<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, 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    March 31, 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
   incorporation or organization)                      Identification No.)

   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.

            CLASS                              Outstanding at March 31, 1997
---------------------------------             ---------------------------------
Common Stock, $.33 1/3 par value                       4,199,150 shares


                                       -1-
<PAGE>   2
                        DAWSON GEOPHYSICAL COMPANY

                                   INDEX


<TABLE>
<CAPTION>
                                                                       Page No.
                                                                       --------
<S>                                                                     <C>
Part I.  Financial Information:

         Statements of Operations --
             Three Months and Six Months
             ended March 31, 1997 and 1996                                3

         Balance Sheets --
             March 31, 1997 and September 30, 1996                        4

         Statements of Cash Flows --
             Six Months Ended March 31, 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              Six Months Ended
                                                     March 31                        March 31
                                           ----------------------------    ----------------------------
                                               1997           1996             1997            1996
                                           ------------    ------------    ------------    ------------
<S>                                        <C>             <C>             <C>             <C>         
Operating revenues                         $ 11,721,000    $  8,572,000    $ 21,784,000    $ 15,930,000

Operating costs:
    Operating expenses                        7,913,000       5,935,000      14,713,000      11,554,000
    General and administrative                  346,000         355,000         666,000         738,000
    Depreciation                              1,906,000       1,351,000       3,771,000       2,651,000
                                           ------------    ------------    ------------    ------------
                                             10,165,000       7,641,000      19,150,000      14,943,000
                                           ------------    ------------    ------------    ------------
Income from operations                        1,556,000         931,000       2,634,000         987,000

Other income (expense):
   Interest income                               56,000          55,000          81,000         112,000
   Interest expense                            (112,000)           --          (230,000)           --
   Gain on disposal of assets                   175,000           2,000         193,000           9,000
   Other income                                   1,000            --             9,000            --
                                           ------------    ------------    ------------    ------------

Income before income tax                      1,676,000         988,000       2,687,000       1,108,000

Income tax expense:
   Current                                     (413,000)       (162,000)       (600,000)       (297,000)
   Deferred                                    (173,000)       (196,000)       (340,000)       (104,000)
                                           ------------    ------------    ------------    ------------
                                               (586,000)       (358,000)       (940,000)       (401,000)
                                           ------------    ------------    ------------    ------------

Net income                                 $  1,090,000    $    630,000    $  1,747,000    $    707,000
                                           ============    ============    ============    ============
Net income per common share                $        .26    $        .15    $        .42    $        .17
                                           ============    ============    ============    ============
Weighted average equivalent shares
    outstanding                               4,186,920       4,195,111       4,177,204       4,200,333
                                           ============    ============    ============    ============
</TABLE>


See accompanying notes to the financial statements.







                                        -3-
<PAGE>   4
                            DAWSON GEOPHYSICAL COMPANY

                                  BALANCE SHEETS

<TABLE>
<CAPTION>
                                                      March 31, 1997     September 30,1996
                                                      --------------     -----------------
                                                       (UNAUDITED)
<S>                                                   <C>                  <C>          
ASSETS 
Current assets: 
   Cash and cash equivalents                          $  1,249,000         $   1,493,000
   Marketable securities                                 3,632,000               988,000
   Accounts receivable                                   7,240,000             6,161,000
   Income taxes receivable                                    --                 193,000
   Prepaid expenses                                        277,000               148,000
                                                      ------------         -------------
           Total current assets                         12,398,000             8,983,000
                                                      ------------         -------------

Property, plant and equipment                           54,396,000            56,368,000
   Less accumulated depreciation                       (23,697,000)          (23,442,000)
                                                      ------------         -------------
         Net property, plant and equipment              30,699,000            32,926,000
                                                      ------------         -------------
                                                      $ 43,097,000         $  41,909,000
                                                      ============         =============

LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
  Current maturities of long-term debt                $    857,000         $     857,000
   Accounts payable                                      1,197,000             2,079,000
   Accrued liabilities:
      Payroll and other taxes                              611,000               560,000
     Income taxes payable                                  162,000                  --
      Other                                                174,000               144,000
                                                      ------------         -------------
           Total current liabilities                     3,001,000             3,640,000
                                                      ------------         -------------
Long-term debt, less current maturities                  4,429,000             4,857,000

Deferred income taxes                                      948,000               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                                    16,148,000            14,401,000
                                                      ------------         -------------
           Total stockholders' equity                   34,719,000            32,804,000
                                                      ------------         -------------
                                                      $ 43,097,000         $  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>
                                                                 Six Months Ended
                                                                     March 31
                                                           ----------------------------
                                                               1997           1996
                                                           ------------    ------------
<S>                                                        <C>             <C>         
Cash flows from operating activities:
     Net income                                            $  1,747,000    $    707,000
     Adjustments to reconcile net income
       to net cash provided by operating
       activities:
     Depreciation                                             3,771,000       2,651,000
      Gain on disposal of assets                               (193,000)         (9,000)
     Other                                                        2,000         (57,000)
     Deferred income taxe expense                               340,000         104,000
      Change in current assets and liabilities:
       Increase in accounts receivable                       (1,079,000)     (1,107,000)
        Decrease (increase) in prepaid expenses                (129,000)        227,000
        Decrease (increase) in income taxes receivable          193,000        (109,000)
       Decrease in accounts payable                            (882,000)       (169,000)
        Increase in accrued liabilities                          81,000         113,000
       Increase in federal and state income
          taxes payable                                         162,000            --
                                                           ------------    ------------
Net cash provided by operating activities                     4,013,000       2,351,000
                                                           ------------    ------------
Cash flows from investing activities:
     Proceeds from disposal of assets                           285,000          31,000
      Capital expenditures                                   (1,636,000)     (3,443,000)
      Proceeds from sale of marketable securities               742,000         745,000
     Investment in marketable securities                     (3,377,000)           --
                                                           ------------    ------------
Net cash used in investing activities                        (3,986,000)     (2,667,000)
                                                           ------------    ------------
Cash flows from financing activities:
     Principal payments on debt                                (428,000)           --
     Proceeds from exercise of stock options                    157,000            --
                                                           ------------    ------------
Net cash used in financing activities                          (271,000)           --
                                                           ------------    ------------
Net decrease in cash and cash equivalents                      (244,000)       (316,000)

