<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, 1999
                                                 -------------

                                       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, 1999        Commission File number 2-71058
                       -------------                               -------

                           DAWSON GEOPHYSICAL COMPANY
             ------------------------------------------------------
             (Exact name of Registrant as specified in its Charter)

           TEXAS                                          75-0970548
-------------------------------                ---------------------------------
(State or other jurisdiction of                (IRS Employer Identification No.)
incorporation or organization)

508 West Wall, Suite 800, Midland, Texas                      79701
----------------------------------------                    ----------
(Address of principal executive offices)                    (Zip Code)

        (Registrant's telephone number, including area code) 915/684-3000
                                                             ------------

                                      NONE
                                      ----
 (Former Name, Former Address & Former Fiscal Year if changed since last report)

  Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.  Yes X .  No   .
                                              ---     ---

  Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the latest practicable date.

            CLASS                                  Outstanding at June 30, 1999
--------------------------------                   ----------------------------
Common Stock, $.33 1/3 par value                         5,406,794 shares


                                      -1-
<PAGE>   2

                           DAWSON GEOPHYSICAL COMPANY

                                      INDEX

<TABLE>
<CAPTION>

                                                                        PAGE NO.
                                                                        --------
<S>                     <C>                                             <C>
Part I.           Financial Information

    Item 1.       Financial Statements:

                  Statements of Operations --
                        Three Months and Nine Months
                           ended June 30, 1999 and 1998                     3

                  Balance Sheets --
                        June 30, 1999 and September 30,
                        1998                                                4

                  Statements of Cash Flows --
                        Nine Months Ended June 30,
                        1999 and 1998                                       5

                  Notes to Financial Statements                             6

    Item 2.       Management's Discussion and Analysis of
                        Financial Condition and Results of
                        Operations                                          8

    Item 3.       Quantitative and Qualitative Disclosures
                        About Market Risk                                  12

Part II.          Other Information

    Item 6.       Exhibits and Reports on Form 8-K                         13
</TABLE>


                                      -2-
<PAGE>   3

FINANCIAL INFORMATION PART I.

Item 1.   FINANCIAL STATEMENTS

                           DAWSON GEOPHYSICAL COMPANY


                            STATEMENTS OF OPERATIONS
                                   (UNAUDITED)

<TABLE>
<CAPTION>

                                               Three Months Ended          Nine Months Ended
                                                    June 30                     June 30
                                          --------------------------   ------------------------

                                              1999           1998          1999         1998
                                          ----------     -----------   -----------  -----------

<S>                                       <C>            <C>           <C>          <C>
Operating revenues                        $4,575,000     $18,647,000   $18,646,000  $45,991,000

Operating costs:
      Operating expenses                   4,425,000      11,193,000    16,166,000   30,094,000
      General and administrative             610,000         478,000     1,650,000    1,443,000
      Depreciation                         2,631,000       2,461,000     8,040,000    6,816,000
                                          ----------     -----------   -----------  -----------
                                           7,666,000      14,132,000    25,856,000   38,353,000
                                          ----------      ----------   -----------  -----------

Income (loss) from operations             (3,091,000)      4,515,000    (7,210,000)   7,638,000

Other income (expense):

      Interest income                        242,000         209,000       640,000      579,000
      Interest expense                            --              --            --      (125,000)
      Gain (loss) on disposal of assets        2,000          19,000       (10,000)     167,000
      Other                                   (1,000)          5,000        41,000       28,000
                                          ----------     -----------   -----------  -----------

Income (loss) before income tax           (2,848,000)      4,748,000    (6,539,000)   8,287,000

      Income tax benefit (expense):
         Current                            (523,000)     (1,386,000)      938,000   (2,333,000)
         Deferred                          1,481,000        (275,000)    1,276,000     (567,000)
                                          ----------     -----------   -----------  -----------
                                             958,000      (1,661,000)    2,214,000   (2,900,000)
                                          ----------     -----------   -----------  -----------

Net income (loss)                        $(1,890,000)     $3,087,000   $(4,325,000) $ 5,387,000
                                         ===========      ==========   ===========  ===========
Net income (loss) per common share       $      (.35)     $      .58   $      (.80) $      1.05

Net income (loss) per common share-
         assuming dilution               $      (.35)     $      .57   $      (.80) $      1.04
                                         ===========      ==========   ===========  ===========

Weighted average equivalent common
         shares outstanding                5,406,794       5,353,582    5,393,862     5,136,652
                                         ===========      ==========   ==========   ===========

Weighted average equivalent common
         shares outstanding-assuming
         dilution                          5,406,794       5,379,341    5,393,862     5,165,082
                                          ==========     ===========   ==========    ==========
</TABLE>

See accompanying notes to the financial statements.


