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

                                  SCHEDULE 13D

                   Under the Securities Exchange Act of 1934


                         LANDMARK GRAPHICS CORPORATION
- --------------------------------------------------------------------------------
                                (Name of Issuer)

                     Common Stock, par value $.05 per share
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                         (Title of Class of Securities)

                                   514913102
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                                 (CUSIP Number)

                               Lester L. Coleman
                    Executive Vice President/General Counsel
                              Halliburton Company
                   3600 Lincoln Plaza, 500 North Akard Street
                           Dallas, Texas  75201-3391
                                 (214) 978-2600
- --------------------------------------------------------------------------------
                 (Name, Address and Telephone Number of Person
               Authorized to Receive Notices and Communications)

                                 June 30, 1996
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            (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 which is the subject of this Schedule 13D, and is filing
this schedule because of Rule 13d-1(b)(3) or (4), check the following box. [ ]

     Check the following box if a fee is being paid with this statement. [X]

     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, as amended (the "Act"), or otherwise subject to the liabilities of
that Section of the Act but shall be subject to all other provisions of the Act.

     The total number of shares reported herein is 1,971,263 shares, which
constitutes approximately 11.27% of the total number of shares outstanding.
Ownership percentages set forth herein assume that at June 30, 1996 there were
17,498,396 shares outstanding.

 
- --------------------------------------------------------------------------------
1    NAME OF REPORTING PERSON.............................   HALLIBURTON COMPANY
 
     S.S. OR I.R.S. IDENTIFICATION NO.
     OF ABOVE PERSON......................................            73-0271280
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2    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP                    (a) [ ]
                                                                         (b) [ ]

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3    SEC USE ONLY

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4    SOURCE OF FUNDS

     Not Applicable
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5    CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS
     REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)                                 [ ]

- --------------------------------------------------------------------------------
6    CITIZENSHIP OR PLACE OF ORGANIZATION
 
     Delaware
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                        7    SOLE VOTING POWER
NUMBER
OF                           0
SHARES                  --------------------------------------------------------
BENEFICIALLY            8    SHARED VOTING POWER      
OWNED                                                 
BY                           1,971,263                
EACH                    --------------------------------------------------------
REPORTING               9    SOLE DISPOSITIVE POWER   
PERSON                                                
WITH:                        0                        
                        --------------------------------------------------------
                        10   SHARED DISPOSITIVE POWER  
                                                       
                             0                          
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     1,971,263
- --------------------------------------------------------------------------------
12   CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
     CERTAIN SHARES                                                          [ ]

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

     11.27% (approximate)
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON

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

 
ITEM 1.  SECURITY AND ISSUER.
- ------   ------------------- 

     This Schedule 13D relates to the common stock, par value $.05 per share
("Landmark Common Stock"), of Landmark Graphics Corporation, a corporation
organized under the laws of the State of Delaware ("Landmark"). The principal
executive offices of Landmark are located at 15150 Memorial Drive, Houston,
Texas, 77079-4304.

ITEM 2.  IDENTITY AND BACKGROUND.
- ------   ----------------------- 

     This Schedule 13D is being filed by Halliburton Company, a corporation
organized under the laws of the State of Delaware ("Halliburton"). Halliburton
is one of the world's largest diversified energy services and engineering and
construction services companies. The principal offices of Halliburton are
located at 3600 Lincoln Plaza, 500 North Akard Street, Dallas, Texas, 75201-
3391.

     Other than executive officers and directors, there are no persons or
corporations controlling or ultimately in control of Halliburton.

     During the last five years, to the best of Halliburton's knowledge, neither
Halliburton nor any of its executive officers or directors has been convicted in
a criminal proceeding (excluding traffic violations or similar misdemeanors) or
has been a party to a civil proceeding of a judicial or administrative body of
competent jurisdiction as a result of which Halliburton or such person was or is
subject to a judgment, decree, or final order enjoining future violations of, or
prohibiting or mandating activities subject to, federal or state securities
laws, or finding any violation with respect to such laws.

     With the exception of Lord Clitheroe who is a citizen of the United
Kingdom, each executive officer and director of Halliburton is a citizen of the
United States. The name, business address and present principal occupation of
each executive officer and director of Halliburton are set forth in Exhibit A to
this Schedule 13D and are specifically incorporated herein by reference.

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

     Not applicable.

