<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 June 30, 2001

                                       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 June 30, 2001 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 June 30, 2001
              -----                              ----------------------------
Common Stock, $.33 1/3 par value                        5,445,794 shares

                                       -1-





<PAGE>   2
                           DAWSON GEOPHYSICAL COMPANY

                                      INDEX

<Table>
<Caption>
                                                                                       Page No.
                                                                                       --------
<S>                                                                                    <C>
Part I.           Financial Information:

Item 1.           Financial Statements:

                  Statements of Operations --
                        Three Months and Nine Months
                           ended June 30, 2001 and 2000                                     3

                  Balance Sheets --
                        June 30, 2001 and September 30,
                        2000                                                                4

                  Statements of Cash Flows --
                        Nine Months Ended June 30,
                        2001 and 2000                                                       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

Part II.          Other Information                                                        13
</Table>

















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<PAGE>   3


                          PART I. FINANCIAL INFORMATION

                           DAWSON GEOPHYSICAL COMPANY

Item 1.  Financial Statements

                            STATEMENTS OF OPERATIONS
                                   (UNAUDITED)

<Table>
<Caption>
                                                Three Months Ended                   Nine Months Ended
                                                     June 30                              June 30
                                          ------------------------------       -------------------------------

                                              2001              2000              2001                2000
                                          ------------      ------------       ------------       ------------

<S>                                       <C>               <C>                <C>                <C>
Operating revenues                        $ 12,051,000      $  2,712,000       $ 28,471,000       $ 11,880,000
                                          ------------      ------------       ------------       ------------
Operating costs:
         Operating expenses                  9,216,000         4,192,000         24,640,000         14,826,000
         General and administrative            439,000           508,000          1,355,000          1,939,000
         Depreciation                        2,071,000         2,189,000          6,740,000          7,125,000
                                          ------------      ------------       ------------       ------------
                                            11,726,000         6,889,000         32,735,000         23,890,000
                                          ------------      ------------       ------------       ------------

Income (loss) from operations                  325,000        (4,177,000)        (4,264,000)       (12,010,000)

Other income (expense):

         Interest income                       169,000           291,000            573,000            754,000
         Gain (loss) on disposal
          of assets                              5,000            (9,000)             8,000             (9,000)
         Other income                            1,000            38,000             15,000             41,000
                                          ------------      ------------       ------------       ------------

Income (loss) before income tax                500,000        (3,857,000)        (3,668,000)       (11,224,000)

     Income tax benefit                             --           689,000                 --          2,637,000
                                          ------------      ------------       ------------       ------------

Net income (loss)                         $    500,000      $ (3,168,000)      $ (3,668,000)      $ (8,587,000)
                                          ============      ============       ============       ============

Net income (loss) per common share        $        .09      $       (.58)      $       (.67)      $      (1.58)
                                          ============      ============       ============       ============

Net income (loss) per common share--
         assuming dilution                $        .09      $       (.58)      $       (.67)      $      (1.58)
                                          ============      ============       ============       ============

Weighted average equivalent common
    shares outstanding                       5,445,794         5,428,794          5,441,513          5,424,008
                                          ============      ============       ============       ============

Weighted average equivalent common
         shares outstanding--
         assuming dilution                   5,516,671         5,428,794          5,441,513          5,424,008
                                          ============      ============       ============       ============
</Table>


See accompanying notes to the financial statements.





                                      -3-
<PAGE>   4




                           DAWSON GEOPHYSICAL COMPANY

                                 BALANCE SHEETS

<Table>
<Caption>
                                                              June 30, 2001  September 30, 2000
                                                              -------------  ------------------
                                                               (unaudited)

<S>                                                           <C>             <C>
ASSETS
Current assets:
   Cash and cash equivalents                                  $    658,000       $    509,000
   Short-term investments                                       12,967,000         11,025,000
   Accounts receivable, net of allowance for
         doubtful accounts of $121,000
         and $553,000                                            9,622,000          6,567,000
   Income taxes receivable                                              --          2,165,000
   Prepaid expenses                                                314,000            200,000
                                                              ------------       ------------

           Total current assets                                 23,561,000         20,466,000
                                                              ------------       ------------

Property, plant and equipment                                   73,560,000         73,132,000
   Less accumulated depreciation                               (50,396,000)       (43,817,000)
                                                              ------------       ------------

           Net property, plant and equipment                    23,164,000         29,315,000
                                                              ------------       ------------


                                                              $ 46,725,000       $ 49,781,000
                                                              ============       ============

LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
   Accounts payable                                           $  1,258,000       $  1,038,000
   Accrued liabilities:
      Payroll costs and other taxes                                450,000            253,000
      Other                                                        125,000             22,000
                                                              ------------       ------------

           Total current liabilities                             1,833,000          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 shares issued and outstanding
           respectively                                          1,815,000          1,810,000
   Additional paid-in capital                                   38,711,000         38,624,000
   Retained earnings                                             4,366,000          8,034,000
                                                              ------------       ------------

           Total stockholders' equity                           44,892,000         48,468,000
                                                              ------------       ------------

                                                              $ 46,725,000       $ 49,781,000
                                                              ============       ============
</Table>


Contingencies (See Note 2)

See accompanying notes to the financial statements.





