`
`UNITED STATES PATENT AND TRADEMARK OFFIGE
`
`UNITED STATES DEPARTMENT OF COMMERCE
`United States Patent and Trademark Office
`!
`OX.
`Address: COMMISSIONER FOR PATENTS
`Alexandria, Virginia 22313-1450
`www.uspto.gov
`
`APPLICATION
`NUMBER
`
`FILING or
`371(c) DATE
`
`GRP ART
`UNIT
`
`
`
`
`
`FIL
`
`61/898,960
`
`11/01/2013
`
`FEE REC'D
`
`260
`
`ATTY.DOCKET.NO
`
`42183US01
`
`ITOT CLAIMSJIND CLAIMS
`
`28841
`ConocoPhillips Company
`
`Legal Department- Intellectual Property Docketing AE
`600 North Dairy Ashford (77079-1175)
`0000000649 15606
`P.O. Box 4783
`Houston, TX 77210-4783
`
`CONFIRMATION NO. 3851
`
`FILING RECEIPT
`
`Date Mailed: 11/14/2013
`
`It will not be examined for patentability and will
`Receipt is acknowledged of this provisional patent application.
`become abandonednotlater than twelve monthsafter its filing date. Any correspondence concerning the application
`mustinclude the following identification information: the U.S. APPLICATION NUMBER, FILING DATE, NAME OF
`APPLICANT, and TITLE OF INVENTION. Feestransmitted by checkor draft are subject to collection. Please verify
`the accuracy of the data presented on this receipt. If an error is noted on this Filing Receipt, please submit
`a written request for a Filing Receipt Correction. Please provide a copy of this Filing Receipt with the
`changes noted thereon. If you received a "Notice to File Missing Parts" for this application, please submit
`any corrections to this Filing Receipt with your reply to the Notice. When the USPTO processesthe reply
`to the Notice, the USPTO will generate another Filing Receipt incorporating the requested corrections
`
`Inventor(s)
`
`Chengbo LI, Houston, TX;
`Sam T. KAPLAN, Oakland, CA;
`Charles T. MOSHER, Houston, TX;
`Joel D. BREWER, Houston, TX;
`Robert G. KEYS, Houston, TX;
`
`Applicant(s)
`
`CONOCOPHILLIPS COMPANY, Houston, TX
`Powerof Attorney:
`Sung Pio--63290
`
`Permission to Access - A proper Authorization to Permit Access to Application by Participating Offices
`(PTO/SB/39 or its equivalent) has been received by the USPTO.
`
`If Required, Foreign Filing License Granted: 11/08/2013
`The country code and number of your priority application, to be usedfor filing abroad under the Paris Convention,
`is US 61/898,960
`Projected Publication Date: None, application is not eligible for pre-grant publication
`Non-Publication Request: No
`Early Publication Request: No
`Title
`
`COMPRESSIVE SENSING
`
`Statement under 37 CFR 1.55 or 1.78 for AIA (First Inventor to File) Transition Applications: No
`page 1 of 3
`
`

