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                             ----------------------

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

                             ----------------------
                                  SCHEDULE 13D
                    Under the Securities Exchange Act of 1934

                           DAWSON GEOPHYSICAL COMPANY
                                (Name of Issuer)

                                 --------------

                        COMMON STOCK, $.33 1/3 PAR VALUE
                         (Title of Class of Securities)

                                 --------------

                                   239359 10 2
                                 (CUSIP Number)

                            MR. RICHARD E. BLOHM, JR.
                              1415 LOUISIANA STREET
                              HOUSTON, TEXAS 77002
                                 (713) 739-6500
                       (Name, Address and Telephone Number
                     of Person Authorized to Receive Notices
                               and Communications)

                                 with a copy to:
                              MR. JOHN R. BRANTLEY
                          BRACEWELL & PATTERSON, L.L.P.
                        711 LOUISIANA STREET, SUITE 2900
                              HOUSTON, TEXAS 77002
                                  713-223-2900

                                 --------------

                                 OCTOBER 6, 1998
             (Date of Event which Requires Filing of this Statement)

    If the filing person has previously filed a statement on Schedule 13G to
    report this acquisition that is the subject of this Schedule 13D, and is
      filing this Schedule because of Rule 13d-1(e), Rule 13d-1(f) or Rule
                     13d-1(g), check the following box: [ ]

    The information required on 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
     that section of the Act but shall be subject to all other provisions of
                                    the Act.

                             ----------------------






                                Page 1 of 9 Pages


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CUSIP NO.: 239359 10 2

                                  SCHEDULE 13D

================================================================================
      1       NAME OF REPORTING PERSON; S.S. OR IRS IDENTIFICATION NUMBER

              Pebbleton Corporation N.V.
- --------------------------------------------------------------------------------
      2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
              (a) [ ]
              (b) [ ]
- --------------------------------------------------------------------------------
      3       SEC USE ONLY

- --------------------------------------------------------------------------------
      4       SOURCE OF FUNDS
              WC
- --------------------------------------------------------------------------------
      5       CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
              PURSUANT TO ITEM 2(d) OR 2(e)

              [ ]
- --------------------------------------------------------------------------------
      6       CITIZENSHIP OR PLACE OF ORGANIZATION

              Netherlands Antilles
- --------------------------------------------------------------------------------
      7       Sole Voting Power

              0
- --------------------------------------------------------------------------------
      8       SHARED VOTING POWER

              394,900
- --------------------------------------------------------------------------------
      9       SOLE DISPOSITIVE POWER

              0
- --------------------------------------------------------------------------------
     10       SHARED DISPOSITIVE POWER

              394,900
- --------------------------------------------------------------------------------
     11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

              394,900
- --------------------------------------------------------------------------------
     12       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN
              SHARES*

              [ ]
- --------------------------------------------------------------------------------
     13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

              7.37%
- --------------------------------------------------------------------------------
     14       TYPE OF REPORTING PERSON

              CO
================================================================================




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CUSIP NO.:239359 10 2

                                  SCHEDULE 13D

================================================================================
      1       NAME OF REPORTING PERSON; S.S. OR IRS IDENTIFICATION NUMBER

              Issam M. Fares
- --------------------------------------------------------------------------------
      2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
              (a) [ ]
              (b) [ ]
- --------------------------------------------------------------------------------
      3       SEC USE ONLY

- --------------------------------------------------------------------------------
      4       SOURCE OF FUNDS
              AF
- --------------------------------------------------------------------------------
      5       CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
              PURSUANT TO ITEM 2(d) OR 2(e)

              [ ]
- --------------------------------------------------------------------------------
      6       CITIZENSHIP OR PLACE OF ORGANIZATION

              Lebanese
- --------------------------------------------------------------------------------
      7       Sole Voting Power

              0
- --------------------------------------------------------------------------------
      8       SHARED VOTING POWER

              394,900
- --------------------------------------------------------------------------------
      9       SOLE DISPOSITIVE POWER

