STOCK OPTION AGREEMENT


         STOCK OPTION AGREEMENT (the "Agreement"), dated as of June 30, 1996, by
and  between  Landmark  Graphics   Corporation,   a  Delaware  corporation  (the
"Company"), and Halliburton Company, a Delaware corporation (the "Grantee").

                                    Recitals

         The  Grantee,  the Company and  Halliburton  Acq.  Company,  a Delaware
corporation and a wholly-owned  subsidiary of the Grantee  ("Newco")  propose to
enter into an  Agreement  and Plan of Merger  dated as of the date  hereof  (the
"Merger Agreement") providing for, among other things, the merger (the "Merger")
of the Company with and into Newco which shall be the surviving corporation.

         The Board of Directors of the Company has  recommended  the approval of
the Merger Agreement and the Merger by the holders of Company Common Stock.

         As a condition and  inducement to the  Grantee's  willingness  to enter
into the Merger Agreement, the Grantee has requested that the Company agree, and
the Company has agreed, to grant the Grantee the Option (as defined below).

         NOW,  THEREFORE,  in  consideration of the foregoing and the respective
representations,  warranties,  covenants and  agreements set forth herein and in
the Merger Agreement, the Company and the Grantee agree as follows:

                  1. Capitalized  Terms.  Capitalized terms used but not defined
         herein are defined in the Merger Agreement and are used herein with the
         same meanings as ascribed to them therein; provided,  however, that, as
         used in this  Agreement,  "Person" shall have the meaning  specified in
         Sections 3(a)(9) and 13(d)(3) of the Exchange Act.

                  2. Grant of Option.  Subject to the terms and  conditions  set
         forth herein,  the Company  hereby grants to the Grantee an irrevocable
         option (the  "Option") to purchase,  out of the authorized but unissued
         Company  Common  Stock,  a number of shares equal to up to 15.0% of the
         shares of Company  Common Stock  outstanding  as of the date hereof (as
         adjusted as set forth  herein)  (the  "Option  Shares"),  at a purchase
         price of $31.857 per Option Share (the "Exercise Price").

                  3. Term.  The Option shall be exercisable and shall remain in
         full force and effect until the earliest to occur of (i) the Effective
         Time, (ii) the first anniversary of the receipt by Grantee of written 
         notice from the Company of the occurrence of an Exercise 
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         Event (as  hereinafter  defined)  or (iii)  termination  of the  Merger
         Agreement  prior to the occurrence of an Exercise  Event, at which time
         the Option shall  terminate  and be of no further  force or effect (the
         "Term").  The rights and  obligations set forth in Sections 7, 8, 9 and
         10 shall not terminate when the right to exercise the Option terminates
         as set forth  herein,  but shall  extend to such time as is provided in
         those Sections.

                  4. Exercise of Option.

                           (a) The Grantee may exercise the Option,  in whole or
                  in part,  at any time and from  time to time  during  the Term
                  following the occurrence of an Exercise Event. Notwithstanding
                  the  expiration of the Term,  the Grantee shall be entitled to
                  purchase  those  Option  Shares  with  respect to which it has
                  exercised the Option in accordance with the terms hereof prior
                  to the expiration of the Term.

                           (b) As used herein, an "Exercise Event" shall mean 
                  any of the following events:

                                    (i) any Person  (other  than the  Grantee or
                           any  subsidiary of the Grantee)  shall have commenced
                           (as such  term is  defined  in Rule  14d-2  under the
                           Exchange  Act) or  shall  have  filed a  registration
                           statement  under the Securities Act with respect to a
                           tender offer or exchange offer to purchase any shares
                           of Company Common Stock such that, upon  consummation
                           of such offer,  such Person  would own or control 25%
                           or more of the then outstanding Company Common Stock;

                                    (ii) the  Company or any  subsidiary  of the
                           Company shall have authorized,  recommended, proposed
                           or publicly  announced  an  intention  to  authorize,
                           recommend or propose,  or entered  into, an agreement
                           with  any  Person  (other  than  the  Grantee  or any
                           subsidiary  of the  Grantee)  to (A) effect a merger,
                           consolidation,  share exchange or similar transaction
                           involving  the  Company  or any  of  its  Significant
                           Subsidiaries, (B) sell, lease or otherwise dispose of
                           assets   of   the   Company   or   its   subsidiaries
                           representing 15% or more of the  consolidated  assets
                           of the  Company  and its  subsidiaries  or (C) issue,
                           sell or  otherwise  dispose of  (including  by way of
                           merger, consolidation,  share exchange or any similar
                           transaction)   securities  (or  options,   rights  or
                           warrants to purchase, or securities  convertible into
                           or exchangeable  for, such  securities)  representing
                           15% or more of the voting power of the Company or any
                           of its Significant Subsidiaries;

