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

                              AMENDMENT NO. 1 TO

                                  SCHEDULE 13D

                   Under the Securities Exchange Act of 1934


                         LANDMARK GRAPHICS CORPORATION
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                                (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
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                 (Name, Address and Telephone Number of Person
               Authorized to Receive Notices and Communications)

                                October 4, 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. [ ]

     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.


 
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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)                                 [ ]

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6    CITIZENSHIP OR PLACE OF ORGANIZATION
 
     Delaware
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                        7    SOLE VOTING POWER
NUMBER
OF                           All outstanding capital stock
SHARES                  --------------------------------------------------------
BENEFICIALLY            8    SHARED VOTING POWER      
OWNED                                                 
BY                           0                        
EACH                    --------------------------------------------------------
REPORTING               9    SOLE DISPOSITIVE POWER   
PERSON                                                
WITH:                        All outstanding capital stock
                        --------------------------------------------------------
                        10   SHARED DISPOSITIVE POWER  
                                                       
                             0                          
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11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     All outstanding capital stock
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12   CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
     CERTAIN SHARES                                                          [ ]

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

     100%
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14   TYPE OF REPORTING PERSON

     CO
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     This Amendment No. 1 (this "Amendment") to the Schedule 13D filed by 
Halliburton Company ("Halliburton") with the Securities and Exchange on July 25,
1996 (the "Original Schedule 13D") amends and restates each of the items of the 
original Schedule 13D set forth below.


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 was merged with and into Merger Sub on October 4,
1996 (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") was converted into 0.574 shares (the "Exchange
Ratio") of common stock, par value $2.50 per share, of Halliburton (the
"Halliburton Common Stock"). 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.

     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, 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 could interfere or be inconsistent
with the Merger (including a competing transaction). The Stockholders also
agreed, if reasonably requested by Halliburton in order to facilitate the
Merger, that they would not, and they would 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 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"), would, 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.
 

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

     Pursuant to the Merger Agreement and as a result of the Merger, Halliburton
acquired all of the outstanding capital stock of Landmark on October 4, 1996.

     Except as set forth above, no transactions in Landmark Common Stock have,
since the filing of the Original Schedule 13D, been effected 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.

 
                                      -1-


 
                                   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:  October 16, 1996                 HALLIBURTON COMPANY



                                        By: /s/ ROBERT M. KENNEDY 
                                            ------------------------------------
                                               Robert M. Kennedy 
                                               Vice President - Legal