                                      -4-
<PAGE>   5

                           DAWSON GEOPHYSICAL COMPANY

                            STATEMENTS OF CASH FLOWS
                                   (UNAUDITED)

<Table>
<Caption>
                                                                 Nine Months Ended
                                                                      June 30
                                                           -----------------------------

                                                               2001              2000
                                                           -----------       -----------
<S>                                                        <C>               <C>
Cash flows from operating activities:
         Net loss                                          $(3,668,000)      $(8,587,000)

Adjustments to reconcile net loss to
   net cash provided by operating activities:
         Depreciation                                        6,740,000         7,125,000
         Loss (gain) on disposal of assets                      (8,000)            9,000
         Non-cash compensation                                  92,000           101,000
         Deferred income taxes                                      --          (645,000)
         Other                                                  31,000           207,000
         Change in current assets and liabilities:
           Decrease (increase) in accounts receivable       (3,055,000)        3,245,000
           Decrease (increase) in prepaid expenses            (114,000)          223,000
           Decrease (increase) in income taxes
                   receivable                                2,165,000          (497,000)
           Increase in accounts payable                        220,000            39,000
           Increase (decrease) in accrued
                   liabilities                                 300,000          (313,000)
                                                           -----------       -----------

Net cash provided by operating activities                    2,703,000           907,000
                                                           -----------       -----------

Cash flows from investing activities:
  Proceeds from disposal of assets                              49,000           110,000
  Capital expenditures                                        (629,000)         (251,000)
  Proceeds from maturity of short-term
         investments                                         3,500,000         2,501,000
  Investment in short-term investments                      (5,474,000)       (2,499,000)
                                                           -----------       -----------

Net cash used in investing activities                       (2,554,000)         (139,000)
                                                           -----------       -----------

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                      149,000           800,000

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

Cash and cash equivalents at end of period                 $   658,000       $ 5,793,000
                                                           ===========       ===========
</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 and the nine
months ended June 30, 2001, are not necessarily indicative of the results to be
expected for the fiscal year.

2.       CONTINGENCIES

         The Company was 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, et al.) relating to a July
1995 accident. This litigation has been settled and terminated within the limits
of the Company's insurance coverage with no direct expense to the Company.

         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.


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              Nine Months Ended
                                                            June 30                           June 30
                                                 ----------------------------       -----------------------------
                                                    2001             2000              2001              2000
                                                 -----------      -----------       -----------       -----------

<S>                                              <C>              <C>               <C>               <C>
Numerator:
  Net income (loss) and numerator for basic
    and diluted net income per
    common share-income available
    to common stockholders                       $   500,000      $(3,168,000)      $(3,668,000)      $(8,587,000)
                                                 -----------      -----------       -----------       -----------

Denominator:
  Denominator for basic net income (loss)
    per common share-weighted
    average common shares                          5,445,794        5,428,794         5,441,513         5,424,008
  Effect of dilutive securities-
    employee stock options                            70,877               --                --                --
                                                 -----------      -----------       -----------       -----------
  Denominator for diluted net income
    (loss) per common share-
    adjusted weighted average
    common shares and assumed
    conversions                                    5,516,671        5,428,794         5,441,513         5,424,008
                                                 -----------      -----------       -----------       -----------

Net income (loss) per common share               $       .09      $      (.58)      $      (.67)      $     (1.58)
                                                 ===========      ===========       ===========       ===========

Net income (loss) per common
  share-assuming dilution                        $       .09      $      (.58)      $      (.67)      $     (1.58)
                                                 ===========      ===========       ===========       ===========
</Table>



                                      -6-
<PAGE>   7



     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

Continued favorable prices of crude oil and natural gas have sustained increased
exploration budgets among our petroleum industry clients, and the Company's
results of operations improved significantly as net income was reported for the
quarter ended June 30, 2001. While excess capacity remains in the land-based
seismic industry, moderate price recovery has positively impacted the Company's
revenues in fiscal 2001. The Company's order book is sufficient to sustain five
of its six data acquisition crews for several months.