                                    (iii) any Person  (other than the Grantee or
                           any Subsidiary of the Grantee or the Company or, in a
                           fiduciary  capacity,  any of its Subsidiaries)  shall
                           have,  subsequent  to the  date  of  this  Agreement,
                           acquired  beneficial   ownership  (as  such  term  is
                           defined in Rule 13d-3 under the Exchange Act)

                             STOCK OPTION AGREEMENT
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                           or the right to acquire  beneficial  ownership of, or
                           any  "Group"  (as  such  term is  defined  under  the
                           Exchange   Act)   shall   have  been   formed   which
                           beneficially   owns  or  has  the  right  to  acquire
                           beneficial  ownership  of,  25% or more  of the  then
                           outstanding Company Common Stock; or

                                    (iv) the  holders  of Company  Common  Stock
                           shall not have  approved the Merger  Agreement at the
                           meeting of such  stockholders held for the purpose of
                           voting on the Merger  Agreement or such meeting shall
                           not have been  called as required by the terms of the
                           Merger Agreement or shall have been canceled, in each
                           case after any Person  (other than the Grantee or any
                           subsidiary  of  the  Grantee)   shall  have  publicly
                           announced  a  proposal,   or  publicly  disclosed  an
                           intention  to  make  a  proposal,  to  engage  in any
                           transaction  described in clauses (i),  (ii) or (iii)
                           above, or the Company's Board of Directors shall have
                           withdrawn or modified in a manner materially  adverse
                           to the Grantee the  recommendation  of the  Company's
                           Board of  Directors  that the  holders of the Company
                           Common  Stock  approve the Merger  Agreement  and the
                           Merger.

                  (c) If the  Grantee  wishes to exercise  the Option,  it shall
         send a written  notice (the date of which being  herein  referred to as
         the "Notice  Date") to the Company  specifying  (i) the total number of
         Option Shares it intends to purchase pursuant to such exercise and (ii)
         a place and a date not earlier than three (3)  Business  Days nor later
         than fifteen (15) Business Days from the Notice Date for the closing of
         such purchase (the "Closing  Date");  provided,  however,  that, if the
         closing of the purchase and sale pursuant to the Option (the "Closing")
         cannot be consummated by reason of any  applicable  Law,  Regulation or
         Order,  the period of time that  otherwise  would run  pursuant to this
         sentence  shall run instead from the date on which such  restriction on
         consummation has expired or been terminated;  and,  provided,  further,
         that,  without  limiting the  foregoing,  if prior  notification  to or
         approval of any  Governmental  Authority is required in connection with
         such  purchase,  the Grantee  and,  if  applicable,  the Company  shall
         promptly file the required notice or application for approval and shall
         expeditiously  process the same (and the Company shall  cooperate  with
         the  Grantee in the filing of any such  notice or  application  and the
         obtaining of any such approval),  and the period of time that otherwise
         would run pursuant to this sentence  shall run instead from the date on
         which,  as the case may be, (i) any  required  notification  period has
         expired or been terminated or (ii) such approval has been obtained and,
         in either event, any requisite waiting period has passed.

                  (d)  Notwithstanding  Section  4(c),  in no  event  shall  any
         Closing Date be more than eighteen (18) months after the related Notice
         Date,  and, if the Closing Date shall not have occurred within eighteen
         (18) months after the related  Notice Date due to the failure to obtain
         any required approval of a Governmental Authority,  the exercise of the
         Option effected on the Notice Date shall be deemed to have expired.  If
         (i) the  Grantee  receives  official  notice  that an  approval  of any
         Governmental Authority required for the purchase of

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         Option  Shares  will not be issued or  granted  or (ii) a Closing  Date
         shall not have occurred  within  eighteen (18) months after the related
         Notice Date due to the failure to obtain any such required  approval of
         a Governmental Authority, the Grantee shall be entitled to exercise its
         right as set forth in Section 6 or to exercise the Option in connection
         with the  resale  of the  Company  Common  Stock  or  other  securities
         pursuant  to a  registration  statement  as  provided in Section 8. The
         provisions of this Section 4 and Section 5 shall apply with appropriate
         adjustments to any such exercise.

                  5.       Payment and Delivery of Certificates.

                           (a) On each Closing  Date,  the Grantee  shall pay to
                  the Company in immediately available funds by wire transfer to
                  a bank  account  designated  by the Company an amount equal to
                  the  Exercise  Price  multiplied  by the  Option  Shares to be
                  purchased on such Closing Date.

                           (b) At each Closing, simultaneously with the delivery
                  of  immediately  available  funds as provided in Section 5(a),
                  the  Company  shall  deliver to the Grantee a  certificate  or
                  certificates representing the Option Shares to be purchased at
                  such  Closing,  which  Option  Shares  shall be fully paid and
                  nonassessable  and free and clear of all  Liens,  and  Grantee
                  shall  deliver to the Company its written  agreement  that the
                  Grantee  will not offer to sell or  otherwise  dispose of such
                  Option Shares in violation of applicable Law or the provisions
                  of this Agreement.