ITEM 4.  PURPOSE OF TRANSACTION.
- ------   ---------------------- 

     Halliburton, Halliburton Acq. Company, a Delaware corporation and wholly-
owned subsidiary of Halliburton ("Merger Sub"), and Landmark entered into an
Agreement and Plan of Merger, dated June 30, 1996 (the "Merger Agreement"),
pursuant to which Landmark will be merged with and into Merger Sub (the
"Merger"). Pursuant to the Merger Agreement, each share of Landmark Common Stock
issued and outstanding immediately prior to the effective time of the Merger
(the "Effective Time") will be converted into 0.574 shares (the "Exchange
Ratio") of common stock, par value $2.50 per share, of Halliburton (the
"Halliburton Common Stock"). Notwithstanding the foregoing, if between June 30,
1996 and the Effective Time the outstanding shares of Halliburton Common Stock
or Landmark Common Stock are changed into a different number of shares or a
different class by reason of any stock dividend, subdivision, combination or
exchange of shares or any reclassification or recapitalization, the Exchange
Ratio will be correspondingly adjusted to reflect such stock dividend,
subdivision, combination or exchange of shares or any reclassification or
recapitalization. A copy of the Merger Agreement is included as Exhibit B to
this Schedule 13D, and the Merger Agreement is specifically incorporated by
reference herein.

     Consummation of the transactions contemplated by the Merger Agreement is
subject to the terms and conditions contained in the Merger Agreement, including
the receipt of approval of the Merger by the

                                      -1-

 
stockholders of Landmark, the receipt of certain regulatory approvals, and the
receipt of legal opinions that the Merger will be tax-free and will be accounted
for as a pooling of interests. The Merger Agreement and the transactions
contemplated by the Merger will be submitted for approval at a special meeting
of the stockholders of Landmark that is expected to take place during the latter
part of the third or early part of the fourth calendar quarter of 1996.

     In connection with the Merger Agreement, Halliburton entered into a Voting
Agreement, dated as of June 30, 1996 (the "Voting Agreement"),with S. Rutt
Bridges, a director and executive officer of Landmark, and Barbara Ann Bridges,
his wife (collectively, the "Stockholders"), holding in the aggregate 1,971,263
shares of Landmark Common Stock (or approximately 11.27% of the number of shares
outstanding on June 30, 1996). Pursuant to the Voting Agreement, the
Stockholders have, among other things, agreed to vote, and to cause each member
of the Stockholder Group (as defined below) to vote, all Landmark Common Stock
beneficially owned by them in favor of the Merger and against any business
combination proposal or other matter that may interfere or be inconsistent with
the Merger (including a competing transaction). The Stockholders also have
agreed, if reasonably requested by Halliburton in order to facilitate the
Merger, that they will not, and they will cause each member of the Stockholder
Group not to, attend or vote any Landmark Common Stock beneficially owned by
them at any annual or special meeting of stockholders or execute any written
consent of stockholders. A copy of the Voting Agreement is included as Exhibit C
to this Schedule 13D, and the Voting Agreement is specifically incorporated by
reference herein.

  The Stockholders also have agreed that no Stockholder or any corporation or
other person or entity controlled by any Stockholder or any affiliate or
associate thereof, other than Landmark and its subsidiaries (collectively, the
"Stockholder Group"), will, directly or indirectly, sell, transfer, pledge or
otherwise dispose of, or grant a proxy with respect to, any shares of Landmark
Common Stock beneficially owned by any member of the Stockholder Group to any
person or entity (other than to any member of the Stockholder Group or its
designee), or grant an option with respect to any of the foregoing, or enter
into any other agreement or arrangement with respect to any of the foregoing.
 
     Except as set forth herein, Halliburton presently does not have any plans
or proposals that relate to or would result in any of the actions specified in
clauses (a) through (j) of Item 4 of Schedule 13D.

ITEM 5.  INTEREST IN SECURITIES OF ISSUER.
- ------   -------------------------------- 

     Pursuant to the Voting Agreement, the Stockholders, as described above in
Item 4, have agreed to vote, and will cause each member of the Stockholder Group
to vote, all Landmark Common Stock beneficially owned by them in favor of the
Merger and against any business combination proposal or other matter that may
interfere or be inconsistent with the Merger (including a competing
transaction). The Stockholders also have agreed, if reasonably requested by
Halliburton in order to facilitate the Merger, that they will not, and they will
cause each member of the Stockholder Group not to, attend or vote any Landmark
Common Stock beneficially owned by them at any annual or special meeting of
stockholders or execute any written consent of stockholders. Consequently,
Halliburton shares voting, but not dispositive, power as to such 1,971,263
shares of Landmark Common Stock.

