<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, 1997 
                                                -------------
                                       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, 1997     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)

    208 S. Marienfeld, Midland, Texas                        79701 
 ----------------------------------------                  ----------
 (Address of principal executive offices)                  (Zip Code)

       (Registrant's telephone number, including area code) 915/682-7356
                                                            ------------

                                     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.

<TABLE>
<CAPTION>

            CLASS                       Outstanding at June 30, 1997 
--------------------------------        ----------------------------
<S>                                     <C>
Common Stock, $.33 1/3 par value              4,199,150 shares

</TABLE>


                                      -1-
<PAGE>   2
                           DAWSON GEOPHYSICAL COMPANY

                                     INDEX


<TABLE>
<CAPTION>
                                                          Page No.
                                                          --------
<S>         <C>                                           <C>
Part I.     Financial Information:                         
                                                           
            Statements of Operations --                    
                  Three Months and Nine Months             
                  ended June 30, 1997 and 1996                 3
                                                           
            Balance Sheets --                              
                  June 30, 1997 and September 30,          
                  1996                                         4
                                                           
            Statements of Cash Flows --                    
                  Nine Months Ended June 30, 1997          
                  and 1996                                     5
                                                           
            Notes to Financial Statements                      6
                                                           
            Management's Discussion and Analysis of        
                  Financial Condition and Results of       
                  Operations                                   8
                                                           
                                                           
Part II.    Other Information                              
</TABLE>                                                   





                                      -2-
<PAGE>   3
                         PART I. FINANCIAL INFORMATION

                           DAWSON GEOPHYSICAL COMPANY

                            STATEMENTS OF OPERATIONS
                                  (UNAUDITED)

<TABLE>
<CAPTION>
                                                      Three Months Ended                     Nine Months Ended
                                                          June 30                                June 30 
                                              -------------------------------         ------------------------------
                                                 1997                 1996               1997               1996 
                                              -----------          ----------         -----------        -----------
<S>                                           <C>                  <C>                <C>                <C>
Operating revenues                            $12,520,000          $8,555,000         $34,304,000        $24,485,000
Operating costs:
    Operating expenses                          8,127,000           6,059,000          22,840,000         17,613,000
    General and administrative                    386,000             293,000           1,052,000          1,031,000
    Depreciation                                1,685,000           1,453,000           5,456,000          4,104,000
                                              -----------          ----------         -----------        -----------
                                               10,198,000           7,805,000          29,348,000         22,748,000
                                              -----------          ----------         -----------        -----------

Income from operations                          2,322,000             750,000           4,956,000          1,737,000

Other income (expense):
      Interest income                              86,000              75,000             167,000            187,000
      Interest expense                           (111,000)            (26,000)           (341,000)           (26,000)
      Gain on disposal of assets                    3,000                 --              196,000              9,000
      Other income                                  6,000               1,000              15,000              1,000
                                              -----------          ----------         -----------        -----------

Income before income tax                        2,306,000             800,000           4,993,000          1,908,000

Income tax expense:
      Current                                    (622,000)            (76,000)         (1,222,000)          (373,000)
      Deferred                                   (183,000)           (210,000)           (523,000)          (314,000)
                                              -----------          ----------         -----------        -----------
                                                 (805,000)           (286,000)         (1,745,000)          (687,000)
                                              -----------          ----------         -----------        -----------

Net income                                    $ 1,501,000          $  514,000         $ 3,248,000        $ 1,221,000
                                              ===========          ==========         ===========        ===========

Net income per common share                          $.36                $.12                $.78               $.29
                                                     ====                ====                ====               ====
Weighted average equivalent shares
 outstanding                                    4,216,545           4,204,912           4,190,713          4,197,520
                                              ===========          ==========         ===========        ===========
</TABLE>


See accompanying notes to the financial statements.


                                      -3-
<PAGE>   4

                           DAWSON GEOPHYSICAL COMPANY

                                 BALANCE SHEETS


<TABLE>
<CAPTION>
                                                                      June 30, 1997                 September 30,1996
                                                                      -------------                 -----------------
                                                                       (UNAUDITED)
<S>                                                                   <C>                               <C>
ASSETS
Current assets:
     Cash and cash equivalents                                         $ 2,645,000                       $ 1,493,000
     Marketable securities                                               3,680,000                           988,000
     Accounts receivable                                                 8,454,000                         6,161,000
     Income taxes receivable                                                    --                           193,000
     Prepaid expenses                                                      293,000                           148,000
                                                                       -----------                       -----------

         Total current assets                                           15,072,000                         8,983,000
                                                                       -----------                       -----------


Property, plant and equipment                                           55,225,000                        56,368,000
     Less accumulated depreciation                                    (25,550,000)                      (23,442,000)
                                                                       -----------                       -----------