                           (c)  Certificates  for the Option Shares delivered at
                  each Closing shall be endorsed with a restrictive legend which
                  shall read substantially as follows:

                           THE  TRANSFER  OF  THE  STOCK   REPRESENTED  BY  THIS
                           CERTIFICATE IS SUBJECT TO RESTRICTIONS  ARISING UNDER
                           THE SECURITIES ACT OF 1933, AS AMENDED,  AND PURSUANT
                           TO THE TERMS OF A STOCK OPTION  AGREEMENT DATED AS OF
                           JUNE  30,  1996.  A COPY  OF SUCH  AGREEMENT  WILL BE
                           PROVIDED  TO THE HOLDER  HEREOF  WITHOUT  CHARGE UPON
                           RECEIPT BY THE COMPANY OF A WRITTEN REQUEST THEREFOR.

                  A new certificate or  certificates  evidencing the same number
                  of shares of the  Company  Common  Stock will be issued to the
                  Grantee in lieu of the  certificate  bearing the above legend,
                  which new certificate  shall not bear such legend,  insofar as
                  it applies to the  Securities  Act, if the Grantee  shall have
                  delivered  to the Company a copy of a letter from the staff of
                  the Commission, or an opinion of counsel in form and substance
                  reasonably satisfactory to the Company and its counsel, to the
                  effect that such legend is not  required  for  purposes of the
                  Securities Act.


                             STOCK OPTION AGREEMENT
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                  6.       Adjustment Upon Changes in Capitalization, Etc.

                           (a) In the event of any change in the Company  Common
                  Stock by reason of a stock  dividend,  split-up,  combination,
                  recapitalization,  exchange of shares or similar  transaction,
                  the type and  number of shares or  securities  subject  to the
                  Option,  and the Exercise  Price  therefor,  shall be adjusted
                  appropriately,  and  proper  provision  shall  be  made in the
                  agreements  governing  such  transaction,  so that the Grantee
                  shall  receive upon  exercise of the Option the same class and
                  number of outstanding  shares or other  securities or property
                  that  Grantee  would have  received  in respect of the Company
                  Common  Stock if the  Option  had been  exercised  immediately
                  prior  to  such  event,  or  the  record  date  therefor,   as
                  applicable.  If any  additional  shares of the Company  Common
                  Stock are issued after the date of this Agreement  (other than
                  pursuant to an event  described in the first  sentence of this
                  Section  6(a)),  the Company shall give written notice thereof
                  to the Grantee and, at the Grantee's option exercisable within
                  ten (10)  Business  Days after the  Grantee's  receipt of such
                  notice,  the  number  of shares of the  Company  Common  Stock
                  subject to the Option  shall be adjusted  so that,  after such
                  issuance,  it  equals  15.0% of the  number  of  shares of the
                  Company  Common  Stock then  issued and  outstanding,  so that
                  shares issued  pursuant to the Option and shares  remaining to
                  be issued pursuant to the Option will, in the aggregate, equal
                  15% of the then  issued  and  outstanding  shares  of  Company
                  Common Stock; provided,  however, that the number of shares of
                  the Company  Common Stock  subject to the Option shall only be
                  increased  to  the  extent  the  Company  then  has  available
                  authorized but unissued and  unreserved  shares of the Company
                  Common Stock.

                           (b) If the Company  shall enter into an agreement (i)
                  to  consolidate  or  exchange  shares  with or merge  into any
                  Person, other than the Grantee or one of its subsidiaries, and
                  shall not be the continuing or surviving  corporation or other
                  Person of such  consolidation  or  merger,  (ii) to permit any
                  Person, other than the Grantee or one of its Subsidiaries,  to
                  merge into the Company and the Company shall be the continuing
                  or surviving corporation, but, in connection with such merger,
                  the then  outstanding  shares of Company Common Stock shall be
                  changed into or exchanged for stock or other securities of the
                  Company or any other Person or cash or any other property,  or
                  the shares of Company  Common  stock  outstanding  immediately
                  before such merger shall after such merger represent less than
                  50%  of  the  outstanding   common  shares  and  common  share
                  equivalents  of  the  Company  or  (iii)  to  sell,  lease  or
                  otherwise  transfer all or substantially  all of its assets to
                  any Person, other than the Grantee or one of its Subsidiaries,
                  then,  and in each such case,  the  agreement  governing  such
                  transaction  shall make proper  provisions  so that the Option
                  shall,  upon the consummation of any such transaction and upon
                  the terms and conditions set forth herein,  be converted into,
                  or exchanged  for, an option,  at the election of the Grantee,
                  of any of the following Persons (as designated by the Grantee)
                  (A) the Acquiring  Corporation (as hereinafter  defined),  (B)
                  any Person that controls the

                             STOCK OPTION AGREEMENT
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                  Acquiring Corporation or (C) in the case of a merger described
                  in clause (ii), the Company.

