SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                  SCHEDULE 13D

                               (AMENDMENT NO. 11)

                   Under the Securities Exchange Act of 1934*

                           Dawson Geophysical Company
--------------------------------------------------------------------------------
                                (Name of Issuer)

                   Common Stock, par value $.33 1/3 per share
--------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                   239359 10 2
--------------------------------------------------------------------------------
                                 (CUSIP Number)

                              Richard E. Blohm, Jr.
                        1415 Louisiana Street, Suite 3000
                              Houston, Texas 77002
                                 (713) 739-6500
--------------------------------------------------------------------------------
            (Name, Address and Telephone Number of Person Authorized
                     to Receive Notices and Communications)

                                  July 30, 2004
--------------------------------------------------------------------------------
             (Date of Event which Requires Filing of this Statement)


If the filing person has previously filed a statement on Schedule 13G to report
the acquisition that is the subject of this Schedule 13D, and is filing this
schedule because of Sections 240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check
the following box [ ].

Note: Schedules filed in paper format shall include a signed original and five
copies of the schedule, including all exhibits. See Rule 13d-7 for other parties
to whom copies are to be sent.

*The remainder of this cover page should 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
disclosures provided in a prior cover page.

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 (however, see the
Notes).



--------------------------------------------------------------------------------
 CUSIP No.       239359 10 2         SCHEDULE 13D          Page 2 of 6 pages
--------------------------------------------------------------------------------
   1      NAME OF REPORTING PERSON
          S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

          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*

          00
--------------------------------------------------------------------------------
   5      CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
          PURSUANT TO ITEMS 2(d) OR 2(e)                                     [ ]

--------------------------------------------------------------------------------
   6      CITIZENSHIP OR PLACE OF ORGANIZATION

          Netherlands Antilles
--------------------------------------------------------------------------------
   NUMBER OF     7    SOLE VOTING POWER

    SHARES            0
               -----------------------------------------------------------------
 BENEFICIALLY    8    SHARED VOTING POWER

   OWNED BY           566,000
               -----------------------------------------------------------------
    EACH         9    SOLE DISPOSITIVE POWER

  REPORTING           0
               -----------------------------------------------------------------
   PERSON       10    SHARED DISPOSITIVE POWER

    WITH              566,000
--------------------------------------------------------------------------------
  11      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

          566,000
--------------------------------------------------------------------------------
  12      CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
          CERTAIN SHARES*                                                    [ ]

--------------------------------------------------------------------------------
  13      PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 11

          10.16%
--------------------------------------------------------------------------------
  14      TYPE OF REPORTING PERSON*

          CO
--------------------------------------------------------------------------------


--------------------------------------------------------------------------------
 CUSIP No.       239359 10 2         SCHEDULE 13D          Page 3 of 6 pages
--------------------------------------------------------------------------------
   1      NAME OF REPORTING PERSON
          S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

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

--------------------------------------------------------------------------------
   3      SEC USE ONLY


--------------------------------------------------------------------------------
   4      SOURCE OF FUNDS*

          00
--------------------------------------------------------------------------------
   5      CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
          PURSUANT TO ITEMS 2(d) OR 2(e)                                     [ ]

--------------------------------------------------------------------------------
   6      CITIZENSHIP OR PLACE OF ORGANIZATION

          Lebanon
--------------------------------------------------------------------------------
   NUMBER OF     7    SOLE VOTING POWER

    SHARES            0
               -----------------------------------------------------------------
 BENEFICIALLY    8    SHARED VOTING POWER

   OWNED BY           566,000
               -----------------------------------------------------------------
    EACH         9    SOLE DISPOSITIVE POWER

  REPORTING           0
               -----------------------------------------------------------------
   PERSON       10    SHARED DISPOSITIVE POWER

    WITH              566,000
--------------------------------------------------------------------------------
  11      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

          566,000
--------------------------------------------------------------------------------
  12      CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
          CERTAIN SHARES*                                                    [ ]