Cash and cash equivalents at beginning of period              1,493,000       1,671,000
                                                           ------------    ------------
Cash and cash equivalents at end of period                 $  1,249,000    $  1,355,000
                                                           ============    ============
</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 six
months ended March 31, 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 March 31,
1997). The term note requires monthly principal and interest payments.

The Company is negotiating with a bank to amend the loan agreement of April 1,
1996. 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.



                                      -6-



<PAGE>   7

3.   CONTINGENCIES

On July 1, 1995, an accident involving an automobile owned by the Company
claimed the lives of four employees. The Company is a defendant in a lawsuit by
the families of two of the employees whose deaths resulted from the accident.
The families filed suit against the Company under the gross negligence
provisions of the Texas Workers' Compensation Act. Accordingly, the Company
believes its exposure is limited to claimed exemplary damages of $36 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
this suit. However, the Company believes, based on knowledge of the facts to
date and consultation with its legal advisors, that liabilities, if any, from
this suit 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

The Company's performance for the quarter ended March 31, 1997 set records for
revenues, income from operations and net income.  The results of the six month
period ended March 31, 1997 as compared to the same period of the prior year,
reflect the benefit of five operating crews versus four and improved conditions
with regard to weather and permit problems.

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 six months 1997 totaled
$21,784,000 versus $15,930,000 for the same period of fiscal 1996, an increase
of 36.7%.  For the three months ended March 31, 1997, operating revenues
increased $3,149,000 or 36.7%.  During the third quarter of fiscal 1996, the
Company's capacity increased from four to five crews.  In addition the revenues
of the first quarter of fiscal 1996 were negatively impacted by inclement
weather and permit problems.  The Company believes that the revenues of the
quarter ended March 31, 1997 are indicative of a level of operations that may
be sustained for the remainder of fiscal 1997 based on continued demand, the
current complement of equipment, favorable weather, and other factors.  Minimal
revenues were generated through the acquisition and processing of 2-D seismic
data.

Operating expenses for the six months ended March 31, 1997 totaled $14,713,000,
an increase of $3,159,000, or 27.3%, over the same period of fiscal 1996.  For
the quarter ended March 31, 1997, operating expenses increased $1,978,000, or
33.3%. 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.

General and administrative expenses for the six months ended March 31, 1997
totaled $666,000,  a decrease of $72,000 from the same period of fiscal 1996.
For the quarter ended March 31, 1997, general and administrative expenses
totaled $346,000, a decrease of


                                      -8-
<PAGE>   9




$9,000 over the same period of fiscal 1996.  The decrease 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 six months
ended March 31, 1997 versus 4.6% of operating revenues for the same period of
the prior year.

Depreciation for the six months ended March 31, 1997 totaled $3,771,000, an
increase of $1,120,000 from the same period of fiscal 1996.  For the quarter
ended March 31, 1997, depreciation increased $555,000, or 41.1%.  Depreciation
increased as a result of the capital expansion discussed below in "Liquidity
and Capital Resources".

Total operating costs for the first six months of fiscal 1997 totaled
$19,150,000, an increase of 28.2%, over the first six months of fiscal 1996 due
to the factors described above.  Income from operations increased to
$2,634,000, 12.1% of revenues, from $987,000, 6.2% of revenues, in the
comparable six month period of the prior year.  For the quarter ended March 31,
1997, income from operations is 13.3% of operating revenues as compared to
10.9% 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

Net cash provided by operating activities increased to $4,013,000 for the six
months ended March 31, 1997 from $2,351,000 for the same period of the prior
year due to the increase in net income to $1,747,000 from $707,000 and the
increase in depreciation combined with fluctuations in working capital
components.

Net cash used in investing activities increased to $3,986,000 for the first six
months of fiscal 1997 from $2,667,000 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.

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.


                                      -9-
<PAGE>   10
   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.

Capital expenditures of $1,636,000 for the six months ended March 31, 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 currently assessing the market and anticipating the introduction
of pending developments as announced by an instrument supplier.  The Company's
next major expansion may be influenced by an evaluation of this new seismic
instrumentation.

   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 Company is finalizing negotiations with a bank to amend the loan agreement
of April 1, 1996.  The amendment to the loan agreement is expected 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.

   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
                                             Treasurer, Chief Financial Officer



DATE:      May 9, 1997
     ---------------------



                                      -11-
<PAGE>   12
                              INDEX TO EXHIBITS


EXHIBIT
NUMBER          DESCRIPTION
-------         -----------
 27             Financial Data Schedule