                           (c)  For  purposes  of  this  Section  6,  "Acquiring
                  Corporation" means (i) the continuing or surviving corporation
                  or other Person of a  consolidation,  share exchange or merger
                  with the Company (if other than the Company), (ii) the Company
                  in a merger  or share  exchange  in which the  Company  is the
                  continuing or surviving  corporation  and (iii) the transferee
                  of all or  substantially  all of  the  Company's  assets.  The
                  provisions  of  Sections  7, 8, 9, 10 and 11 shall  apply with
                  appropriate adjustments to any securities for which the Option
                  becomes exercisable pursuant to this Section 6.

                  7.       Repurchase at the Option of Grantee.

                           (a) Unless the Option shall have theretofore  expired
                  or been terminated in accordance with the terms hereof, at the
                  request of the Grantee  made at any time  commencing  upon the
                  first   occurrence  of  a  Repurchase  Event  (as  hereinafter
                  defined) and ending on the first anniversary thereof (the "Put
                  Period"),   the  Company  (or  any  successor  thereto)  shall
                  repurchase  from the  Grantee  (i) that  portion of the Option
                  that then remains  unexercised and (ii) all (but not less than
                  all) the  shares of  Company  Common  Stock  purchased  by the
                  Grantee  pursuant hereto and with respect to which the Grantee
                  then has beneficial  ownership.  The date on which the Grantee
                  exercises  its rights  under this  Section 7 is referred to as
                  the "Request Date." Such  repurchase  shall be at an aggregate
                  price (the "Section 7 Repurchase  Consideration") equal to the
                  sum of:

                                    (i) the  aggregate  exercise  price paid for
                           any shares of Company Common Stock acquired  pursuant
                           to the Option and with  respect to which the  Grantee
                           then has beneficial ownership;

                                    (ii) the excess,  if any, of the  Applicable
                           Price (as defined  below),  over the  Exercise  Price
                           (subject  to  adjustment  pursuant to Section 6) paid
                           (or,  in the case of Option  Shares  with  respect to
                           which the Option has been  exercised  but the Closing
                           Date has not  occurred,  payable)  by the Grantee for
                           each share of Company  Common  Stock with  respect to
                           which the Option has been  exercised and with respect
                           to which the Grantee then has  beneficial  ownership,
                           multiplied by the number of such shares; and

                                    (iii)  the  excess,   if  any,  of  (x)  the
                           Applicable  Price for each  share of  Company  Common
                           Stock  over  (y)  the  Exercise   Price  (subject  to
                           adjustment  pursuant to Section 6), multiplied by the
                           number of shares of Company Common Stock with respect
                           to which the Option has not been exercised.

                             STOCK OPTION AGREEMENT
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                           (b) If the Grantee  exercises  its rights  under this
                  Section 7, the Company  shall,  within ten (10)  Business Days
                  after  the  Request   Date,   pay  the  Section  7  Repurchase
                  Consideration  to the Grantee in immediately  available funds,
                  and the Grantee shall  surrender to the Company the Option and
                  the certificates evidencing the shares of Company Common Stock
                  purchased  thereunder  with  respect to which the Grantee then
                  has beneficial ownership, and the Grantee shall warrant to the
                  Company  that,  immediately  prior to the  repurchase  thereof
                  pursuant  to this  Section 7, the  Grantee had sole record and
                  beneficial  ownership of such shares and that such shares were
                  then held free and clear of all Liens.

                           (c) For purposes of this  Agreement,  the "Applicable
                  Price' means the highest of (i) the highest price per share at
                  which a tender or  exchange  offer has been made for shares of
                  Company  Common Stock after the date hereof and on or prior to
                  the Request  Date,  (ii) the price per share to be paid by any
                  third Person for shares of Company Common Stock,  in each case
                  pursuant  to an  agreement  for a  merger  or  other  business
                  combination  transaction  with the Company  entered into on or
                  prior to the Request Date, or (iii) the highest  closing sales
                  price per share of Company Common Stock quoted on the New York
                  Stock Exchange Composite Transactions or, if not so quoted, on
                  the New York Stock Exchange (or if Company Common Stock is not
                  quoted on the New York Stock  Exchange,  the highest bid price
                  per share as  quoted on The  NASDAQ  Stock  Market  or, if the
                  shares of Company Common Stock are not quoted thereon,  on the
                  principal  trading  market on which such  shares are traded as
                  reported  by  a  recognized  source)  during  the  sixty  (60)
                  Business Days preceding the Request Date. If the consideration
                  to be  offered,  paid or  received  pursuant  to either of the
                  foregoing clauses (i) or (ii) shall be other than in cash, the
                  value of such consideration  shall be determined in good faith
                  by an independent  nationally  recognized  investment  banking
                  firm selected by the Grantee and reasonably  acceptable to the
                  Company,  which  determination  shall  be  conclusive  for all
                  purposes of this Agreement.