RESULTS OF OPERATIONS

The Company's operating revenues for the first nine months of fiscal 2001
increased 139.7% to $28,471,000 from $11,880,000 for the same period of fiscal
2000. For the three months ended June 30, 2001, operating revenues totaled
$12,051,000 versus






                                      -8-
<PAGE>   9

$2,712,000 for the same period of fiscal 2000. Demand for the Company's services
has improved as compared to the prior year due continuing increases in crude oil
and natural gas exploration activity. The Company has experienced moderate
success in securing improved bid prices as some of the land based seismic
industry's excess capacity has been absorbed over the last year. The Company
began fiscal 2000 operating four crews, dropped to two in March, and expanded
from June to August to end the fiscal year operating five crews. The Company has
operated five crews continually in fiscal 2001.

Operating expenses for the nine months ended June 30, 2001 totaled $24,640,000,
an increase of 66.2% from the same period of fiscal 2000. For the quarter ended
June 30, 2001, operating expenses totaled $9,216,000 versus $4,192,000 for the
same period of fiscal 2000. For fiscal 2001, the increases in operating expenses
appear moderate as compared to the increases in operating revenues due to the
relatively fixed nature of certain operating expenses. In January 2001 the
Company restored salary reductions that had been enacted in January 1999.

General and administrative expenses for the nine months ended June 30, 2001
totaled $1,355,000 as compared to $1,939,000 for the same period of fiscal 2000.
For the quarter ended June 30, 2001, general and administrative expenses totaled
$439,000, as compared to $508,000 for the same period of fiscal 2000. The
decrease primarily consists of a decrease in the provision for doubtful accounts
from the prior year. The Company has not made a provision for bad debts in
fiscal 2001 as favorable prices for crude oil and natural gas have correlated to
collectibility of accounts receivable.

Depreciation decreased slightly, about 5%, for the nine months and the three
months ended June 30, 2001 as compared to the same periods of the prior year as
a result of a suspension of capital expansion during fiscal 1999 and fiscal 2001
due to industry conditions. In fiscal 2000 the Company purchased additional data
acquisition channels that became available late in the year as a result of the
idle capacity that exists in our industry.

Total operating costs for the first nine months of fiscal 2001 were $32,735,000,
an increase of 37%, from the same period of fiscal 2000 due to the factors
described above. For the quarter ended June 30, 2001, total operating costs of
$11,726,000 represent a 70.2% increase from the same period of the prior fiscal
year. The 139.7% increase of revenues as compared to the 37% increase of total
operating costs for the first nine months 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.

No income tax expense was recorded for the three months ended June 30, 2001 due
to the pretax loss for the nine months and the loss position anticipated at the
end of fiscal year 2001. The Company has no income tax benefit for the nine
months 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 $2,703,000 for the nine months
ended June





                                      -9-
<PAGE>   10

30, 2001 primarily reflects the net loss offset by depreciation and of 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. The decrease in income taxes
receivable reflects the proceeds received as a result of the carryback generated
by the net operating loss for fiscal 2000.

Net cash used in investing activities in the first nine months of fiscal 2001
represents management of short-term investments and limited capital
expenditures. Proceeds from and investment in short-term investments at June 30,
2001 reflects a timing difference between the purchase of certificates of
deposit and settlement of the maturing instrument being replaced in the
portfolio. The Company's capital expenditures in fiscal 2001 are primarily
replacements to maintain efficient field operations.

The cash flows provided by financing activities for the first nine months 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. 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, which employs two modes of shear wave energy in addition to
the conventional compression wave energy. 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 was a defendant in two lawsuits relating to a July 1995 accident
involving a van owned by the Company in which four Company employees died. This
litigation has been settled and terminated within the limits of the Company's
insurance coverage with no direct expense to the Company.

RECENTLY ANNOUNCED ACCOUNTING PRONOUNCEMENTS

In July 2001, The Financial Accounting Standards Board (FASB) issued Statements
of Financial Accounting Standards No. 141 "Business Combinations" and No. 142



                                      -10-
<PAGE>   11

"Goodwill and Other Intangible Assets." Statement 141 requires that all business
combinations initiated after June 30, 2001 be accounted for under the purchase
method, and Statement 142 requires that goodwill no longer be amortized to
earnings, but instead be reviewed for impairment. As of June 30, 2001 there is
no impact to the Company's financial statements as no business combinations have
been entered into, thus the potential for associated goodwill has not been
acquired.

Also, the FASB has voted to issue Statement No. 143 "Accounting for
Asset-Retirement Obligations" which establishes requirements for the accounting
of removal-type costs associated with asset retirements. The standard is
effective for fiscal years beginning after June 15, 2002, with earlier
application encouraged. As of June 30, 2001, there is no impact to the Company's
financial statements as we have not incurred any obligations associated with
asset retirements.


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 June 30, 2001 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
                                Chief Executive Officer



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



DATE: July 31, 2001





                                      -12-
<PAGE>   13


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 June 30, 2001.









                                      -13-