                                       -3-

<PAGE>   4
                           DAWSON GEOPHYSICAL COMPANY

                                 BALANCE SHEETS
<TABLE>
<CAPTION>

                                                             June 30, 1999         September 30, 1998
                                                            ---------------        ------------------
                                                              (unaudited)
<S>                                                         <C>                        <C>
ASSETS
Current assets:
   Cash and cash equivalents                                $   6,698,000             $  5,745,000
   Short-term investments                                      12,528,000                6,515,000
   Accounts receivable, net of allowance for
         doubtful accounts of $120,000 in
         1999 and none in 1998                                  5,473,000               11,821,000
   Income taxes receivable                                      1,154,000                1,050,000
   Prepaid expenses                                               374,000                  416,000
                                                            -------------             ------------
           Total current assets                                26,227,000               25,547,000
                                                            -------------             ------------
Property, plant and equipment                                  71,744,000               73,584,000
   Less accumulated depreciation                              (33,978,000)             (27,672,000)
                                                            -------------             ------------
           Net property, plant and equipment                   37,766,000               45,912,000
                                                            -------------             ------------

                                                            $  63,993,000             $ 71,459,000
                                                            =============             ============

LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
   Accounts payable                                         $     809,000             $  1,766,000
   Accrued liabilities:
      Payroll costs and other taxes                               278,000                  635,000
      Other                                                         3,000                  810,000
                                                            -------------             ------------
           Total current liabilities                            1,090,000                3,211,000
                                                            -------------             ------------
Deferred income taxes                                           1,330,000                2,606,000

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, 5,406,794
           and 5,361,000 shares issued and outstanding
           in 1999 and 1998, respectively                       1,802,000                1,787,000
   Additional paid-in capital                                  38,497,000               38,256,000
   Retained earnings                                           21,274,000               25,599,000
                                                            -------------             ------------
           Total stockholders' equity                          61,573,000               65,642,000
                                                            -------------             ------------
                                                            $  63,993,000             $ 71,459,000
                                                            =============             ============
</TABLE>

Contingencies (See Note 2)

See accompanying notes to the financial statements.


                                      -4-
<PAGE>   5

                           DAWSON GEOPHYSICAL COMPANY

                            STATEMENTS OF CASH FLOWS
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                                     Nine Months Ended
                                                                                          June 30
                                                                             --------------------------------

                                                                                 1999                1998
                                                                             -----------          -----------
<S>                                                                          <C>                  <C>
Cash flows from operating activities:
Net income (loss)                                                            $(4,325,000)         $ 5,387,000

Adjustments to reconcile net income to net cash provided by operating
  activities:
         Depreciation                                                          8,040,000            6,816,000
         Loss (gain) on disposal of assets                                        10,000             (167,000)
         Non-cash interest income                                                (35,000)             (20,000)
         Non-cash compensation                                                   256,000               11,000
         Deferred income taxes                                                (1,276,000)             567,000
         Provision for losses on trade
           Receivables                                                           120,000                   --
         Other                                                                   248,000              108,000
         Change in current assets and liabilities:
           Decrease (increase) in accounts
             receivable                                                        6,228,000           (4,380,000)
           Decrease (increase) in prepaid expenses                                42,000             (261,000)
         Increase in income taxes receivable                                    (104,000)                  --
           Decrease in accounts payable                                         (957,000)          (2,414,000)
           Decrease in accrued liabilities                                    (1,164,000)            (183,000)
                                                                              ----------          -----------

Net cash provided by operating activities                                      7,083,000            5,464,000
                                                                              ----------          -----------

Cash flows from investing activities:
  Proceeds from disposal of assets                                                24,000              264,000
  Capital expenditures                                                          (147,000)         (17,322,000)
  Proceeds from maturity of short-term
         investments                                                           5,500,000           14,993,000
  Investment in short-term investments                                       (11,507,000)         (17,531,000)
                                                                             -----------          -----------

Net cash used in investing activities                                         (6,130,000)         (19,596,000)
                                                                             -----------          -----------

Cash flows from financing activities:
  Principal payments on debt                                                          --           (9,583,000)
  Proceeds from exercise of stock options                                             --               43,000
  Issuance of common stock                                                            --           21,371,000
                                                                             -----------          -----------

Net cash provided by financing activities                                             --           11,831,000
                                                                             -----------          -----------