         Net property, plant and equipment                              29,675,000                        32,926,000
                                                                       -----------                       -----------

                                                                       $44,747,000                       $41,909,000
                                                                       ===========                       ===========
LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
     Current maturities of long-term debt                                $ 857,000                         $ 857,000
     Accounts payable                                                    1,560,000                         2,079,000
     Accrued liabilities:
         Payroll and other taxes                                           294,000                           560,000
         Income taxes payable                                              174,000                                --
         Other                                                             297,000                           144,000
                                                                       -----------                       -----------

                 Total current liabilities                               3,182,000                         3,640,000
                                                                       -----------                       -----------
Long-term debt, less current maturities                                  4,214,000                         4,857,000
                                                                       -----------                       -----------

Deferred income taxes                                                    1,131,000                           608,000

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, 4,199,150
         and 4,161,550 shares issued and
         outstanding                                                     1,400,000                         1,387,000
     Additional paid-in capital                                         17,171,000                        17,016,000
     Retained earnings                                                  17,649,000                        14,401,000
                                                                       -----------                       -----------

         Total stockholders' equity                                     36,220,000                        32,804,000
                                                                       -----------                       -----------

                                                                       $44,747,000                       $41,909,000
                                                                       ===========                       ===========
</TABLE>

Contingencies (See Note 3)

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
                                                                               -----------------------------------
                                                                                  1997                    1996 
                                                                               ----------               ----------
<S>                                                                          <C>                      <C>
Cash flows from operating activities:                                                          
         Net income                                                            $3,248,000               $1,221,000
                                                                                               
         Adjustments to reconcile net income to net cash                                       
            provided by operating activities:                                                  
         Depreciation                                                           5,456,000                4,104,000
         Gain on disposal of assets                                              (196,000)                  (9,000)
         Other                                                                     (3,000)                 (82,000)
         Deferred income tax expense                                              523,000                  314,000
         Change in current assets and liabilities:                                             
            Increase in accounts receivable                                    (2,293,000)                (613,000)
            Decrease (increase) in prepaid expenses                              (145,000)                  13,000
            Decrease (increase) in income taxes receivable                        193,000                 (285,000)
            Increase (decrease) in accounts payable                              (519,000)               2,163,000
            Increase (decrease) in accrued liabilities                           (113,000)                  22,000
            Increase in federal and state income                                               
                 taxes payable                                                    174,000                       -- 
                                                                               ----------               ----------
                                                                                               
Net cash provided by operating activities                                       6,325,000                6,848,000
                                                                               ----------               ----------
                                                                                               
Cash flows from investing activities:                                                          
         Proceeds from disposal of assets                                         288,000                   31,000
         Capital expenditures                                                  (2,340,000)             (10,490,000)
         Proceeds from sale and maturity of                                                    
                 marketable securities                                            742,000                2,845,000
         Investment in marketable securities                                   (3,377,000)              (2,096,000)
                                                                               ----------               ----------
                                                                                               
Net cash used in investing activities                                          (4,687,000)              (9,710,000)
                                                                               ----------               ----------
Cash flows from financing activities:                                                          
         Principal payments on debt                                              (643,000)                 (71,000)
         Proceeds from debt                                                            --                3,854,000
         Proceeds from exercise of stock options                                  157,000                   52,000
                                                                               ----------               ----------
Net cash provided (used) by financing activities                                 (486,000)               3,835,000
                                                                               ----------               ----------
Net increase in cash and cash equivalents                                       1,152,000                  973,000
                                                                                               
Cash and cash equivalents at beginning of period                                1,493,000                1,671,000
                                                                               ----------               ----------
Cash and cash equivalents at end of period                                     $2,645,000               $2,644,000
                                                                               ==========               ==========
</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
period presented. The results of operations for the three months and the nine
months ended June 30, 1997, are not necessarily indicative of the results to be
expected for the fiscal year.

2.       NOTES PAYABLE

As of April 1, 1996, two notes payable exist under a loan agreement with a
bank. The loan agreement consists of (1) a revolving line of credit of
$5,000,000 which matured April 15, 1997 with funding availability determined by
a borrowing base calculation; and (2) a term note of $6,000,000 to mature March
15, 2003. Both notes are secured by eligible accounts receivable and equipment
purchased from loan proceeds. The loan agreement contains various restrictive
covenants and compliance requirements. Among others, the agreement requires
that no liens exist upon any of the collateral nor any vehicle owned by the
Company. The notes bear interest at the bank's prime rate (8.50% at June 30,
1997). The term note requires monthly principal and interest payments.