--------------------------------------------------------------------------------
  13      PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 11

          10.16%
--------------------------------------------------------------------------------
  14      TYPE OF REPORTING PERSON*

          IN
--------------------------------------------------------------------------------


--------------------------------------------------------------------------------
 CUSIP No.       239359 10 2         SCHEDULE 13D          Page 4 of 6 pages
--------------------------------------------------------------------------------

         Unless otherwise defined or indicated in this Amendment No. 11,
capitalized terms which are used herein and are defined in the Schedule 13D
filed October 16, 1998, as heretofore amended (the "Original 13D"), shall have
the meanings assigned to them in the Original 13D. All information herein with
respect to Dawson Geophysical Company, a Texas corporation (the "Issuer"), is to
the best knowledge and belief of the Reporting Persons, as defined herein.

ITEM 2.  IDENTITY AND BACKGROUND

         The text of Item 2 of the Original 13D is hereby deleted in its
entirety and the following substituted therefor:

         This Amendment No. 11 is filed by (a) Pebbleton Corporation N.V., a
corporation organized under the laws of the Netherlands Antilles ("Pebbleton"),
and (b) Mr. Issam M. Fares, a Lebanese citizen ("Mr. Fares" and together with
Pebbleton, the "Reporting Persons").

         The principal business of Pebbleton is to hold investments in other
companies. The address of the principal business offices of Pebbleton and the
address of Mr. Fares is Pietermaai 15, Curacao, Netherlands Antilles. Mr. Fares
serves as a managing director of Pebbleton. N.V. Fides, a Netherlands Antilles
corporation, functions as a Managing Director of Pebbleton in order to comply
with Netherlands Antilles regulations requiring resident directors. There are no
other officers or directors of Pebbleton. The filing of this statement 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 of the Reporting Persons, nor, to their knowledge, 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 4.  PURPOSE OF TRANSACTION

         The text of Item 4 of the Original 13D is hereby deleted in its
entirety and the following substituted therefor:

         The purchases of the Common Stock of the Issuer by the Reporting
Persons were made on The Nasdaq Stock Market, Inc., the principal market in
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, the Issuer's business and



--------------------------------------------------------------------------------
 CUSIP No.       239359 10 2         SCHEDULE 13D          Page 5 of 6 pages
--------------------------------------------------------------------------------

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 decrease the
size of their investment in the Issuer.

ITEM 5.  INTEREST IN SECURITIES OF THE ISSUER

         The text of Item 5 is hereby deleted in its entirety and the following
substituted therefor:

         (a)      As set forth herein, Pebbleton owns 566,000 shares of Common
                  Stock of the Issuer, which represents approximately 10.16% of
                  the outstanding Common Stock (based upon 5,570,294 shares of
                  Common Stock outstanding, as reported in the Issuer's
                  Quarterly Report on Form 10-Q for the period ending March 31,
                  2004).

                  As set forth herein, Mr. Fares may be deemed to beneficially
                  own 566,000 shares of Common Stock of the Issuer, which
                  represents approximately 10.16% of the outstanding Common
                  Stock (based upon 5,570,294 shares of Common Stock
                  outstanding, as reported in the Issuer's Quarterly Report on
                  Form 10-Q for the period ending March 31, 2004).

         (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 Amendment No. 11 is a list of
                  all transactions effected in the Issuer's Common Stock by
                  Pebbleton since the filing of Amendment No. 10 on July 23,
                  2004, 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 in this Item 5, neither of the Reporting Persons nor
                  to the knowledge of the Reporting Persons, any of their
                  officers or directors, has effected any transaction in the
                  Common Stock since the filing of Amendment No. 10.

ITEM 7.  MATERIAL TO BE FILED AS EXHIBITS.