Net increase (decrease) in cash and cash
  equivalents                                                                    953,000           (2,301,000)

Cash and cash equivalents at beginning
  of period                                                                    5,745,000            4,774,000
                                                                             -----------          -----------

Cash and cash equivalents at end of period                                   $ 6,698,000          $ 2,473,000
                                                                             ===========          ===========
</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 Dawson Geophysical Company (the "Company"), the accompanying
financial statements reflect all adjustments (consisting only of normal
recurring accruals) necessary for a fair presentation of the financial
condition and results of operations for the periods presented. The results of
operations for the three months and the nine months ended June 30, 1999, 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, et al.) relating to a
July 1995 accident involving a van owned by the Company which was used to
transport employees to various job sites and a non-Company owned vehicle. The
accident resulted in the deaths of four Company employees who were passengers
in such van. The Company is one of several named defendants in such suits.
Other named defendants include the estate of the deceased driver of such van,
who was an employee of the Company, the driver of such non-Company owned
vehicle, who was then an employee of the Company, the owner of such vehicle,
and Ford Motor Company, the manufacturer of the Company van involved in such
accident. In general, the claims against the Company include allegations of
negligence, gross negligence and/or intentional tort as a result of, among
other things, the Company's alleged failure to provide safe transportation for
its employees and to properly select, train and supervise the deceased driver
of such van. The plaintiffs in such suits are seeking actual damages from the
defendants of $15.5 million, additional unspecified actual damages, prejudgment
and post-judgment interest and costs of suit as well as exemplary and punitive
damages in an amount not to exceed four times the amount of actual damages. The
Company believes that it has meritorious defenses to the claims asserted
against it in such suits and it intends to vigorously defend itself against
such claims. In addition, the Company believes that it has approximately $11
million of liability insurance coverage to provide against an unfavorable
outcome. The two suits are currently in the discovery stage and the Company
currently has pending before the court a motion for summary judgment in Cause
No. 8812 requesting that the Company be dismissed from such suit based upon
various legal theories. A hearing for summary judgment was held July 29, 1999.
The court has not yet ruled on the motion for summary judgment. Due to the
uncertainties inherent in litigation, no assurance can be given as to the
ultimate outcome of such suits or the adequacy or availability of the Company's
liability insurance to cover the damages, if any, which may be assessed against
the Company in such suits. A judgment awarding plaintiffs an amount
significantly exceeding the Company's available insurance coverage could have a
material adverse effect on the Company's financial condition, results of
operations and liquidity.



                                      -6-
<PAGE>   7
         The Company is party to other legal actions arising in the ordinary
course of its business, none of which management believes will result in a
material adverse effect on the Company's financial position or results of
operation, as the Company believes it is adequately insured.


3.       NET INCOME PER COMMON SHARE

         The following table sets forth the computation of basic and diluted net
income per common share:

<TABLE>
<CAPTION>
                                                                Three Months Ended               Nine Months Ended
                                                                      June 30                         June 30
                                                           ----------------------------     ---------------------------
                                                               1999            1998            1999            1998
                                                               ----            ----            ----            ----
<S>                                                        <C>              <C>             <C>              <C>
     Numerator:
       Net income (loss) and numerator for basic
         and diluted net income (loss) per
         common share-income available
         to common stockholders                            $(1,890,000)     $ 3,087,000     $(4,325,000)     $5,387,000
                                                           -----------      -----------     -----------      ----------
     Denominator:
       Denominator for basic net income (loss)
         per common share-weighted
         average common shares                               5,406,794        5,353,582       5,393,862       5,136,652
       Effect of dilutive securities-
         employee stock options                                   --             25,759            --            28,430
                                                           -----------      -----------     -----------      ----------
       Denominator for diluted net
         income (loss) per common share-
         adjusted weighted average
         common shares and assumed
         conversions                                         5,406,794        5,379,341       5,393,862       5,165,082
                                                           -----------      -----------     -----------      ----------
     Net income (loss) per common share                    $      (.35)     $       .58     $      (.80)     $     1.05
                                                           ===========      ===========     ===========      ==========
     Net income (loss) per common
       share--assuming dilution                            $      (.35)     $       .57     $      (.80)     $     1.04
                                                           ===========      ===========     ===========      ==========
</TABLE>

         Employee stock options to purchase shares of common stock were
outstanding during fiscal year 1999 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

Item 2.   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 directly relate to oil
and gas exploration and production activity and fluctuations in the Company's
results of operations may occur due to weather, land use permitting and other
factors. Decreases in oil and gas activities have adversely affected the demand
for the Company's services and the Company's results of operations.