  The Stockholders also have agreed that no Stockholder or any member of the 
Stockholder Group will, directly or indirectly, sell, transfer, pledge or
otherwise dispose of, or grant a proxy with respect to, any shares of Landmark
Common Stock beneficially owned by any member of the Stockholder Group to any
person or entity (other than to any member of the Stockholder Group or its
designee), or grant an option with respect to any of the foregoing, or enter
into any other agreement or arrangement with respect to any of the foregoing.
 
     Pursuant to a Stock Option Agreement, dated as of June 30, 1996 (the "Stock
Option Agreement"), by and between Halliburton and Landmark, Landmark has
granted to Halliburton an irrevocable option (the "Stock Option") to purchase a
number of shares equal to up to 15% of the shares of Landmark Common Stock
outstanding as of June 30, 1996 (as adjusted) for an exercise price of $31.857
per share. The Stock Option is exercisable only after the occurence of certain
specific events which, in general, involve (i) a proposal (together with certain
actions or the failure to take certain actions by Landmark) by a person other
than Halliburton and its affiliates to acquire Landmark, any of its significant
subsidiaries, or a percentage of Landmark's consolidated assets or a percentage
of its securities, (ii) the actual (or, in certain circumstances, proposed)
acquisition by such person of a percentage of Landmark's outstanding common
stock or (iii) the withdrawals or modification of the favorable recommendation
of the Merger by the Board of Directors of Landmark. The Stock Option was
granted by Landmark to Halliburton in connection with, and as an inducement for,
Halliburton's entering into the Merger Agreement. A copy of the Stock Option
Agreement is included as Exhibit D to this Schedule 13D, and the Stock Option
Agreement is specifically incorporated by reference herein.

     No transactions in Landmark Common Stock were effected during the past
sixty days by Halliburton or, to the best of Halliburton's knowledge, by any
executive officer or director of Halliburton. In addition, no other person is
known by Halliburton to have the right to receive or the power to direct the
receipt of dividends from, or the proceeds from the sale of, the securities
covered by this Schedule 13D.

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

     Contracts, arrangements, understandings or relationships with respect to
securities of Landmark consist of the Merger Agreement, the Voting Agreement,
the Stock Option Agreement and certain affiliate's agreements, by and between
Halliburton and the affiliates of Landmark (collectively, the "Affiliate's
Agreements"). The Merger Agreement, the Voting Agreement, the Stock Option
Agreement, and a form of the Affiliate's Agreements are attached hereto as
Exhibits B, C, D, and E, respectively, and are specifically incorporated herein
by reference. See also description of certain of the aforementioned documents in
Items 4 and 5 above.

ITEM 7.  MATERIAL TO BE FILED AS EXHIBITS.
- ------   -------------------------------- 

     The following Exhibits are filed as part of this Schedule 13D:
 
                                      -2-

 
Exhibit A      -   Name, Business Address, and Present Principal Occupation of
                   Each Executive Officer and Director of Halliburton.
 
Exhibit B      -   Agreement and Plan of Merger, dated as of June 30, 1996, by
                   and among Halliburton, Merger Sub and Landmark.
 
Exhibit C      -   Voting Agreement, dated as of June 30, 1996, by and among
                   Halliburton, S. Rutt Bridges, and Barbara Ann Bridges.

Exhibit D      -   Stock Option Agreement, dated as of June 30, 1996, by and 
                   between Halliburton and Landmark. 

Exhibit E      -   Form of Affiliate's Agreement by and between Halliburton and 
                   Certain Affiliates of Landmark.





                                      -3-

 
                                   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.


Date:  July 25, 1996                    HALLIBURTON COMPANY



                                        By: /s/ LESTER L. COLEMAN
                                            ------------------------------------
                                               Lester L. Coleman
                                               Executive Vice President and
                                               General Counsel

 
                                 EXHIBIT INDEX
                                 -------------
 
                                                                      SEQUENTIAL
EXHIBIT                      DESCRIPTION                             PAGE NUMBER
- -------                      -----------                             -----------

   A       Name, Business Address, and Present Principal Occupation of
           Each Executive Officer and Director of Halliburton Company.

   B       Agreement and Plan of Merger, dated as of June 30, 1996, by
           and among Halliburton Company, Halliburton Acq. Company and
           Landmark Graphics Corporation (incorporated by reference to
           Exhibit 2(a) to Halliburton Company's Current Report on Form 8-K
           dated June 30, 1996).

   C       Voting Agreement, dated as of June 30, 1996, by and among
           Halliburton Company, S. Rutt Bridges, and Barbara Ann Bridges
           (incorporated by reference to Exhibit 2(c) to Halliburton
           Company's Current Report on Form 8-K dated June 30, 1996).