              0
- --------------------------------------------------------------------------------
     10       SHARED DISPOSITIVE POWER

              394,900
- --------------------------------------------------------------------------------
     11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

              394,900
- --------------------------------------------------------------------------------
     12       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN
              SHARES*

              [ ]
- --------------------------------------------------------------------------------
     13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

              7.37%
- --------------------------------------------------------------------------------
     14       TYPE OF REPORTING PERSON

              IN
================================================================================




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                            STATEMENT ON SCHEDULE 13D

         Introductory Note: All information herein with respect to Dawson
Geophysical Company, a Texas corporation is to the best knowledge and belief of
the Reporting Persons, as defined herein.

ITEM 1.  SECURITY AND ISSUER.

         This Statement on Schedule 13D relates to the common stock, par value
$.33 1/3 per share of Dawson Geophysical Company, a Texas corporation
("Issuer"). The principal executive offices of the Issuer are located at 508
West Wall, Suite 800, Midland, Texas 79701.

ITEM 2.  IDENTITY AND BACKGROUND.

         This Statement is filed by (i) Pebbleton Corporation N.V., a
corporation organized under the laws of the Netherlands Antilles ("Pebbleton"),
and (ii) by Mr. Issam M. Fares, an individual (together with Pebbleton, the
"Reporting Persons").

The address of the principal business offices of Pebbleton and a business
address of Mr. Fares is Pietermaai 15, Curacao, Netherlands Antilles. Mr. Fares
serves as a Managing Director of Pebbleton. In addition, N.V. Fides, a
Netherlands Antilles corporation, functions as a Managing Director of Pebbleton
in order to comply with Netherlands Antilles regulations requiring resident
Managing Directors. There are no other officers or directors of Pebbleton.  The
filing of this statement on Schedule 13D shall not be construed as an admission
that N.V. Fides is, for the purposes of Section 13(d) or 13(g) of the
Securities Exchange Act of 1934, as amended (the "Act"), the beneficial owner
of any securities covered by this statement.

         Neither Pebbleton nor Mr. Fares, nor to the knowledge of the Reporting
Persons, N.V. Fides, has been during the last five years (a) convicted of any
criminal proceeding (excluding traffic violations or similar misdemeanors) or
(b) a party to a civil proceeding of a judicial or administrative body of
competent jurisdiction and as a result of such proceeding was or is subject to a
judgment, decree or final order enjoining future violations of, or prohibiting
or mandating activities subject to, United States federal or state securities
laws or finding any violations with respect to such laws.

ITEM 3.  SOURCE AND AMOUNT OF FUNDS OR OTHER CONSIDERATION.

         The source of the funds used for the purchases of the Common Stock by
Pebbleton was working capital on hand.

ITEM 4.  PURPOSE OF THE TRANSACTION.

         The purchases of the Common Stock of the Issuer were made on The Nasdaq
Stock Market, Inc., the exchange on which shares of the Issuer's Common Stock
are traded, and such acquisitions were made for investment purposes.

         The Reporting Persons intend to review their investment in the Issuer
on a continuing basis and, depending upon the price of, and other market
conditions relating to the Common Stock, subsequent developments affecting the
Issuer (including opportunities to provide financing from time to time to the
Issuer for expansion of its business), the Issuer's business and prospects,
other investment and business opportunities available to the Reporting Persons,
general stock market and economic conditions, tax considerations and other
factors deemed relevant, may decide to increase or decrease the size of their
investment in the Issuer.


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         Other than the transactions described herein, none of the Reporting
Persons, nor to their knowledge N.V. Fides, has any plan or proposal that would
result in any of the consequences listed in paragraphs (a) - (j) of Item 4 of
Schedule 13D.

ITEM 5.  INTEREST IN SECURITIES OF THE ISSUER.

         (a) As set forth in this Schedule 13D, Pebbleton owns 394,900 shares of
Common Stock of the Issuer, which represents approximately 7.37% of the
outstanding Common Stock (based on the number of shares of Common Stock
outstanding as of June 30, 1998, as represented by the Issuer in its Form 10-Q
for the quarter ended June 30, 1998, as filed with the Securities and Exchange
Commission on August 12, 1998).
See Item 4.