All statements other than statements of historical fact included in this report
on Form 10-Q, 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 on Form 10-Q, 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 revenues of the Company continue to be severely impacted although crude oil
prices have recovered relative to earlier this year. Demand for the Company's
services is expected to be directly related to crude oil prices; however, the
Company is prepared for some delay in demand for its services as its clients and
potential clients recover from their losses. The Company has taken cost
reduction measures in response to price


                                       -8-
<PAGE>   9

competition and decreased demand for its services. In addition, the Company has
initiated (for the first time in its forty-seven year history) an allowance for
doubtful accounts. While the Company is pursuing collection of all accounts
receivable, it recognizes that the drop in crude oil prices has had a negative
effect on cash flow for many companies.


Results of Operations

The Company's operating revenues for the first nine months of 1999 totaled
$18,646,000 versus $45,991,000 for the same period of fiscal 1998, a decrease of
59%. For the three months ended June 30, 1999, operating revenues totaled
$4,575,000 versus $18,647,000 for the same period of fiscal 1998, a decrease of
75%. Demand for the Company's services has been negatively impacted by low crude
oil prices. During the quarter ended December 31, 1998, the Company reduced the
number of operating crews from six to three. The Company operated three crews
throughout the quarter ended March 31, 1999. The Company is currently operating
three crews although for a brief period of time during the quarter ended June
30, 1999 the Company operated only one crew. In addition to the decrease in the
number of operating crews, the decrease in revenues reflects severe price
competition.

Operating expenses for the nine months ended June 30, 1999 totaled $16,166,000,
a decrease of 46% from the same period of fiscal 1998. For the comparative
quarters ended June 30, operating expenses decreased from $11,193,000 in 1998 to
$4,425,000 in 1999, or 60%. Operating expenses decreased as a result of
decreased demand for the Company's services. Additional cost reduction measures,
such as employee layoffs and salary reductions, were implemented in January
1999. The Company has reduced the number of employees from 377 at September 30,
1998 to 230 at June 30, 1999. The Company has retained key field personnel in
anticipation of increased demand. In December 1998, the Company received
insurance proceeds of approximately $280,000 for lightning induced damages to
equipment, which occurred and was expensed in fiscal 1997. The insurance
proceeds were recognized as an offset to operating expense in fiscal 1999.

General and administrative expenses for the nine months ended June 30, 1999
totaled $1,650,000, an increase of 14% from the same period of fiscal 1998. For
the quarter ended June 30, 1999, general and administrative expenses totaled
$610,000, an increase of $132,000, or 28%, over the same period of fiscal 1998.
The increase primarily consists of the implementation of an allowance for
doubtful accounts of $120,000 at June 30, 1999. Cost reduction measures were
implemented in January 1999 to contain general and administrative expenses. Rent
expense is also reflected in the nine month period and the quarter ended June
30, 1999 as the office building owned and occupied since 1960 became outgrown,
and the functions performed in that building were moved to a more accommodating,
leased facility in July 1998.


                                       -9-
<PAGE>   10

Depreciation for the nine months ended June 30, 1999 totaled $8,040,000, an
increase of $1,224,000 from the same period of fiscal 1998. For the quarter
ended June 30, 1999, depreciation increased $170,000. Depreciation continued to
increase as a result of capital expansion during fiscal 1998.

Total operating costs for the first nine months of fiscal 1999 totaled
$25,856,000, a decrease of 33%, from the same period of fiscal 1998 due to the
same factors that caused a decrease in operating expenses described above. For
the quarter ended June 30, 1999, operating costs decreased 46%. The 59% decrease
of revenues as compared to the 33% decrease of total operating costs for the
nine months ended June 30, 1999 reflects the high proportion of relatively fixed
total operating costs (including personnel costs of active crews and
depreciation costs) inherent in the Company and fierce price competition in the
bidding process.


Liquidity and Capital Resources

Cash Flows

Net cash provided by operating activities of $7,083,000 for the nine months
ended June 30, 1999 reflects decreases in accounts receivable offset by
decreases in current liabilities which occurred due to reduced revenues and cost
cutting measures. The increase in income taxes receivable in fiscal 1999 is a
result of the Company's recognition of a tax benefit generated by the net loss
for the nine-month period ended June 30, 1999.

Net cash used in investing activities decreased to $6,130,000 from $19,596,000
resulting from significantly decreased capital expenditures in fiscal 1999 as
compared to fiscal 1998.

The cash flows provided by financing activities for the nine month period ended
June 30, 1998 represent the net of the offering proceeds reduced by the
retirement of debt.