   D       Stock Option Agreement, dated as of June 30, 1996, by and between
           Halliburton Company and Landmark Graphics Corporation (incorporated
           by reference to Exhibit 2(b) to Halliburton Company's Current Report
           on Form 8-K dated June 30, 1996).

   E       Form of Affiliate's Agreement by and between Halliburton Company and
           Certain Affiliates of Landmark Graphics Corporation (incorporated by
           reference to Annex B to Exhibit 2(a) to Halliburton Company's Current
           Report on Form 8-K dated June 30, 1996).


 
                                   EXHIBIT A
                                   ---------

           NAME, BUSINESS ADDRESS AND PRESENT PRINCIPAL OCCUPATION OF
           ----------------------------------------------------------
               EACH EXECUTIVE OFFICER AND DIRECTOR OF HALLIBURTON
               --------------------------------------------------
 
I.   Executive Officers of Halliburton
     ---------------------------------

                                                         Present Principal
Name                         Business Address                Occupation
- ----                         ----------------            -----------------

Richard B. Cheney        3600 Lincoln Plaza,         Chairman of the Board,
                          500 North Akard Street     President and Chief
                         Dallas, Texas  75201-3391   Executive Officer and
                                                     Director
 
David J. Lesar           3600 Lincoln Plaza,         Executive Vice President
                          500 North Akard Street     and Chief Financial Officer
                         Dallas, Texas  75201-3391
 
Lester L. Coleman        3600 Lincoln Plaza,         Executive Vice President
                          500 North Akard Street     and General Counsel
                         Dallas, Texas  75201-3391
 
Dale P. Jones            3600 Lincoln Plaza,         Vice Chairman and
                          500 North Akard Street     Director
                         Dallas, Texas  75201-3391
 
Kenneth R. LeSuer        3600 Lincoln Plaza,         President and Chief
                          500 North Akard Street     Executive Officer of
                         Dallas, Texas  75201-3391   Halliburton Energy
                                                     Services

Tommy E. Knight          3600 Lincoln Plaza,         President and Chief
                          500 North Akard Street     Executive Officer of
                         Dallas, Texas  75201-3391   Brown & Root, Inc.
 
 
 
II.  Non-Employee Directors of Halliburton
     -------------------------------------
[CAPTION]

                                                         Present Principal
Name                      Business Address                  Occupation
- ----                      ----------------               -----------------
                                                

Anne L. Armstrong     Kleberg National Bank Bldg.    Chairman of the Board of Trustees,
                      6th and Kleberg Streets        Center for Strategic and 
                      Kingsville, Texas 78363        International Studies,
                                                     Washington, DC 
                    
Richard B. Cheney     3600 Lincoln Plaza             Chairman of the Board,
                      500 North Akard Street         President and Chief Executive 
                      Dallas, Texas 75201            Officer of Halliburton Company 

Lord Clitheroe        Downham Hall, Clitheroe        Chairman, The Yorkshire Bank,
                      Lancashire, BB7 4DN            PLC 

Robert L. Crandall    AMR Corporation                Chairman, President and Chief
                      4333 Amon Carter Blvd.,        Executive Officer, AMR Corporation; 
                      6 North                        and Chairman and Chief Executive 
                      Fort Worth, Texas 76155        Officer, American Airlines, Inc.

W. R. Howell          6501 Legacy Drive, Bldg. D,    Chairman of the Board, 
                      2nd Floor                      J.C. Penney Company, Inc.
                      Plano, Texas 75024                    
     
Delano E. Lewis 635 Massachusetts Ave., N.W. President and Chief Executive Washington, DC 20001-3753 Officer, National Public Radio Dale P. Jones 3600 Lincoln Plaza Vice Chairman, Halliburton 500 North Akard Street Company Dallas, Texas 75201 C. J. Silas P. O. Box 2127 Retired Chairman of the Board 408 Professional Building and Chief Executive Officer, 4th & Keeler Streets Phillips Petroleum Company Bartlesville, Oklahoma 74003 Roger T. Staubach 6750 LBJ Freeway, Suite 1100 Chairman and Chief Executive Dallas, Texas 75240 Officer, The Staubach Company Richard J. 376 South Valencia Avenue Chairman Emeritus, Unocal Stegemeier Brea, California 92621 Corporation E. L. Williamson 83 Dogwood Drive Retired Chairman of the Board Covington, Louisiana 70433 and Chief Executive Officer, The Louisiana Land and Exploration Company