         (b) Mr. Fares may be deemed to beneficially own and thereby share
voting and dispositive power over the shares of Common Stock described herein
which are held by Pebbleton. See Item 2.

         (c) Set forth in Exhibit A to this Schedule 13D is a list of all
transactions effected in the Issuer's Common Stock within the past sixty (60)
days, including (i) the identity of the person effecting transactions in the
Issuer's Common Stock; (ii) the date of the transaction; (iii) the amount of
securities involved; (iv) the price per share of Common Stock; and (v) where and
how the transaction was effected. Other than the transactions described herein,
neither of the Reporting Persons nor to the knowledge of the Reporting Persons,
N.V. Fides, has effected any transactions in the Common Stock during the
preceding sixty days.

ITEM 6.  CONTRACTS, ARRANGEMENTS, UNDERSTANDINGS OR RELATIONSHIPS WITH RESPECT
         TO SECURITIES OF THE ISSUER.

         There are none.

ITEM 7.  MATERIAL TO BE FILED AS EXHIBITS.

         1.       Joint Filing Agreement by and between the Reporting Persons.



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                                   SIGNATURES


         After reasonable inquiry and to the best of the undersigned's knowledge
and belief, each of the undersigned hereby certifies that the information set
forth in this statement is true, complete and correct.


Dated: October 15, 1998.               PEBBLETON CORPORATION N.V.



                                       By: /s/ Issam M. Fares
                                          --------------------------------
                                       Name:  Issam M. Fares
                                       Title: Managing Director



Dated: October 15, 1998.               /s/ Issam M. Fares
                                       -----------------------------------
                                       Mr. Issam M. Fares




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                                INDEX TO EXHIBITS


         1.       Joint Filing Agreement by and between the Reporting Persons.




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                                    EXHIBIT A
                        TRANSACTIONS IN THE COMMON STOCK

         With respect to the transactions set forth below, all purchases were
made by Pebbleton Corporation N.V. and were effected on The Nasdaq Stock Market,
Inc., the exchange on which the shares of Common Stock of Dawson Geophysical
Company are traded.



DATE OF PURCHASE NUMBER OF SHARES PRICE PER SHARE PURCHASED ($) 08/14/98 14,000 14.000 08/14/98 13,100 14.000 08/14/98 16,900 14.000 08/14/98 30,000 14.500 08/19/98 6,600 14.625 08/19/98 1,000 14.500 08/26/98 10,000 14.125 09/08/98 22,000 12.500 10/06/98 75,000 8.750 10/06/98 8,000 8.625 10/06/98 10,000 8.8125 10/06/98 7,000 9.000 10/13/98 30,000 9.350 10/13/98 2,000 9.500
   1
                                                                     EXHIBIT 1

                             JOINT FILING AGREEMENT

         The undersigned each agree that (i) the Statement on Schedule 13D
relating to the Common Stock, $.33 1/3 par value, of Dawson Geophysical Company
is adopted and filed on behalf of each of them, (ii) all future amendments to
such Statement on Schedule 13D will, unless written notice to the contrary is
delivered as described below, be jointly filed on behalf of each of them, and
(iii) the provisions of Rule 13d-1(k) under the Securities Exchange Act of 1934
apply to each of them. This agreement may be terminated with respect to the
obligation to jointly file future amendments to such Statement on Schedule 13D
as to any of the undersigned upon such person giving written notice thereof to
the other person signatory hereto, at the principal office thereof.

         IN WITNESS WHEREOF, the undersigned hereby execute this Joint Filing
Agreement as of the date set forth below.


Dated: October 15, 1998.               PEBBLETON CORPORATION N.V.


                                       By:/s/ Issam M. Fares
                                          --------------------------------
                                       Name: Issam M. Fares
                                       Title: Managing Director



Dated: October 15, 1998.               By:/s/ Issam M. Fares
                                          --------------------------------
                                           Issam M. Fares