                           (d) As used herein,  a  "Repurchase  Event" means the
                  occurrence  of  any  Exercise   Event   specified  in  Section
                  4(b)(ii), (iii) or (iv).

                           (e)  Notwithstanding any provision to the contrary in
                  this  Agreement,  the  Grantee  may not  exercise  its  rights
                  pursuant to this  Section 7 in a manner  that would  result in
                  the cash payment to the Grantee of an  aggregate  amount under
                  this Section 7 of more than $24 million, including the amount,
                  if any, of the Termination Fee paid to the Grantee pursuant to
                  Section 9.05 of the Merger Agreement;  provided, however, that
                  nothing in this sentence shall limit the Grantee's  ability to
                  exercise the Option in accordance with its terms.


                             STOCK OPTION AGREEMENT
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                  8.       Repurchase at the Option of The Company.

                           (a)  Unless  the   Grantee   shall  have   previously
                  exercised  its rights  under  Section 7, at the request of the
                  Company  during  the  six-month   period   commencing  at  the
                  expiration of the Put Period (the "Call Period"),  the Company
                  may repurchase from the Grantee, and the Grantee shall sell to
                  the Company, all (but not less than all) the shares of Company
                  Common Stock acquired by the Grantee  pursuant hereto and with
                  respect to which the Grantee has  beneficial  ownership at the
                  time of such  repurchase  at a price  per  share  equal to the
                  greater  of (A)  the  Current  Market  Price  (as  hereinafter
                  defined) or (B) the Exercise Price per share in respect of the
                  shares so  acquired  (such price  multiplied  by the number of
                  shares of Company Common Stock to be  repurchased  pursuant to
                  this Section 8 being  herein  called the "Section 8 Repurchase
                  Consideration");  provided,  however, that the Grantee, within
                  thirty  (30)  days  following  the  Company's  notice  of  its
                  intention to purchase  shares  pursuant to this Section 8, may
                  deliver an Offeror's  Notice  pursuant to Section 10, in which
                  case  the  provisions  of  Section  10 and not  those  of this
                  Section 8 shall  control  (unless  the sale to a third  Person
                  contemplated  thereby  is  not  consummated);   and  provided,
                  further,  that the Company's rights under this Section 8 shall
                  be   suspended   (and  the  Call  Period   shall  be  extended
                  accordingly)  during  any  period  when the  exercise  of such
                  rights  would  subject  the Grantee to  liability  pursuant to
                  Section 16(b) of the Exchange Act by reason of the issuance of
                  the Option,  any adjustment  pursuant to Section 6 hereof, the
                  Grantee's purchase of shares of Company Common Stock hereunder
                  or the  Grantee's  sale of shares  pursuant to Section 7, 8 or
                  10.

                           (b) If the Company  exercises  its rights  under this
                  Section 8 and the Grantee does not deliver an Offeror's Notice
                  or, having delivered an Offeror's Notice, the Grantee does not
                  sell  the  shares  to a third  Person  pursuant  thereto,  the
                  Company  shall,  within  ten  (10)  Business  Days  after  the
                  expiration  of the  Grantee's  rights to deliver an  Offeror's
                  Notice or to sell the shares subject to an Offeror's Notice to
                  a third Person, pay the Section 8 Repurchase  Consideration in
                  immediately  available  funds, and the Grantee shall surrender
                  to the Company  certificates  evidencing the shares of Company
                  Common  Stock  purchased  hereunder,  and  the  Grantee  shall
                  warrant  to  the  Company  that,   immediately  prior  to  the
                  repurchase thereof pursuant to this Section 8, the Grantee had
                  sole record and  beneficial  ownership of such shares and that
                  such shares were then held free and clear of all Liens.

                           (c) As used herein,  "Current Market Price" means the
                  average  closing sales price per share of Company Common Stock
                  quoted on the New York Stock Exchange Composite  Transactions,
                  or, if not so quoted,  on the New York Stock  Exchange  (or if
                  Company  Common  Stock is not  quoted  on the New  York  Stock
                  Exchange,  on The  NASDAQ  Stock  Market  or, if the shares of
                  Company Common Stock are not quoted thereon,  on the principal
                  trading market on which such shares

                             STOCK OPTION AGREEMENT
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                  are traded as  reported  by a  recognized  source) for the ten
                  (10) Business Days preceding the date of the Company's request
                  for repurchase pursuant to this Section 8.