`

`PROTECTING YOUR INVENTION OUTSIDE THE UNITED STATES
`
`Since the rights granted by a U.S. patent extend only throughout the territory of the United States and have no
`effect in a foreign country, an inventor who wishes patent protection in another country must apply for a patent
`in a specific country or in regional patent offices. Applicants may wish to consider thefiling of an international
`application under the Patent Cooperation Treaty (PCT). An international (PCT) application generally has the same
`effect as a regular national patent application in each PCT-member country. The PCT process simplifies the filing
`of patent applications on the same invention in member countries, but does notresult in a grantof "an international
`patent" and doesnoteliminate the needof applicantsto file additional documents and fees in countries where patent
`protection is desired.
`
`Almost every country has its own patent law, and a person desiring a patent in a particular country must make an
`application for patent in that country in accordancewith its particular laws. Since the laws of many countries differ
`in various respects from the patent law of the United States, applicants are advised to seek guidance from specific
`foreign countries to ensure that patent rights are not lost prematurely.
`
`Applicants also are advised that in the case of inventions madein the United States, the Director of the USPTO must
`issue a license before applicants can apply for a patent in a foreign country. Thefiling of a U.S. patent application
`serves as a request for a foreign filing license. The application's filing receipt contains further information and
`guidance asto the status of applicant's license for foreign filing.
`
`Applicants may wish to consult the USPTO booklet, "General Information Concerning Patents”(specifically, the
`section entitled "Treaties and Foreign Patents") for more information on timeframes and deadlinesfor filing foreign
`patent applications. The guide is available either by contacting the USPTO Contact Center at 800-786-9199, or it
`can be viewed on the USPTO website at http://“www.uspto.gov/web/offices/pac/doc/general/index.html.
`
`For information on preventing theft of your intellectual property (patents, trademarks and copyrights), you may wish
`to consult the U.S. Government website, http:/Avww.stopfakes.gov. Part of a Department of Commerceinitiative,
`this website includes self-help "toolkits" giving innovators guidance on how to protectintellectual property in specific
`countries such as China, Korea and Mexico. For questions regarding patent enforcementissues, applicants may
`call the U.S. Governmenthotline at 1-866-999-HALT (1-866-999-4258).
`
`LICENSE FOR FOREIGN FILING UNDER
`
`Title 35, United States Code, Section 184
`
`Title 37, Code of Federal Regulations, 5.11 & 5.15
`
`GRANTED
`
`if the phrase "IF REQUIRED, FOREIGN FILING
`The applicant has been granted a license under 35 U.S.C. 184,
`LICENSE GRANTED"followed by a date appears on this form. Such licenses are issuedin all applications where
`the conditions for issuance of a license have been met, regardless of whether or not a license may be required as
`set forth in 37 CFR 5.15. The scope andlimitations of this license are set forth in 37 CFR 5.15(a) unless an earlier
`license has been issued under 37 CFR 5.15(b). The license is subject to revocation upon written notification. The
`date indicatedis the effective date of the license, unless an earlier license of similar scope has been granted under
`37 CFR 5.13 or 5.14.
`
`page 2 of 3
`
`

`

`This licenseis to be retained by the licensee and maybe usedat any time onor after the effective date thereof unless
`it is revoked. This license is automatically transferred to any related applications(s) filed under 37 CFR 1.53(d). This
`license is not retroactive.
`
`The grantof a license doesnot in any way lessen the responsibility of a licensee for the security of the subject matter
`as imposed by any Governmentcontract or the provisions of existing laws relating to espionage and the national
`security or the export of technical data. Licensees should apprise themselvesof current regulations especially with
`respect to certain countries, of other agencies, particularly the Office of Defense Trade Controls, Department of
`State (with respect to Arms, Munitions and Implements of War (22 CFR 121-128)); the Bureau of Industry and
`Security, Department of Commerce (15 CFR parts 730-774); the Office of Foreign AssetsControl, Department of
`Treasury (31 CFR Parts 500+) and the Department of Energy.
`
`NOT GRANTED
`
`No license under 35 U.S.C. 184 has been granted at this time, if the phrase "IF REQUIRED, FOREIGN FILING
`LICENSE GRANTED" DOESNOTappear on this form. Applicant maystill petition for a license under 37 CFR 5.12,
`if a license is desired before the expiration of 6 months from thefiling date of the application. If 6 months has lapsed
`from thefiling date of this application and the licensee has not received any indication of a secrecy order under 35
`U.S.C. 181, the licensee mayforeign file the application pursuant to 37 CFR 5.15(b).
`
`
`SelectUSA
`
`The United States represents the largest, most dynamic marketplace in the world and is an unparalleled location for
`businessinvestment, innovation, and commercialization of new technologies. The U.S. offers tremendous resources
`and advantages for those who invest and manufacture goods here. Through SelectUSA, our nation works to
`promote andfacilitate business investment. SelectUSAprovides information assistance to the international investor
`community; serves as an ombudsmanfor existing and potential investors; advocates on behalf of U.S. cities, states,
`and regions competing for global investment; and counsels U.S. economic developmentorganizations on investment
`attraction best practices. To learn more about why the United States is the best country in the world to develop
`technology, manufacture products, deliver services, and grow your business, visit http:/Awww.SelectUSA.govor call
`+1-202-482-6800.
`
`page 3 of 3
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`

