UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  SCHEDULE 13G

                    Under the Securities Exchange Act of 1934

                           DAWSON GEOPHYSICAL COMPANY
        -----------------------------------------------------------------
                                (Name of Issuer)

                                  Common Stock
        -----------------------------------------------------------------
                         (Title of Class of Securities)

                                    239359102
                              --------------------
                                 (CUSIP Number)

                                 October 6, 1998
        ----------------------------------------------------------------
             (Date of Event Which Requires Filing of this Statement)

Check the  appropriate box to designate the rule pursuant to which this Schedule
is filed:

      / X / Rule 13d-1(b)
      /   / Rule 13d-1(c)
      /   / Rule 13d-1(d)

*The  remainder of this cover page shall be filled out for a reporting  person's
initial filing on this form with respect to the subject class of securities, and
for any  subsequent  amendment  containing  information  which  would  alter the
disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the  Securities  Exchange  Act of
1934 ("Act") or otherwise  subject to the  liabilities of the section of the Act
but  shall be  subject  to all other  provisions  of the Act  (however,  see the
Notes).





                                  SCHEDULE 13G
                               CUSIP NO. 239359102

1.    Names of Reporting Persons.
      I.R.S. Identification Nos. of above persons (entities only).

      Quaker Capital Management Corporation
      --------------------------------------------------------------------

2.    Check the Appropriate Box if a Member of a Group 
      (a)
            -----
      (b)     X
            -----

3.    SEC Use Only
                     -----------------------------------------------------

4.    Citizenship or Place of Organization                   Pennsylvania
                                                            --------------

Number of         5.    Sole Voting Power                                0
Shares                                                      --------------
Beneficially      6.    Shared Voting Power                        398,200
Owned by                                                    --------------
Each Reporting    7.    Sole Dispositive Power                           0
Person With:                                                --------------
                  8.    Shared Dispositive Power                   398,200
                                                            --------------

9.    Aggregate Amount Beneficially Owned by Each Reporting Person

                                                                  398,200
                                                            --------------

10.   Check if the Aggregate Amount in Row (9) Excludes Certain
      Shares
                                                            --------------

      The Reporting Person disclaims beneficial ownership of 398,200 shares
      owned by its clients.

11.   Percent of Class Represented by Amount in Row (9)              7.43%
                                                            --------------

12.   Type of Reporting Person                                          IA
                                                            --------------


                               Page 2 of 6 Pages

                                  SCHEDULE 13G
                               CUSIP NO. 239359102

Item 1.

      (a)   Name of Issuer

            Dawson Geophysical Company
            -------------------------------------------------------

      (b)   Address of Issuer's Principal Executive Offices

            208 South Marienfeld Street, Midland, TX 79701
            -------------------------------------------------------
Item 2.

      (a)   Name of Persons Filing

            Quaker Capital Management Corporation
            -------------------------------------------------------

      (b)   Address of Principal Business Office or, if none, Residence

            401 Wood Street, Suite 1300, Pittsburgh, PA  15222
            -------------------------------------------------------

      (c)   Citizenship

            Pennsylvania, USA
            -------------------------------------------------------

      (d)   Title of Class of Securities

            Common Stock
            -------------------------------------------------------

      (e)   CUSIP Number

            239359102
            -------------------------------------------------------


                               Page 3 of 6 Pages

                                  SCHEDULE 13G
                               CUSIP NO. 239359102


Item 3.     If this  statement  is filed  pursuant to  ss.ss.240.13d-1(b)  or
            240.13d-2(b) or (c), check whether the person filing is a:

   (a)  /   /    Broker of dealer registered under section 15 of
                 the Act;

   (b)  /   /    Bank as defined in section 3(a)(6) of the Act;

   (c)  /   /    Insurance  company as defined in section  3(a)(19) of the Act;

   (d)  /   /    Investment company registered under section 8 of the Investment
                 Company Act of 1940;

   (e)  / X /    An  investment  adviser in accordance  with  ss.240.13d-1(b)(l)
                 (ii)(E);

   (f)  /   /    An  employee  benefit plan or endowment fund in accordance with
                 ss.240.13d-1(b)(1)(ii)(F);

   (g)  /   /    A parent  holding  company or control person in accordance with
                 ss.240.13d-1(b)(1)(ii)(G);

   (h)  /   /    A savings association as defined in Section 3(b) of the Federal
                 Deposit Insurance Act;

   (i)  /   /    A  church  plan  that  is  excluded  from  the definition of an
                 investment company under section  3(c)(14) of  the  Investment
                 Company Act of 1940;

   (j)  /   /    Group, in accordance with ss.240.13d-1((b)(l)(ii)(J)

Item 4.   Ownership.

          Provide the following  information  regarding the aggregate number and
percentage of the class of securities of the issuer identified in Item 1.

      (a)   Amount beneficially owned:                              398,200
                                                            ---------------

      (b)   Percent of class:                                         7.43%
                                                            ---------------


                               Page 4 of 6 Pages


                                  SCHEDULE 13G
                               CUSIP NO. 239359102


      (c)   Number of shares as to which the person has:

            (i)   Sole power to vote or to direct the
                  vote                                                   0
                                                                ----------

            (ii)  Shared power to vote or to direct
                  the vote                                         398,200
                                                                ----------

            (iii) Sole power to dispose or to direct
                  the vote                                               0
                                                                ----------

            (iv)  Shared power to dispose or to direct
                  the disposition of                               398,200
                                                                ----------

Item 5.     Ownership of Five Percent or Less of a Class

            If this statement is being filed to report the  fact  that as of the
date hereof,  the reporting person has ceased to be the beneficial owner of more
than five percent of the class of securities, check the following:

                                                                ----------

Item 6.     Ownership of More than Five Percent on Behalf of 
            Another Person

            The shares with respect to which this report is filed are owned by a
variety of investment  advisory clients of the Reporting  Person,  which clients
are  entitled to receive  dividends  on and the  proceeds  from the sale of such
shares. No client is known to own more than 5% of the class.

Item 7.     Identification and Classification of the Subsidiary  Which  Acquired
            the Security Being Reported on by the Parent Holding Company

            Not applicable.

Item 8.     Identification and Classification of Members of the Group

            Not applicable.

Item 9.     Notice of Dissolution of Group

            Not applicable.

                                Page 5 of 6 Pages

                                  SCHEDULE 13G
                               CUSIP NO. 239359102

Item 10.    Certification

            By signing  below I certify  that,  to the best of my knowledge  and
belief,  the  securities  referred  to above were  acquired  and are held in the
ordinary  course  of  business  and were not  acquired  and are not held for the
purpose of or with the effect of  changing  or  influencing  the  control of the
issuer of the  securities  and were not acquired and are not held in  connection
with or as a participant in any transaction having that purpose or effect.


                                    SIGNATURE

            After reasonable inquiry and to the best of my knowledge and belief,
I certify that the information set forth in this statement is true, complete and
correct.


                              QUAKER CAPITAL MANAGEMENT CORPORATION


                                          February 14, 1999    
                                          -----------------------------         
                                                      Date


                                          /s/ Mark G. Schoeppner
                                          ------------------------------
                                                    Signature


                                          Mark G. Schoeppner, President
                                          ------------------------------
                                                   Name/Title


                               Page 6 of 6 Pages