                  9. Registration Rights. The Company shall, if requested by the
         Grantee  at any time and from time to time  within  three  years of the
         first  exercise  of  the  Option  (the   "Registration   Period"),   as
         expeditiously  as  practicable  prepare,  file  and  cause  to be  made
         effective up to two registration statements under the Securities Act if
         such  registration  is  necessary  or  desirable in order to permit the
         offering,  sale and  delivery  of any or all shares of  Company  Common
         Stock or other securities that have been acquired by or are issuable to
         the Grantee upon exercise of the Option in accordance with the intended
         method of sale or other disposition  stated by the Grantee,  including,
         at the sole discretion of the Company, a "shelf" registration statement
         under Rule 415 under the Securities Act or any successor provision, and
         the Company shall use all reasonable  efforts to qualify such shares or
         other securities  under any applicable  state securities laws.  Without
         the  Grantee's  prior  written  consent,  no  other  securities  may be
         included  in any  such  registration.  The  Grantee  agrees  to use all
         reasonable  efforts to cause, and to cause any underwriters of any sale
         or other disposition to cause, any sale or other  disposition  pursuant
         to such registration  statement to be effected on a widely  distributed
         basis so that upon  consummation  thereof no  purchaser  or  transferee
         shall  own  beneficially  more than 2% of the then  outstanding  voting
         power of the Company.  The Company shall use all reasonable  efforts to
         cause each such registration  statement to become effective,  to obtain
         all consents or waivers of other  parties  which are required  therefor
         and to keep such registration  statement  effective for such period not
         in excess of 180 days from the day such  registration  statement  first
         becomes effective as may be reasonably necessary to effect such sale or
         other  disposition.  The obligations of the Company hereunder to file a
         registration  statement  and  to  maintain  its  effectiveness  may  be
         suspended for one or more periods of time not exceeding sixty (60) days
         in the  aggregate if the Board of  Directors of the Company  shall have
         determined  in good faith that the filing of such  registration  or the
         maintenance of its effectiveness  would require disclosure of nonpublic
         information that would materially and adversely affect the Company. The
         expenses  associated  with  the  preparation  and  filing  of any  such
         registration  statement pursuant to this Section 9 and any sale covered
         thereby  (including  any fees  related to blue sky  qualifications  and
         filing  fees in  respect  of the  National  Association  of  Securities
         Dealers,  Inc.)  ("Registration  Expenses") shall be for the account of
         the  Company  except  for  underwriting  discounts  or  commissions  or
         brokers'  fees in respect to shares to be sold by the  Grantee  and the
         fees and  disbursements of the Grantee's  counsel;  provided,  however,
         that the  Company  shall not be  required  to pay for any  Registration
         Expenses with respect to such registration if the registration  request
         is  subsequently  withdrawn  at the request of the  Grantee  unless the
         Grantee  agrees to  forfeit  its  right to  request  one  registration;
         provided further,  however, that, if at the time of such withdrawal the
         Grantee  has  learned of a material  adverse  change in the  results of
         operations,  condition  (financial or other),  business or prospects of
         the  Company  from that known to the Grantee at the time of its request
         and has  withdrawn  the request with  reasonable  promptness  following
         disclosure by the Company of such

                             STOCK OPTION AGREEMENT
                                       -9-





         material adverse change,  then the Grantee shall not be required to pay
         any of such expenses and shall retain all  remaining  rights to request
         registration.  The Grantee  shall  provide all  information  reasonably
         requested by the Company for inclusion in any registration statement to
         be filed hereunder. If during the Registration Period the Company shall
         propose to register  under the  Securities  Act the offering,  sale and
         delivery  of Company  Common  Stock for cash for its own account or for
         any other  stockholder of the Company pursuant to a firm  underwriting,
         it shall,  in addition to the Company's  other  obligations  under this
         Section  9,  allow  the  Grantee  the  right  to  participate  in  such
         registration   provided   that   the   Grantee   participates   in  the
         underwriting;  provided,  however, that, if the managing underwriter of
         such  offering  advises the Company in writing  that in its opinion the
         number of shares of Company  Common  Stock  requested to be included in
         such  registration  exceeds  the  number  which  can be  sold  in  such
         offering,   the  Company  shall,  after  fully  including  therein  all
         securities to be sold by the Company,  include the shares  requested to
         be included  therein by Grantee pro rata (based on the number of shares
         intended  to be  included  therein)  with  the  shares  intended  to be
         included therein by Persons other than the Company.  In connection with
         any offering,  sale and delivery of Company  Common Stock pursuant to a
         registration statement effected pursuant to this Section 9, the Company
         and the Grantee  shall provide each other and each  underwriter  of the
         offering with  customary  representations,  warranties  and  covenants,
         including covenants of indemnification  and contribution.  For purposes
         of  determining  whether two requests have been made under this Section
         9, only requests  relating to a registration  statement that has become
         effective  under the  Securities  Act and pursuant to which the Grantee
         has disposed of all shares covered  thereby in the manner  contemplated
         therein shall be counted.