         Item 7 of the Original Statement is hereby amended to add the following
exhibit:

         Exhibit A         Transactions in Common Stock by Pebbleton



--------------------------------------------------------------------------------
 CUSIP No.       239359 10 2         SCHEDULE 13D          Page 6 of 6 pages
--------------------------------------------------------------------------------


                                    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.

         Dated:  August 5, 2004.

                                          PEBBLETON CORPORATION N.V.

                                          By:Issam M. Fares,
                                             its Managing Director

                                             By: /s/ Richard E. Blohm, Jr.
                                                 -------------------------------
                                                 Richard E. Blohm, Jr.
                                                 Attorney-in-Fact



                                          ISSAM M. FARES



                                          By: /s/ Richard E. Blohm, Jr.
                                              ----------------------------------
                                              Richard E. Blohm, Jr.
                                              Attorney-in-Fact



                                    EXHIBIT A

                  TRANSACTIONS IN THE COMMON STOCK BY PEBBLETON

         With respect to the transactions set forth below, all sales 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, since the filing of Amendment No. 10 on July 23, 2004.



        DATE OF                    NUMBER OF                   PRICE PER
         SALE                     SHARES SOLD                  SHARE ($)
                                                           
      07/30/2004                      8,500                      22.00
      07/30/2004                      4,000                      21.86
      07/30/2004                      5,000                      21.70
      07/30/2004                      3,000                      21.77
      07/30/2004                     11,500                      21.97
      07/30/2004                      3,000                      21.95
      07/30/2004                      3,000                      21.99
      07/30/2004                      6,000                      21.92
      07/30/2004                      9,500                      21.85
      07/30/2004                      2,000                      21.84
      07/30/2004                      2,000                      21.87
      07/30/2004                      8,000                      21.89
      07/30/2004                      2,000                      21.90
      07/30/2004                      2,500                      21.83
      07/30/2004                      4,000                      22.05
      07/30/2004                      7,000                      22.03
                                    -------
                                     81,000

      08/02/2004                     30,000                      22.60
      08/02/2004                      7,500                      22.62
      08/02/2004                     20,000                      22.66
      08/02/2004                      5,000                      22.64
      08/02/2004                      5,000                      22.68
      08/02/2004                      5,000                      22.63
      08/02/2004                      7,500                      22.55
      08/02/2004                     17,000                      22.80
      08/02/2004                      5,000                      22.90
      08/02/2004                      7,500                      22.72
      08/02/2004                      7,500                      22.65
      08/02/2004                      2,500                     22.405
      08/02/2004                     10,000                      22.25
      08/02/2004                      5,500                      22.34
      08/02/2004                      5,000                      22.46
      08/02/2004                      7,000                      22.54



                                      A-1



        DATE OF                    NUMBER OF                   PRICE PER
         SALE                     SHARES SOLD                  SHARE ($)
                                                           
      08/02/2004                     10,000                      22.83
                                   --------
                                    157,000

      08/03/2004                     10,000                      22.66
      08/03/2004                      5,000                      22.61
      08/03/2004                      5,000                      22.58
      08/03/2004                      2,500                      22.42
      08/03/2004                      2,500                      22.31
      08/03/2004                      2,500                      22.29
      08/03/2004                      7,500                      22.36
      08/03/2004                      3,500                      23.00
      08/03/2004                      2,500                      22.90
      08/03/2004                      4,000                      22.85
      08/03/2004                      5,000                      22.75
      08/03/2004                      5,000                      22.49
      08/03/2004                      5,000                      22.50
      08/03/2004                      5,000                      22.55
      08/03/2004                     10,000                      22.67
      08/03/2004                      5,000                      22.69
      08/03/2004                      5,000                      22.70
      08/03/2004                      5,000                      22.51
                                    -------
                                     90,000

      08/04/2004                      6,000                      22.45
      08/04/2004                      3,500                      22.25
      08/04/2004                      1,500                      22.00
      08/04/2004                      5,000                      22.05
                                    -------
                                     16,000



                                      A-2