<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 March 31, 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 March 31, 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 March 31, 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>                                                                  <C>
Part I.           Financial Information:

Item I.  Financial Statements

                  Statements of Operations --
                        Three Months and Six Months
                           ended March 31, 2001 and 2000                                    3

                  Balance Sheets --
                        March 31, 2001 and September 30,
                        2000                                                                4

                  Statements of Cash Flows --
                        Six Months Ended March 31,
                        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                                                       10
Risk


Part II.          Other Information                                                        12
</TABLE>


                                       -2-


<PAGE>   3

                          PART I. FINANCIAL INFORMATION

                           DAWSON GEOPHYSICAL COMPANY

                            STATEMENTS OF OPERATIONS
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                               Three Months Ended               Six Months Ended
                                                     March 31                        March 31
                                           ----------------------------    ---------------------------
                                               2001            2000            2001            2000
                                           ------------    ------------    ------------    -----------
<S>                                        <C>             <C>             <C>             <C>
Operating revenues                         $ 10,071,000    $  4,275,000    $ 16,420,000    $ 9,168,000
                                           ------------    ------------    ------------    -----------
Operating costs:
         Operating expenses                   8,368,000       5,104,000      15,424,000     10,634,000
         General and administrative             469,000         668,000         916,000      1,431,000
         Depreciation                         2,338,000       2,473,000       4,669,000      4,936,000
                                           ------------    ------------    ------------    -----------
                                             11,175,000       8,245,000      21,009,000     17,001,000
                                           ------------    ------------    ------------    -----------
Loss from operations                         (1,104,000)     (3,970,000)     (4,589,000)    (7,833,000)

Other income (expense):

         Interest income                        216,000         235,000         404,000        463,000
         Gain on disposal of assets               2,000              --           3,000             --
         Other income                            10,000           3,000          14,000          3,000
                                           ------------    ------------    ------------    -----------

Loss before income tax                         (876,000)     (3,732,000)     (4,168,000)    (7,367,000)
Income tax benefit                                   --         712,000              --      1,948,000
                                           ------------    ------------    ------------    -----------

Net loss                                   $   (876,000)   $ (3,020,000)   $ (4,168,000)   $(5,419,000)
                                           ============    ============    ============    ===========

Net loss per common share                  $       (.16)   $       (.56)   $      (.77)    $     (1.00)
                                           ============    ============    ===========     ===========


Weighted average equivalent common
    shares outstanding                        5,445,794       5,428,772       5,439,442      5,421,627
                                           ============    ============    ============    ===========
</TABLE>


See accompanying notes to the financial statements.


                                       -3-

<PAGE>   4

                           DAWSON GEOPHYSICAL COMPANY

                                 BALANCE SHEETS

<TABLE>
<CAPTION>
                                                            March 31, 2001   September 30, 2000
                                                            --------------   ------------------
                                                              (unaudited)
<S>                                                         <C>              <C>
ASSETS
Current assets:
   Cash and cash equivalents                                 $  2,046,000      $    509,000
   Short-term investments                                      12,550,000        11,025,000
   Accounts receivable,net of allowance
         for doubtful accounts of $121,000
         and $300,000                                           5,966,000         6,567,000
   Income taxes receivable                                             --         2,165,000
   Prepaid expenses                                               195,000           200,000
                                                             ------------      ------------

           Total current assets                                20,757,000        20,466,000
                                                             ------------      ------------

Property, plant and equipment                                  73,449,000        73,132,000
   Less accumulated depreciation                              (48,403,000)      (43,817,000)
                                                             ------------      ------------

           Net property, plant and equipment                   25,046,000        29,315,000
                                                             ------------      ------------


                                                             $ 45,803,000      $ 49,781,000
                                                             ============      ============

LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
   Accounts payable                                          $  1,066,000      $  1,038,000
   Accrued liabilities:
      Payroll costs and other taxes                               308,000           253,000
      Other                                                        37,000            22,000
                                                             ------------      ------------

           Total current liabilities                            1,411,000         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                                            3,866,000         8,034,000
                                                             ------------      ------------

           Total stockholders' equity                          44,392,000        48,468,000
                                                             ------------      ------------


Contingencies (See Note 2)
                                                             $ 45,803,000      $ 49,781,000
                                                             ============      ============
</TABLE>


See accompanying notes to the financial statements.

                                       -4-


<PAGE>   5


                           DAWSON GEOPHYSICAL COMPANY

                            STATEMENTS OF CASH FLOWS
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                   Six Months Ended
                                                                        March 31
                                                             ----------------------------
                                                                 2001             2000
                                                             -----------      -----------
<S>                                                          <C>              <C>
Cash flows from operating activities:
         Net loss                                            $(4,168,000)     $(5,419,000)

Adjustments to reconcile net income to net cash
  provided by (used in) operating activities:
         Depreciation                                          4,669,000        4,936,000
         Gain on disposal of assets                               (3,000)              --
         Non-cash compensation                                    92,000          101,000
         Deferred income taxes                                        --         (474,000)
         Other                                                    13,000          201,000
         Change in current assets and liabilities:
           Decrease (increase) in accounts
             receivable                                          601,000         (346,000)
           Decrease in prepaid expenses                            5,000          280,000
           Decrease in income taxes receivable
                                                               2,165,000           22,000
           Increase (decrease) in accounts payable                28,000         (370,000)
           Increase (decrease) in accrued
             liabilities                                          70,000         (322,000)
                                                             -----------      -----------

Net cash provided by (used in)
         operating activities                                  3,472,000       (1,391,000)
                                                             -----------      -----------

Cash flows from investing activities:
  Proceeds from disposal of assets                                14,000               --
  Capital expenditures                                          (411,000)        (130,000)
  Proceeds from maturity of short-term
         investments                                           2,000,000        1,000,000
  Investment in short-term investments                        (3,538,000)        (998,000)
                                                             -----------      -----------

Net cash used in investing activities                         (1,935,000)        (128,000)
                                                             -----------      -----------

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                                                  1,537,000       (1,487,000)

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

Cash and cash equivalents at end of period                   $ 2,046,000      $ 3,506,000
                                                             ===========      ===========
</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 six months
ended March 31, 2001, 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. A portion of the
claims has been settled and the balance is subject to court approval of
settlements agreed to by all of the remaining plaintiffs within the limits of
liability insurance coverage applicable to the Company. If the court approves
such settlements said litigation is expected to be dismissed.