                  10. First Refusal.  At any time after the first  occurrence of
         an  Exercise  Event and prior to the  second  anniversary  of the first
         purchase of shares of Company Common Stock  pursuant to the Option,  if
         the Grantee shall desire to sell, assign, transfer or otherwise dispose
         of all or any of the shares of Company Common Stock or other securities
         acquired  by it  pursuant  to the  Option,  it shall  give the  Company
         written notice of the proposed  transaction  (an  "Offeror's  Notice"),
         identifying the proposed transferee, accompanied by a copy of a binding
         offer to  purchase  such  shares  or other  securities  signed  by such
         transferee and setting forth the terms of the proposed transactions. An
         Offeror's  Notice  shall  be  deemed  an offer  by the  Grantee  to the
         Company,  which may be accepted,  in whole but not in part,  within ten
         (10) Business Days of the receipt of such Offeror's Notice, on the same
         terms and  conditions  and at the same  price at which the  Grantee  is
         proposing  to  transfer  such  shares  or  other   securities  to  such
         transferee.  The purchase of any such shares or other securities by the
         Company  shall be settled  within ten (10) Business Days of the date of
         the acceptance of the offer and the purchase price shall be paid to the
         Grantee in immediately  available funds. In the event of the failure or
         refusal of the Company to purchase  all the shares or other  securities
         covered by an Offeror's Notice, the Grantee may, within sixty (60) days
         from the date of the Offeror's Notice, sell all, but not less than all,
         of such shares or other  securities  to the proposed  transferee  at no
         less than the price specified and on terms no more favorable than those
         set  forth  in  the  Offeror's  Notice;  provided,  however,  that  the
         provisions of this

                             STOCK OPTION AGREEMENT
                                      -10-





         sentence  shall not limit the rights the Grantee may otherwise  have if
         the Company has accepted the offer  contained in the  Offeror's  Notice
         and  wrongfully  refuses to  purchase  the  shares or other  securities
         subject thereto. The requirements of this Section 10 shall not apply to
         (a) any disposition as a result of which the proposed  transferee would
         own  beneficially  not more than 2% of the outstanding  voting power of
         the  Company,  (b) any  disposition  of Company  Common  Stock or other
         securities  by a Person to whom the  Grantee  has  assigned  its rights
         under the Option with the consent of the Company, (c) any sale by means
         of a public  offering  registered  under the  Securities Act or (d) any
         transfer to a  wholly-owned  Subsidiary  of the Grantee which agrees in
         writing to be bound by the terms hereof.

                  11.  Listing.  If  the  Company  Common  Stock  or  any  other
         securities  then  subject to the Option are then listed on the New York
         Stock Exchange,  the Company, upon the occurrence of an Exercise Event,
         will  promptly  file an  application  to list  on the  New  York  Stock
         Exchange  the shares of the Company  Common  Stock or other  securities
         then subject to the Option and will use all reasonable efforts to cause
         such listing application to be approved as promptly as practicable.

                  12.  Replacement of Agreement.  Upon receipt by the Company of
         evidence reasonably satisfactory to it of the loss, theft,  destruction
         or mutilation  of this  Agreement,  and (in the case of loss,  theft or
         destruction)  of  reasonably  satisfactory  indemnification,  and  upon
         surrender and cancellation of this Agreement, if mutilated, the Company
         will execute and deliver a new  Agreement  of like tenor and date.  Any
         such  new  Agreement   shall   constitute  an  additional   contractual
         obligation  of the  Company,  whether  or not the  Agreement  so  lost,
         stolen,  destroyed or  mutilated  shall at any time be  enforceable  by
         anyone.

                  13.      Miscellaneous.

                           (a)  Expenses.  Except as  otherwise  provided in the
                  Merger Agreement or in Sections 7, 8 and 9 hereof, each of the
                  parties  hereto  shall  bear and pay all  costs  and  expenses
                  incurred  by  it or on  its  behalf  in  connection  with  the
                  transactions   contemplated  hereunder,   including  fees  and
                  expenses of its own financial consultants, investment bankers,
                  accountants and counsel.

                           (b)  Waiver  and  Amendment.  Any  provision  of this
                  Agreement  may be  waived  at any  time by the  party  that is
                  entitled to the benefits of such provision. This Agreement may
                  not be modified,  amended, altered or supplemented except upon
                  the execution and delivery of a written agreement  executed by
                  the parties hereto.

                           (c) Entire  Agreement;  No Third  Party  Beneficiary;
                  Severability.  Except as  otherwise  set  forth in the  Merger
                  Agreement,  this Agreement (including the Merger Agreement and
                  the other  documents and  instruments  referred to herein) (i)
                  constitutes  the entire  agreement  and  supersedes  all prior
                  agreements and understandings,  both written and oral, between
                  the parties with respect to the subject

                             STOCK OPTION AGREEMENT
                                      -11-





                  matter  hereof  and (ii) is not  intended  to confer  upon any
                  Person  other than the  parties  hereto any rights or remedies
                  hereunder. If any term, provision,  covenant or restriction of
                  this Agreement is held by a court of competent jurisdiction to
                  be invalid, void or unenforceable, the remainder of the terms,
                  provisions, covenants and restrictions of this Agreement shall
                  remain  in  full  force  and  effect  and  shall  in no way be
                  affected, impaired or invalidated.