In May 1997, the Company amended the April 1, 1996 loan agreement with a bank.
The amendment to the loan agreement includes: (1) a renewal and increase of the
principal amount of the revolving line of credit to $6,000,000 with a maturity
date of April 15, 1999; and (2) an additional six year term facility for the
purchase of capital equipment of $5,000,000.

During fiscal 1996, the Company was advanced $6,000,000 on the term note for
the purchase of capital equipment. For the fiscal years 1997 through 2002, the
annual maturity is $857,000, and for fiscal 2003 the balance will be due. The
Company did not utilize the revolving line of credit which expired April 15,
1997 and has not utilized the existing line of credit.

3.       CONTINGENCIES

On July 1, 1995, an accident involving an automobile owned by the Company
claimed the



                                      -6-
<PAGE>   7
lives of four employees. The Company is a defendant in two lawsuits by a
brother individually and the families of four of the employees whose deaths
resulted from the accident. The parties filed suit against the Company under
the negligence and/or gross negligence provisions of the Texas Workers'
Compensation Act. Accordingly, based on currently filed pleadings, the Company
believes its exposure is limited to claimed exemplary damages up to $23
million. The litigation is currently in the discovery stage. The Company has
approximately $12 million of insurance coverage available to provide against an
unfavorable outcome in this matter. Due to the uncertainties inherent in
litigation, no absolute assurance can be given as to the ultimate outcome of
these suits. However, the Company believes, based on knowledge of the facts to
date and consultation with its legal advisors, that liabilities, if any, from
these suits should not have a material adverse effect on the Company's
financial position.

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 operations, as
the Company believes it is adequately insured.


                                      -7-
<PAGE>   8


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

OVERVIEW

Through three quarters of fiscal 1997, the Company has reported quarterly
income from operations to revenues of 14.4% as compared to 7.1% for the same
period of the prior year. The Company's performance in fiscal 1997 is
indicative of the operational potential of our five fully complemented crews,
demand, and mostly favorable weather. The Company is preparing to place a sixth
crew into service which will be equipped with a 2,000 channel Input/Output
System Two remote seismic recording system.

Certain statements contained herein constitute "forward-looking statements"
within the meaning of the Private Securities Litigation Reform Act of 1995.
Such forward-looking statements involve known and unknown risks, uncertainties,
and other factors which may cause the actual results, performance, or
achievements of the Company to be materially different from any future results,
performance, or achievements expressed or implied by such forward-looking
statements. Such factors include, among others, the following: weather, the
volatility of oil and gas prices, and the availability of capital resources.

RESULTS OF OPERATIONS

The Company's operating revenues for the first nine months of 1997 totaled
$34,304,000 versus $24,485,000 for the same period of fiscal 1996, an increase
of 40.1%. For the three months ended June 30, 1997, operating revenues
increased $3,965,000 or 46.3%. The increase in revenues is primarily due to
increased capacity and improved efficiency resulting from fiscal 1996 capital
expenditures. The fiscal 1996 capital expenditures consisted of the addition of
a fifth crew in the third quarter combined with additional channel capacity of
the existing crews and additional energy source units.  The Company believes
that the revenues of the quarter ended June 30, 1997 are indicative of the
level of operations that may be sustained for the remainder of fiscal 1997 and
for 1998 based on continued demand, equipment capacity, favorable weather, and
other factors. Minimal revenues were generated through the acquisition and
processing of 2-D seismic data.

Operating expenses for the nine months ended June 30, 1997 totaled $22,840,000,
an increase of $5,227,000, or 29.7%, over the same period of fiscal 1996. For
the quarter ended June 30, 1997, operating expenses increased $2,068,000, or
34.1%. Operating expenses increased primarily as a result of increased
personnel and other expenses associated with the equipment acquisitions and
technological upgrades made primarily during the third quarter of fiscal 1996.
The quarter ended June 30, 1997 also contains start up expenses for the new
crew to be fielded in August 1997.

General and administrative expenses for the nine months ended June 30, 1997
totaled $1,052,000, an increase of $21,000 from the same period of fiscal 1996.
For the quarter

                                      -8-
<PAGE>   9
ended June 30, 1997, general and administrative expenses totaled $386,000, an
increase of $93,000 over the same period of fiscal 1996. The increase for
fiscal year 1997 is primarily due to timing adjustments of certain expenses.
General and administrative expenses totaled 3.1% of operating revenues for the
nine months ended June 30, 1997 versus 4.2% of operating revenues for the same
period of the prior year.

Depreciation for the nine months ended June 30, 1997 totaled $5,456,000, an
increase of $1,352,000, or 32.9%, from the same period of fiscal 1996. For the
quarter ended June 30, 1997, depreciation increased $232,000, or 16.0%.
Depreciation increased as a result of the capital expansion discussed below in
"Liquidity and Capital Resources".

