarter ended December 31, 1999.

Depreciation for the quarter ended December 31, 1999 totaled $2,463,000, a
decrease of $248,000 from the same period of fiscal 1999. Depreciation decreased
as a result of a suspension of capital expansion during fiscal 1999 due to
industry conditions.

Total operating costs for the first quarter of fiscal 2000 totaled $8,756,000, a
decrease of 9.6% from the same period of fiscal 1999 due to the factors
described above. The 39% decrease of revenues as compared to the 9.6% decrease
of total operating costs for the first quarter of fiscal 2000 reflects the high
proportion of relatively fixed total operating costs (including personnel costs
of active crews and depreciation costs) inherent in the Company's business and
continued fierce price competition in the bidding process for geophysical
services.



LIQUIDITY AND CAPITAL RESOURCES

Cash Flows

Net cash used in operating activities of $1,155,000 in the quarter ended
December 31, 1999 primarily reflects the net loss for the quarter offset by
changes in working capital components and the decrease in deferred income taxes.
The decrease in deferred income taxes in fiscal 2000 is a result of the reversal
of temporary differences due to depreciation and recognition of net operating
loss carryback.

Net cash used in investing activities in the first quarter of fiscal 2000 is
consistent with the same period of the prior year representing management of
short-term investments and severely limited capital expenditures.

The cash flows provided by financing activities for the first quarter of fiscal
2000 represent the proceeds from the exercise of a stock option.

Capital Expenditures

The Company continually strives to supply market demand with technologically
advanced 3-D data acquisition recording systems and leading edge data processing
capabilities. Capital expenditures for fiscal 1999 were minimal in comparison to
the capital expansion effort in fiscal 1998 and the five prior fiscal years.
Depreciation



                                       -9-
<PAGE>   10

increased each fiscal year through 1999 as a new crew as well as additions and
replacements of cables and geophones, vehicles, and other data acquisition
peripheral equipment has been placed into service each year for the past several
years. Depreciation for fiscal 2000 is expected to be less than in fiscal 1999
due to the restricted capital expenditures of fiscal 1999. The Company will
maintain equipment in and out of service in anticipation of increased future
demand of the Company's services.


Capital Resources

The Company believes that its capital resources including its short-term
investments and cash flow from operations are adequate to meet its current
operational needs and finance capital needs as determined by market demand and
technological developments.

LITIGATION

The Company is a defendant in two lawsuits relating to a July 1995 accident
involving a van owned by the Company in which four Company employees died. The
Company believes that it has meritorious defenses to the claims asserted against
it in such suits. Further, while the plaintiffs seek damages in excess of the
Company's liability insurance policies, the Company believes that its liability
insurance should provide adequate coverage of the damages, if any, which may
be assessed against the Company in such litigation. 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 Company's liability insurance
to cover any such damages. A judgment awarding plaintiffs an amount
significantly exceeding the Company's available insurance coverage could have a
material adverse effect on the Company's financial condition, results of
operations and liquidity.

YEAR 2000

Though the Company has not experienced adverse effects attributable to the year
2000, it continues to monitor for the possibility of disruptions.

The Company utilizes software and technologies throughout its operations that
may be vulnerable to the date change to the year 2000. Identification,
assessment, and in some cases, replacement of equipment that may have been
affected by the year 2000 has been accomplished. Remediation was complete by
December 1, 1999 in those instances in which a problem was identified. Software
controlled by the Company, including its proprietary seismic processing package,
has been tested successfully. Replacements and upgrades have not been
accelerated by the year 2000 issue and do not represent costs in addition to
normal operating expenditures. The Company has completed communications with its
significant suppliers to determine if those parties have appropriate plans to
remedy year 2000 issues when their systems interface with the Company's systems
or may otherwise impact the operations of the Company. However, there can be no
guarantee that the systems of other companies, on which the Company's systems
rely, will be timely converted or that a failure to convert by another company
or a conversion that is incompatible with the Company's systems would not have a
material adverse effect on the Company. Assessment continued throughout the
first quarter of fiscal 2000, with an additional cost of approximately $10,000.
Although the Company is not aware of any material operational issues, there can
be no assurance

                                      -10-

<PAGE>   11


that there will not be a delay in, or increased costs associated with, the
implementation of the necessary systems and changes to address the year 2000. A
potential source of risk includes, but is not limited to, the inability of
principal suppliers to be year 2000 compliant, which could result in an
interruption of the Company's services. The Company currently does not have a
formal contingency plan. If unforeseen problems are encountered that relate to
the year 2000, possible solutions will be evaluated and the most efficient will
be enacted such as converting to manual operations until the problems are
remedied.

The failure to correct a material year 2000 problem could result in an
interruption in, or a failure of, certain normal business activities or
operations that could materially and adversely affect the Company's operations,
liquidity and financial condition. Because of the uncertainty surrounding year
2000 issues, primarily those associated with third party suppliers, the Company
is unable to determine at this time whether year 2000 failures will have a
material impact on operations. However, the Company's remediation efforts are
expected to reduce the risk of year 2000 issues significantly, particularly
regarding the compliance and readiness of material vendors and suppliers. The
Company believes that the timely completion of its remediation efforts will
reduce the possibility of significant interruptions of normal business
operations.


Item 3. Quantitative and Qualitative Disclosure 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 December 31, 1999 the Company had no indebtedness and in
addition the Company's short-term investments were fixed-rate and, therefore, do
not expose the Company to significant risk of earnings or cash flow loss due to
changes in market interest rate. 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.



                                      -11-


<PAGE>   12
                                    SIGNATURE




                              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, thereunto duly authorized.


                                   DAWSON GEOPHYSICAL COMPANY
                                   --------------------------
                                   (REGISTRANT)


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



                                   /s/ Christina W. Hagan
                                   --------------------------------------
                                   Christina W. Hagan
                                   Chief Financial Officer



DATE:   February 2, 2000






                                      -12-
<PAGE>   13


                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>

Exhibit
Number                             Description
------                             -----------
<S>                                <C>

27                                 Financial Data Schedule
</TABLE>