<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, 2000
                                               -----------------

                                       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, 2000       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, 2000  .
 --------------------------------            ----------------------------------
 Common Stock, $.33 1/3 par value                      5,445,794 shares


<PAGE>   2

                           DAWSON GEOPHYSICAL COMPANY

                                      INDEX

<TABLE>
<CAPTION>
                                                                                       Page No.
                                                                                       --------
<S>                                                                                   <C>

Part I.           Financial Information:

Item I.  Financial Statements

                  Statements of Operations --
                        Three Months Ended December 31,
                        2000 and 1999                                                       3

                  Balance Sheets --
                        December 31, 2000 and September 30,
                        2000                                                                4

                  Statements of Cash Flows --
                        Three Months Ended December 31,
                        2000 and 1999                                                       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                                                   10

Part II.          Other Information                                                         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
                                             ------------------------------
                                                 2000              1999
                                             ------------      ------------

<S>                                          <C>               <C>
Operating revenues                           $  6,349,000      $  4,893,000

Operating costs:
    Operating expenses                          7,056,000         5,530,000
    General and administrative                    447,000           763,000
    Depreciation                                2,331,000         2,463,000
                                             ------------      ------------

                                                9,834,000         8,756,000
                                             ------------      ------------
Loss from operations                           (3,485,000)       (3,863,000)

Other income (expense):
     Interest income                              188,000           228,000
     Other                                          4,000                --
     Gain on disposal of assets                     1,000                --
                                             ------------      ------------

Loss before income tax                         (3,292,000)       (3,635,000)

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

Net loss                                     $ (3,292,000)     $ (2,399,000)
                                             ============      ============

Net loss per common share                    $       (.61)     $       (.44)
                                             ============      ============


Weighted average equivalent common
     shares outstanding                         5,433,229         5,414,560
                                             ============      ============
</TABLE>



                                      -3-
<PAGE>   4

                           DAWSON GEOPHYSICAL COMPANY

                                 BALANCE SHEETS

<TABLE>
<CAPTION>
                                                              December 31, 2000  September 30, 2000
                                                              -----------------  ------------------
                                                                 (unaudited)
<S>                                                           <C>                <C>
ASSETS
Current assets:
   Cash and cash equivalents                                     $  1,208,000      $    509,000
   Short-term investments                                          11,018,000        11,025,000
   Accounts receivable, net of allowance
         for doubtful accounts of $226,000
         and $300,000 respectively                                  5,293,000         6,567,000
   Income taxes receivable                                          2,165,000         2,165,000
   Prepaid expenses                                                   203,000           200,000
                                                                 ------------      ------------

           Total current assets                                    19,887,000        20,466,000
                                                                 ------------      ------------

Property, plant and equipment                                      73,194,000        73,132,000
   Less accumulated depreciation                                  (46,121,000)      (43,817,000)
                                                                 ------------      ------------

           Net property, plant and equipment                       27,073,000        29,315,000
                                                                 ------------      ------------

                                                                 $ 46,960,000      $ 49,781,000
                                                                 ============      ============

LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
   Accounts payable                                              $  1,297,000      $  1,038,000
   Accrued liabilities:
      Payroll costs and other taxes                                   395,000           253,000
      Other                                                                --            22,000
                                                                 ------------      ------------

           Total current liabilities                                1,692,000         1,313,000
                                                                 ------------      ------------

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, 5,445,794
           and 5,428,794 issued and outstanding
           respectively                                             1,815,000         1,810,000
   Additional paid-in capital                                      38,711,000        38,624,000
   Retained earnings                                                4,742,000         8,034,000
                                                                 ------------      ------------

           Total stockholders' equity                              45,268,000        48,468,000
                                                                 ------------      ------------

         Contingencies (see note 2)

                                                                 $ 46,960,000      $ 49,781,000
                                                                 ============      ============
</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
                                                                                     ------------------------------
                                                                                         2000              1999
                                                                                     ------------      ------------
<S>                                                                                  <C>               <C>
Cash flows from operating activities:
         Net loss                                                                    $ (3,292,000)     $ (2,399,000)

Adjustments to reconcile net income to net cash provided by (used in) operating
  activities:
         Depreciation                                                                   2,331,000         2,463,000
         Gain on disposal of assets                                                        (1,000)               --
         Non-cash compensation                                                             92,000            99,000
         Deferred income taxes                                                                 --          (509,000)
         Other                                                                              8,000           103,000
         Change in current assets and liabilities:
           Decrease in accounts receivable                                              1,274,000             1,000
           Increase in income taxes receivable                                                 --          (727,000)
           Increase in prepaid expenses                                                    (3,000)         (122,000)
           Increase in accounts payable                                                   259,000           190,000
           Increase (decrease) in accrued
                   liabilities                                                            120,000          (254,000)
                                                                                     ------------      ------------

Net cash provided by (used in)
         operating activities                                                             788,000        (1,155,000)
                                                                                     ------------      ------------

Cash flows from investing activities:
  Proceeds from disposal of assets                                                         (1,000)               --
  Capital expenditures                                                                    (88,000)          (25,000)
  Proceeds from maturity of short-term
         investments                                                                    2,000,000         1,000,000
  Investment in short-term investments                                                 (2,000,000)         (998,000)
                                                                                     ------------      ------------

Net cash used in investing activities                                                     (89,000)          (23,000)
                                                                                     ------------      ------------