Total operating costs for the first nine months of fiscal 1997 totaled
$29,348,000, an increase of 29.0% over the first nine months of fiscal 1996 due
to the factors described above. Income from operations increased to $4,956,000,
14.4% of revenues, from $1,737,000, 7.1% of revenues, in the comparable nine
month period of the prior year. For the quarter ended June 30, 1997, income
from operations is 18.5% of operating revenues as compared to 8.8% in the
comparable quarter of fiscal 1996. This increase is the direct result of the
Company's operating expenses being relatively fixed as compared to revenue
trends. Because of the high proportion of relatively fixed total operating
costs (including personnel costs for active crews and depreciation costs),
income from operations in fiscal 1997 reflects the benefit of efficient
production with steady demand for five crews.

Interest is paid monthly at prime rate on the principal of the term note
described below in "Credit Agreement."

Federal and state income tax expense is calculated at the rates of 35% and 36%
in fiscal years 1997 and 1996, respectively.

LIQUIDITY AND CAPITAL RESOURCES

  Cash Flows

Despite the increase of net income to $3,248,000 in fiscal 1997 versus
$1,221,000 in fiscal 1996, net cash provided by operating activities of
$6,325,000 for the nine months ended June 30, 1997 as compared to $6,848,000
for the same period of the prior year reflects a slight decrease primarily due
to changes in working capital components. The increase in accounts receivable
in fiscal 1997 is the result of increased revenues and all accounts are
considered to be collectible.

Net cash used in investing activities decreased to $4,687,000 for the first
nine months of fiscal 1997 from $9,710,000 in the same period of fiscal 1996.
During the second quarter of fiscal 1997, the Company invested cash generated
from operations in U. S. Treasury instruments. As discussed below in "Capital
Expenditures," the Company is positioning for possible future expansion.

                                      -9-
<PAGE>   10
Net cash used in financing activities primarily reflects principal payments on
debt. As discussed below in "Credit Agreement," the Company is servicing a term
note with monthly principal payments of $71,400.

  Capital Expenditures

Capital expenditures of $15,597,000 during fiscal year 1996 in addition to
capital expenditures during fiscal 1995 and 1994 have positioned the Company to
supply market demand with technologically advanced 3-D data acquisition
recording systems and leading edge data processing capabilities. Depreciation
has increased as a new crew has been placed into service each year for the past
several years. During fiscal 1997, some 3-D equipment became fully depreciated.

Capital expenditures of $2,340,000 for the nine months ended June 30, 1997
include additions and replacements to the myriad of cables and geophones,
enhancements to the surveying operation, and additions in support of quality
control and operational safety efforts. The capital expenditures to date in
fiscal 1997 illustrate an opportunity to examine and fine tune various areas of
operation after several years of aggressive expansion.

The Company is in the process of placing a sixth crew into service. It is
anticipated that it will be operational during August 1997. The cost of the new
crew equipped with a 2,000 channel Input/Output System Two remote seismic
recording (RSR) system is expected to be approximately $6,000,000 to be
financed as discussed below in "Credit Agreement.".

  Credit Agreement

As of April 1, 1996, the Company has a loan agreement with a bank. The loan
agreement consists of (1) a revolving line of credit of $5,000,000 which
matured April 15, 1997 and (2) a term note of $6,000,000 to mature March 15,
2003. Both notes are secured by eligible accounts receivable and equipment
purchased from loan proceeds. The term note was fully advanced during fiscal
1996 and no advances were made on the line of credit that matured April 15,
1997.

The loan agreement of April 1, 1996 was amended in May 1997 to include a
renewal and increase of the principal amount of the revolving line of credit to
$6,000,000 with a maturity date of April 15, 1999, and an additional six year
term facility for the purchase of capital equipment of $5,000,000. The term
facility and working capital will be utilized to finance the equipment to be
placed into service in August 1997.

  Capital Resources

The Company believes that its capital resources, including the availability of
bank borrowings, and cash flow from operations are adequate to meet its current
operational needs and finance future capital needs as determined by market
demand and technological developments.


                                      -10-
<PAGE>   11





                                  SIGNATURE




                    Pursuant to the requirements of the Securities
                    Exchange Act of 1934, the Registrant has
                    duly caused this report to be signed on its behalf by
                    the undersigned, thereunto duly authorized.


                                          DAWSON GEOPHYSICAL COMPANY
                                          (REGISTRANT)



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



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



DATE: August 6, 1997 




                                      -11-



<PAGE>   12

                              INDEX TO EXHIBITS


EXHIBIT
NUMBER                           DESCRIPTION
-------                          -----------

  10             First Amendment to Loan Agreement

  27             Financial Data Schedule