`

`PTO/AIA/14 (03-13)
`Approved for use through 01/31/2014. OMB 0651-0032
`U.S. Patent and Trademark Office; U.S. DEPARTMENT OF COMMERCE
`Under the Paperwork Reduction Act of 1995, no persons are required to respond to a collection ofinformation unless it contains a valid OMB control number.
`
` .
`
`. Attorney Docket Number|42183US01
`
`
`Application Data Sheet 37 CFR 1.76
`
`Application Number
`
`
`
`
`
`
`
`Title of Invention
`
`COMPRESSIVE SENSING
`
`The application data sheetis part of the provisional or nonprovisional application for whichit is being submitted. The following form contains the
`bibliographic data arranged in a format specified by the United States Patent and Trademark Office as outlined in 37 CFR 1.76.
`This document may be completed electronically and submitted to the Office in electronic format using the Electronic Filing System (EFS) or the
`document may be printed and included in a paper filed application.
`
`
`
`
`
`Secrecy Order 37 CFR 5.2
`Portions or all of the application associated with this Application Data Sheet may fall under a Secrecy Order pursuantto
`L] 37CFR52 (Paperfilers only. Applications that fall under Secrecy Order may not be filed electronically.}
`
`Inventor Information:
`
`
`1
`
`Inventor
`Legal Name
`
`Prefix) Given Name
`Middle Name
`Family Name
`Suffix
`
`Chengbo
`Residence Information (Select One)
`(e) US Residency
`©) NonUS Residency
`() Active US Military Service
`
`Mailing Addressof Inventor:
`
`Address 1
`
`Address 2
`
`Postal Code
`
`1405 W.Hilshire Park Dr.
`
`77055
`
`US
`
`2
`Inventor
`
`Legal Name
`
`
`
`Sam
`T.
`KAPLAN
`
`Residence Information (Select One)
`(@} US Residency
`©) NonUS Residency
`() Active US Military Service
`
`
`City|Oakland State/Province|CA Country of Residence i|US
`
`
`
`Mailing Address of Inventor:
`
`Address 1
`
`Address 2
`
`City
`
`Postal Code
`
`Inventor
`Legal Name
`
`3
`
`Oakland
`
`Prefix) Given Name
`Charles
`
`27 Kingwood Rd.
`
`94619
`
`State/Province
`
`CA
`
`US
`
`Middle Name
`T.
`
`Family Name
`MOSHER
`
`Suffix
`
`Residence Information (Select One)
`
`(@) US Residency
`
`©) NonUS Residency
`
`() Active US Military Service
`
`EFS Web 2.2.6
`
`

`

`PTO/AIA/14 (03-13)
`Approved for use through 01/31/2014. OMB 0651-0032
`U.S. Patent and Trademark Office; U.S. DEPARTMENT OF COMMERCE
`Underthe Paperwork Reduction Act of 1995, no persons are required to respond to a collection of information unless it contains a valid OMB control number.
`
`
`Attorney Docket Number|42183US01
`
`
`Application Data Sheet 37 CFR 1.76
`
`
`
`
`
`Title of Invention
`COMPRESSIVE SENSING
`
`
`
`
`City | Country of Residence!|US Houston | State/Province | TX
`
`Application Number
`
`Mailing Address of Inventor:
`
`Address 1
`
`Address 2
`
`5907 Saratoga Springs Ln.
`
`Postal Code
`
`77044
`
`US
`
`Inventor
`4
`Legal Name
`
`Prefix) Given Name
`
`Middle Name
`
`Family Name
`
`Suffix
`
`
`
`
`
`
`
`() Active US Military Service
`©) NonUS Residency
`(@) US Residency
`Residence Information (Select One)
`
`
`City|Houston State/Province|TX Country of Residence i|US
`
`
`
`Mailing Addressof Inventor:
`
`Address 1
`
`Address 2
`
`514 Cypress Vista
`
`Postal Code
`
`77094
`
`US
`
`5
`
`Inventor
`Legal Name
`Prefix)GivenName Middle Name
`
`Family Name
`
`Residence Information (Select One)
`
`(@)} US Residency
`
`©) NonUS Residency
`
`() Active US Military Service
`
`Mailing Address of Inventor:
`
`Address 1
`
`Address 2
`
`12239 N. Shacow CoveDr.
`
`Postal Code
`
`77082
`
`US
`
`Inventor Information blocks may be
`Inventors Must Be Listed - Additional
`All
`generated within this form by selecting the Add button.
`
`Ace
`
`Suffix
`
`CorrespondenceInformation:
`
`Enter either Customer Number or complete the Correspondence Information section below
`
`For further information see 37 CFR 1.33(a).
`
`[|]An Addressis being provided for the correspondenceInformation of this application.
`EFS Web 2.2.6
`
`