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

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

Net increase in cash and cash equivalents                                                 699,000        (1,146,000)

Cash and cash equivalents at beginning
  of period                                                                               509,000         4,993,000
                                                                                     ------------      ------------

Cash and cash equivalents at end of period                                           $  1,208,000      $  3,847,000
                                                                                     ============      ============
</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, 2000, 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. Such
suits are currently pending trial, and the Company's motion for summary judgment
in Cause No. 8812 has been denied. A trial date has been set both in Cause No.
8812 and consolidated Cause No. P5565-83-CV for March 26, 2001. 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 the 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
                                                  ------------------------------
                                                      2000              1999
                                                  ------------      ------------
<S>                                               <C>               <C>

          Numerator:
            Net loss and numerator for basic
              and diluted net income per
              common share-income available
              to common stockholders              $ (3,292,000)     $ (2,399,000)
                                                  ------------      ------------

          Denominator:
            Denominator for basic net loss
              per common share-weighted
              average common shares                  5,433,229         5,414,560
            Effect of dilutive securities-
              employee stock options                        --                --
                                                  ------------      ------------
            Denominator for diluted net
              loss per common share-
              adjusted weighted average
              common shares and assumed
              conversions                            5,433,229         5,414,560
                                                  ------------      ------------

          Net loss per common share               $       (.61)     $       (.44)
                                                  ============      ============

          Net loss per common share-
            assuming dilution                     $       (.61)     $       (.44)
                                                  ============      ============
</TABLE>

     Employee stock options to purchase shares of common stock were outstanding
during fiscal year 2001 and 2000 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

Although crude oil and natural gas prices have led to increased exploration
budgets among our petroleum industry clients, the Company's revenues were
negatively impacted during the quarter ended December 31, 2000 due to
unfavorable weather. Demand for the Company's services is related to crude oil
and natural gas prices; however, there has been a prolonged delay in demand for
geophysical services which has had a negative impact on price recovery.
Accordingly the Company is experiencing some improvement in pricing; however,
during the quarter ended December 31,2000, the Company was completing some
projects that were bid at last year's low rates.

RESULTS OF OPERATIONS

The Company's operating revenues for the first quarter of fiscal 2001 increased
29.8% from $4,893,000 to $6,349,000. Demand for the Company's services has
improved as



                                      -8-
<PAGE>   9

compared to the same quarter of the prior year due to the continuing high prices
for crude oil and natural gas. The Company is beginning to experience some
success in securing improved bid prices; however, revenues for the quarter ended
December 31, 2000, were negatively impacted by unfavorable weather and the
completion of projects that were bid at last year's low rates.

Operating expenses increased 27.6% in the first quarter of fiscal 2001 as
compared to the same period of fiscal 2000 as a result of increased demand for
the Company's services. The Company was operating five crews throughout the
first quarter of fiscal 2001 as compared to four crews throughout the same
quarter of the prior year. While the unfavorable weather experienced in the
quarter ended December 31, 2000 had a negative impact on revenues, the impact
was minimal to operating expenses.

General and administrative expenses for the quarter ended December 31, 2000
totaled $447,000, a decrease of $316,000 from the same period of fiscal 2000.
The decrease primarily consists of a provision for doubtful accounts recognized
during the quarter ended December 31, 1999.

Depreciation for the quarter ended December 31, 2000 totaled $2,331,000, a
decrease of $132,000 from the same period of fiscal 2000. Depreciation decreased
as a result of a suspension of capital expansion during fiscal 1999 and fiscal
2000 due to industry conditions.

Total operating costs for the first quarter of fiscal 2001 totaled $9,834,000,
an increase of 12.3% from the same period of fiscal 2000 due to the factors
described above. The 29.8% increase of revenues as compared to the 12.3%
increase of total operating costs for the first quarter of fiscal 2001 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 price competition in the bidding process for
geophysical services due to the remaining over capacity in our industry.

The Company has no income tax benefit due to the establishment of a valuation
allowance offset by an increase in pretax loss.

LIQUIDITY AND CAPITAL RESOURCES

Cash Flows

Net cash provided by operating activities of $788,000 in the quarter ended
December 31, 2000 primarily reflects the net loss for the quarter offset by
changes in working capital components. 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 2001 is
consistent with the same period of the prior year representing management of
short-term investments and 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.



                                      -9-
<PAGE>   10
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. Depreciation 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 had been placed into service each
year for the past several years. Depreciation for fiscal 2001 is expected to be
less than in fiscal 2000. The Company will maintain equipment in and out of
service in anticipation of increased future demand of the Company's services. In
addition the Company continues to monitor the development of the three component
seismic approach. The Company believes that it is in position to respond to
demand for this technological advancement of the seismic industry.

Capital Resources

The Company believes that its capital resources, including its short-term
investments, cash flow from operations, and relationships with financial
entities, 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.

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, 2000 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.



                                      -10-
<PAGE>   11

Part II.                      OTHER INFORMATION


Item 6.           Exhibits and Reports on Form 8-K

                  (a)      Exhibits

                           The information required by this Item 6(a) is set
                           forth in the Index to Exhibits accompanying this
                           quarterly report and is incorporated herein by
                           reference.

                  (b)      No reports on Form 8-K were filed by the Company
                           during the quarter ended December 31, 2000.



                                      -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
                                             Chief Executive Officer



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



DATE:     January 24, 2001     .
      -------------------------