         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                   Six Months Ended
                                                     March 31                           March 31
                                            ----------------------------      ----------------------------
                                               2001             2000             2001              2000
                                            -----------      -----------      -----------      -----------
<S>                                         <C>              <C>              <C>              <C>
Numerator:
  Net loss and numerator for basic
    and diluted net income per
    common share-income available
    to common stockholders                  $  (876,000)     $(3,020,000)     $(4,168,000)     $(5,419,000)
                                            -----------      -----------      -----------      -----------

Denominator:
  Denominator for basic net loss
    per common share-weighted
    average common shares                     5,445,794        5,428,772        5,439,442        5,421,627
  Effect of dilutive securities-
    employee stock options                           --               --               --               --
                                            -----------      -----------      -----------      -----------
  Denominator for diluted net
    loss per common share-
    adjusted weighted average
    common shares and assumed
    conversions                               5,445,794        5,428,772        5,439,442        5,421,627
                                            -----------      -----------      -----------      -----------

Net loss per common share                   $      (.16)     $      (.56)     $      (.77)     $     (1.00)
                                            ===========      ===========      ===========      ===========

Net loss per common share-
  assuming dilution                         $      (.16)     $      (.56)     $      (.77)     $     (1.00)
                                            ===========      ===========      ===========      ===========
</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

The Company's results of operations improved significantly during the quarter
ended March 31, 2001 as continued favorable prices of crude oil and natural gas
have sustained increased exploration budgets among our petroleum industry
clients. While capacity remains in the land-based seismic industry, moderate
price recovery has positively impacted the Company's revenues in fiscal 2001.
Conversely, unfavorable weather has been a mitigating factor during the period.
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 six months of fiscal 2001
increased 79.1% to $16,420,000 from $9,168,000 for the same period of fiscal
2000. For the three months ended March 31, 2001, operating revenues totaled
$10,071,000 versus


                                      -8-
<PAGE>   9

$4,275,000 for the same period of fiscal 2000, a 135.6% increase. Demand for the
Company's services has improved as compared to the same quarter of the prior
year due to the continuing high prices for crude oil and natural gas. The
Company is experiencing moderate success in securing improved bid prices as some
of the land based seismic industry's excess capacity is being absorbed. The
Company has operated five crews continually in fiscal 2001 as compared to four
crews until a drop to two in March of the prior fiscal year.

Operating expenses for the six months ended March 31, 2001 totaled $15,424,000,
an increase of 45.1% from the same period of fiscal 2000. For the quarter ended
March 31, 2001, operating expenses totaled $8,368,000 versus $5,104,000 for the
same period of fiscal 2000, a 64% increase. In January 2001 the Company restored
salary reductions that had been enacted in January 1999. While unfavorable
weather had a negative impact on revenues during the first six months of fiscal
2001, the impact was minimal to operating expenses.

General and administrative expenses for the six months ended March 31, 2001
totaled $916,000 as compared to $1,431,000 for the same period of fiscal 2000.
For the quarter ended March 31, 2001, general and administrative expenses
totaled $469,000, a decrease of $199,000 from the same period of fiscal 2000.
The decrease primarily consists of a provision for doubtful accounts recognized
at $60,000 per month during the six months ended March 31, 2000. The Company has
not reserved 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 six months and the three
months ended March 31, 2001 as compared to the same period of the prior year 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 six months of fiscal 2001 were $21,009,000,
an increase of 23.6%, from the same period of fiscal 2000 due to the factors
described above. For the quarter ended March 31, 2001, total operating costs of
$11,175,000 represent a 35.5% increase from the same period of the prior fiscal
year. The 79.1% increase of revenues as compared to the 23.6% increase of total
operating costs for the first six 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.

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 $3,472,000 for the six months ended
March 31, 2001 primarily reflects changes in working capital components as
depreciation more than offset the net loss for the period. 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


                                      -9-
<PAGE>   10

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 six months of fiscal 2001
represents management of short-term investments and limited capital
expenditures. Proceeds from and investment in short-term investments at March
31, 2001 reflects a timing difference between the purchase of a treasury note
and settlement of the maturing instrument it 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 six 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 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. A
portion of the claims have been settled and the balance is subject to court
approval of settlements agreed to by all of the remaining plaintiffs within the
limits of liability insurance coverage applicable to the Company. If the court
approves such settlements said litigation is expected to be dismissed.


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 March 31, 2001 the Company had no indebtedness and in addition
the Company's


                                      -10-
<PAGE>   11

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


Part II. OTHER INFORMATION

Item 6. Exhibits and Reports on Form 8-K

                  (a)      Exhibits--None

                  (b)      No reports on Form 8-K were filed by the Company
                           during the quarter ended March 31, 2001.



                                      -12-
<PAGE>   13
                                    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:  April 20, 2001   .
      ------------------



                                      -13-