`

`PTO/AIA/14 (03-13)
`Approved for use through 01/31/2014. OMB 0651-0032
`U.S. Patent and Trademark Office; U.S. DEPARTMENT OF COMMERCE
`Underthe Paperwork Reduction Act of 1995, no persons are required to respond to a collection of information unless it contains a valid OMB control number.
`
`Attorney Docket Number|42183US01
`
`
`
` Application Data Sheet 37 CFR 1.76
`
`Application Number
`
`
`
`
`
`
`
`
`Title of Invention
`COMPRESSIVE SENSING
`
`
`Customer Number
`
`28841
`
`Email Address
`
`
`Application Information:
`
`Legal-IP@conocophillips.com
`
`Title of the Invention
`
`COMPRESSIVE SENSING
`
`Attorney Docket Number] 42183U801, Small Entity Status Claimed [|
`Application Type
`Provisional
`
`Total Numberof Drawing Sheets (if any)
`
`Suggested Figure for Publication {if any)
`
`Publication Information:
`
`[_] Request Early Publication (Fee required at time of Request 37 CFR 1.219)
`
`[]
`
`Req uest Not to Publish. | hereby request that the attached application not be published under
`35 U.S.C. 122(b) and certify that the invention disclosed in the attached application has not and will not be the
`subject of an application filed in another country, or under a multilateral international agreement, that requires
`publication at eighteen monthsafterfiling.
`
`Representative Information:
`
`Representative information should be provided for all practitioners having a power of attorney in the application. Providing
`this information in the Application Data Sheet does not constitute a power of attorneyin the application (see 37 CFR 1.32).
`Either enter Customer Number or complete the Representative Name section below.
`If both sections are completed the customer
`Numberwill be used for the Representative Information during processing.
`
`
`
`
`
`
`Please Select One: USPatentPractitioner|C) Limited Recognition (37 CFR 11.9)(e) Customer Number (©)
`
`Customer Number
`
`28841
`
`
`
`
`
`
`Domestic Benefit/National Stage Information:
`
`This section allows for the applicant to either claim benefit under 35 U.S.C. 119(e), 120, 121, or 365(c) or indicate
`National Stage entry from a PCT application. Providing this information in the application data sheet constitutes the
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` Prior Application Status
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`Add
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`Foreign Priority Information:
`
`EFS Web 2.2.6
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`