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. Capital expenditures for fiscal 1999 are not anticipated to be
material. The Company will maintain equipment in and out of service in
anticipation of increased future demand of the Company's services.


                                      -10-
<PAGE>   11

Capital Resources

The Company believes that its capital resources including its short-term
investments and cash flow from operations are adequate to meet its current
operational needs and finance capital needs as determined by market demand and
technological developments.

Litigation

The Company is a defendant in two lawsuits relating to a July 1995 accident
involving a van owned by the Company in which four Company employees died. The
Company believes that it has meritorious defenses to the claims asserted against
it in such suits. Further, while the plaintiffs seek damages in excess of the
Company's liability insurance policies, the Company believes that its liability
insurance should provide adequate coverage of the damages, if any, which may
be assessed against the Company in such litigation. Due to the uncertainties
inherent in litigation, no assurance can be given as to the ultimate outcome of
such suits or the adequacy or availability of the Company's liability insurance
to cover any such damages. A judgment awarding plaintiffs an amount
significantly exceeding the Company's available insurance coverage could have a
material adverse effect on the Company's financial condition, results of
operations and liquidity.

Year 2000

The Company utilizes software and technologies throughout its operations that
may be vulnerable to the date change in the year 2000. Identification,
assessment, and in some cases, replacement of equipment that may be affected by
the year 2000 is underway. Remediation is expected to be complete by September
1, 1999 in those instances in which a problem has been identified. Software
controlled by the Company, including its propriety seismic processing package,
has been tested successfully. Replacements and upgrades have not been
accelerated by the year 2000 issue and do not represent costs in addition to
normal operating expenditures. The Company has begun communications with its
significant suppliers to determine if those parties have appropriate plans to
remedy year 2000 issues when their systems interface with the Company's systems
or may otherwise impact the operations of the Company. However, there can be no
guarantee that the systems of other companies, on which the Company's systems
rely, will be timely converted or that a failure to convert by another company
or a conversion that is incompatible with the Company's systems would not have a
material adverse effect on the Company. To date, the Company has spent
approximately $30,000 primarily in the assessment of and testing for year 2000
compliance. Assessment will continue throughout fiscal 1999, with an additional
estimated cost of $20,000. Although the Company is not aware of any material
operational issues, there can be no assurance that there will not be a delay in,
or increased costs associated with, the implementation of the necessary systems
and changes to address the year 2000. A potential source of risk


                                      -11-
<PAGE>   12

includes, but is not limited to, the inability of principal suppliers to be year
2000 compliant, which could result in an interruption of the Company's services.
The Company currently does not have a formal contingency plan. If unforeseen
problems are encountered that relate to the year 2000, possible solutions will
be evaluated and the most efficient will be enacted.

The failure to correct a material year 2000 problem could result in an
interruption in, or a failure of, certain normal business activities or
operations that could materially and adversely affect the Company's operations,
liquidity and financial condition. Because of the uncertainty surrounding year
2000 issues, primarily those associated with third party suppliers, the Company
is unable to determine at this time whether year 2000 failures will have a
material impact on operations. However, the Company's remediation efforts are
expected to reduce the risk of year 2000 issues significantly, particularly
regarding the compliance and readiness of material vendors and suppliers. The
Company believes that the timely completion of its remediation efforts will
reduce the possibility of significant interruptions of normal business
operations.


Item 3.   QUANTITATIVE AND QUALITATIVE DISCLOSURE ABOUT MARKET
          RISK

The primary sources of market risk include fluctuations in commodity prices
which effect demand for and pricing of the Company's services and interest rate
fluctuations. At June 30, 1999 the Company had no indebtedness and in addition
the Company's short-term investments were fixed-rate and, therefore, do not
expose the Company to the 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.



                                      -12-
<PAGE>   13

Part II.  OTHER INFORMATION

Item 6.   Exhibits and Reports on Form 8-K

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

          (b)     No reports on Form 8-K were filed by the Company during the
                  quarter ended June 30, 1999.


                                      -13-
<PAGE>   14

                                    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



                                         By: /s/ CHRISTINA W. HAGAN
                                            -----------------------------------
                                            Christina W. Hagan
                                            Chief Financial Officer



DATE: July 30, 1999
     --------------


                                      -14-
<PAGE>   15

                                 EXHIBIT INDEX


<TABLE>
<CAPTION>
EXHIBIT
NUMBER         DESCRIPTION
-------        -----------
<S>            <C>

  27           Financial Data Schedule
</TABLE>