                           (d) Governing Law. This  Agreement  shall be governed
                  by, and construed in accordance with, the Laws of the State of
                  Texas,  regardless  of the Laws that  might  otherwise  govern
                  under  applicable  principles  of conflicts of law;  provided,
                  however,  that any matter  involving  the  internal  corporate
                  affairs  of  any  party   hereto  shall  be  governed  by  the
                  provisions of the GCL.

                           (e) Descriptive Headings.  The descriptive headings 
                  contained herein are for convenience or reference only and 
                  shall not affect in any way the meaning or interpretation of 
                  this Agreement.

                           (f)  Notices.  All notices  and other  communications
                  hereunder  shall be in  writing  and shall be deemed  given if
                  delivered personally, telecopied (with confirmation) or mailed
                  by registered or certified mail (return receipt  requested) to
                  the  parties  at the  following  addresses  (or at such  other
                  address for a party as shall be specified by like notice):

                  If to the Company to:

                           Landmark Graphics Corporation
                           15150 Memorial Drive
                           Houston, Texas  77079-4304
                           Attention:  Patti Massaro, General Counsel
                                              and Corporate Secretary
                           Telecopier No.:  (713) 560-1383

                  with a copy to:

                           Winstead Sechrest & Minick P.C.    
                           5400 Renaissance Tower             
                           1201 Elm Street                    
                           Dallas, Texas  75270                        
                           Attention:  Robert E. Crawford, Jr.         
                           Telecopier No.:  (214) 745-5390

                           Shearman & Sterling
                           599 Lexington Avenue
                           New York, New York 10022
                           Attention:  David W. Heleniak
                           Telecopier No.:  (212) 848-7179
                      
                             STOCK OPTION AGREEMENT
                                      -12-





                  If to Grantee to:

                           Halliburton Company
                           3600 Lincoln Plaza
                           500 North Akard Street
                           Dallas, Texas  75201-3391
                           Attention:  Lester L. Coleman, Executive 
                               Vice President and General Counsel
                           Telecopier No.: (214) 978-2658

                  with a copy to:

                           Vinson & Elkins L.L.P.
                           2300 First City Tower
                           1001 Fannin Street
                           Houston, Texas  77002-6760
                           Attention:  William E. Joor III, Esq.
                           Telecopier No.:  (713) 615-5282

                           (g)  Counterparts.  This Agreement and any amendments
                  hereto  may be  executed  in two  counterparts,  each of which
                  shall be  considered  one and the  same  agreement  and  shall
                  become  effective when both  counterparts  have been signed by
                  each of the parties and delivered to the other party, it being
                  understood  that  both  parties  need  not  execute  the  same
                  counterpart.

                           (h) Assignment. Neither this Agreement nor any of the
                  rights, interests or obligations hereunder or under the Option
                  shall be assigned by either of the parties hereto  (whether by
                  operation  of law or  otherwise)  without  the  prior  written
                  consent of the other party, except that the Grantee may assign
                  this  Agreement to a  wholly-owned  Subsidiary of the Grantee;
                  provided,  however,  that no such  assignment  shall  have the
                  effect  of  releasing   the  Grantee   from  its   obligations
                  hereunder.  Subject to the preceding sentence,  this Agreement
                  shall  be  binding  upon,  inure  to  the  benefit  of  and be
                  enforceable by the parties and their respective successors and
                  assigns.

                           (i) Further Assurances.  In the event of any exercise
                  of the Option by the  Grantee,  the  Company  and the  Grantee
                  shall execute and deliver all other  documents and instruments
                  and take all other action that may be reasonably  necessary in
                  order to  consummate  the  transactions  provided  for by such
                  exercise.

                           (j) Specific Performance.  The parties hereto agree 
                  that this Agreement may be enforced by either party through 
                  specific performance, injunctive relief and other equitable 
                  relief.  Both parties further agree to waive any requirement 
                  for the securing or posting of any bond in connection with 
                  the obtaining of any such

                             STOCK OPTION AGREEMENT
                                      -13-




                  equitable relief and that this provision is without  prejudice
                  to any other  rights that the parties  hereto may have for any
                  failure to perform this Agreement.

         IN WITNESS WHEREOF,  the Company and the Grantee have caused this Stock
Option  Agreement  to be  signed by their  respective  officers  thereunto  duly
authorized, all as of the day and year first written above.

                                        LANDMARK GRAPHICS CORPORATION


                                        By:_______________________________
                                            Robert P. Peebler
                                            President, Chief Executive Officer
                                              and Chief Operating Officer


                                        HALLIBURTON COMPANY


                                        By:_______________________________
                                            Lester L. Coleman
                                            Executive Vice President 
                                              and General Counsel



VEHOU05:17946.1

                             STOCK OPTION AGREEMENT
                                      -14-