`

`PTO/AIA/14 (03-13)
`Approved for use through 01/31/2014. OMB 0651-0032
`U.S. Patent and Trademark Office; U.S. DEPARTMENT OF COMMERCE
`Underthe Paperwork Reduction Act of 1995, no persons are required to respond to a collection of information unless it contains a valid OMB control number.
`
`Attorney Docket Number|42183US01
`
`
`
` Application Data Sheet 37 CFR 1.76
`
`Application Number
`
`
`
`
`Title of Invention
`COMPRESSIVE SENSING
`
`
`
`
`
`
`This section allows for the applicant to claim priority to a foreign application. Providing this information in the application data sheet
`
`constitutes the claim for priority as required by 35 U.S.C. 119(b) and 37 CFR 1.55(d). When priority is claimed to a foreign application
`thatis eligible for retrieval uncer the priority cocument exchange program (PDX) ithe information will be used by the Office to
`automatically attempt retrieval pursuant to 37 CFR 1.55(h){1) and (2). Under the PDX program, applicant bears the ultimate
`responsibility for ensuring that a copy of the foreign application is received by the Office from the participating foreign intellectual
`property office, or a certified copy of the foreign priority application is filed, within the time period specified in 37 CFR 1.55(g){1).
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`Statement under 37 CFR 1.55 or 1.78 for AIA (First Inventor to File) Transition
`Applications
`
`16, 2013.
`
`This application (1} claims priority to or the benefit of an application filed before March 16, 2013 and (2) also
`contains, or contained at any time, a claim to a claimed invention that has an effectivefiling date on or after March
`
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`Authorization to Permit Access:
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`If checked, the undersigned hereby grants the USPTO authority to provide the European Patent Office (EPO),
`the Japan Patent Office (JP©), the Korean Intellectual Property Office {(KIPO), the World Intellectual Property Office (WIPO),
`and any otherintellectual property offices in which a foreign application claiming priority to the instant patent application
`is filed access to the instant patent application. See 37 CFR 1.14(c) and (h). This box should not be checkedif the applicant
`does not wish the EPO, JPO, KIPO, WIPO, or otherintellectual property office in which a foreign application claiming priority
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`In accordance with 37 CFR 1.14(h)(3), access will be provided to a copy of the instant patent application with respect
`to: 1) the instant patent application-as-filed; 2) any foreign application to which the instant patent application
`claims priority under 35 U.S.C. 119(a)-{c) if a copy of the foreign application that satisfies the certified copy requirement of
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`In accordance with 37 CFR 1.14(c}, access may be provided to information concerning the date offiling this Authorization.
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`PTO/AIA/14 (03-13)
`Approved for use through 01/31/2014. OMB 0651-0032
`U.S. Patent and Trademark Office; U.S. DEPARTMENT OF COMMERCE
`Underthe Paperwork Reduction Act of 1995, no persons are required to respond to a collection of information unless it contains a valid OMB control number.
`
`Attorney Docket Number|42183US01
`Application Data Sheet 37 CFR 1.76
`—
`
` oo
`
`Title of Invention
`
`COMPRESSIVE SENSING
`
`Applicant Information:
`
`Providing assignment information in this section does not substitute for compliance with any requirementof part 3 of Title 37 of CFR
`to have an assignment recorded by the Office.
`
`1
`Applicant
`If the applicant is the inventor (or the remaining joint inventor or inventors under 37 CFR 1.45), this section should not be completed.
`The information to be provided in this section is the name and addressof the legal representative who is the applicant under 37 CFR
`1.43; or the name and addressof the assignee, person to whom theinventoris under an obligation to assign the invention, or person
`who otherwise showssufficient proprietary interest in the matter who is the applicant under 37 CFR 1.46. If the applicantis an
`applicant under 37 CFR 1.46 {assignee, person to whem the inventoris obligated to assign, or person who otherwise showssufficient
`proprietary interest) together with one or morejoint inventors, then the joint inventor or inventors who are also the applicant should be
`identified in this section.
`
`(e) Assignee
`
`Joint Inventor
`
`C) Legal Representative under 35 U.S.C. 117
`
`©)
`
`
`
`
`
`
`
`OQ Person to whom theinventoris obligated to assign. O Person who shows sufficient proprietary interest
`
`Organization Name=|CONOCOPHILLIPS COMPANY
`
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`IP Services Group - Attn: Docketing
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`
`
`PTO/AIA/14 (03-13)
`Approved for use through 01/31/2014. OMB 0651-0032
`U.S. Patent and Trademark Office; U.S. DEPARTMENT OF COMMERCE
`Underthe Paperwork Reduction Act of 1995, no persons are required to respond to a collection of information unless it contains a valid OMB control number.
`
`Attorney Docket Number|42183US01
`
`
`
`
`
`
`Title of Invention
`COMPRESSIVE SENSING
`
`
` Application Data Sheet 37 CFR 1.76
`
`Application Number
`
`Assignee
`
`1
`
`Complete this section only if non-applicant assignee information is desired to be included on the patent application publication in
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`
`Signature|/Michael Sungjoon Pio/ Date (YYYY-MM-DD)| 2013-11-01
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`First Name|Michael Registration Number|63290Last Name
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`

`

`IN THE UNITED STATES PATENT AND TRADEMARK OFFICE
`
`Docket No. 42183US01
`
`AN APPLICATION FOR UNITED STATES LETTERS PATENT
`
`COMPRESSIVE SENSING
`
`Inventors:
`
`Chengbo Li
`
`Sam T. Kaplan
`
`Charles C. Mosher
`
`Joel D. Brewer
`
`Robert G. Keys
`
`

`

`Docket No. 42183US01
`
`COMPRESSIVE SENSING
`
`FIELD OF THE INVENTION
`
`[0001}
`
`The present invention relates generally to seismic imaging. More particularly,
`
`but not by way of limitation, embodiments of the present invention include tools and
`
`methods for processing seismic data by compressive sensing.
`
`BACKGROUNDOF THE INVENTION
`
`[0002]
`
`Seismic imaging typically involves not only acquiring seismic data but
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`processing the acquired seismic data.
`
`In some cases, processing requires recovering
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`missing pieces of information from irregularly acquired seismic data.
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`Irregularities may
`
`be caused by, for example, dead or severely corrupted seismic traces, surface obstacles,
`
`acquisition apertures,
`
`economic limits, and the like.
`
`Certain seismic processing
`
`techniques may be employedto spatially transform irregularly acquired seismic data to
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`regularly sampled data that is easier to interpret. This regularization can involve a
`
`numberor processing techniques suchas interpolation and reconstruction of seismic data.
`
`[0003]
`
`In recent years, compressive sensing theories have gained traction. One
`
`application of compressive sensing in geophysics involves seismic data reconstruction
`
`(e.g., Hennenfent and Herrmann, 2008). As an overview, compressive sensing provides
`
`conditions for when an under-determined system of equationshasa desirable solution. A
`
`seismic data reconstruction problem (e.g. Stolt, 2002; Trad, 2003; Liu and Sacchi, 2004;
`
`Abmaand Kabir, 2006; Ramirez et al., 2006; Naghizadeh and Sacchi, 2007; Xuetal.,
`
`2010; Kaplan et al., 2010) provides a coarse set of observed traces along with a desired
`
`set of fine spatial grid points upon which data is reconstructed. Compressive sensing
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`theory can address such issues as, 1) how many observations need to be collected, 2)
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`where the observations should be made (i.e., sampling grid) with respect
`
`to the
`
`reconstruction grid, and 3) what mathematical dictionary (e.g., mutual coherence) should
`
`be used to represent the reconstructed data. While mutual coherence is an important
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`metric in compressive sensing theory, it can also be expensive to compute. Descriptions
`
`and/or overviews of seismic data reconstruction can also be found in Trad, 2003; Liu and
`
`Sacchi, 2004; Abma and Kabir, 2006; Naghizadeh and Sacchi, 2007; Xu et al., 2010, the
`
`relevant parts of which are hereby incorporated by reference.
`
`

`

`Docket No. 42183US01
`
`[0004]
`
`Certain data reconstruction techniques have been developed, which provide a
`
`Sparse representation of reconstructed data. For example, Liu and Sacchi (2004) promote
`
`a sparse solution in wave-number domain using a penalty function constructed from
`
`inverse power spectrum of the reconstructed data.
`
`In compressive sensing, it is common
`
`to apply an ¢; norm to promote somesparse representation of the reconstructed data. The
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`é; norm has becomeofparticular interest due to its relation to the 4) norm which is a
`
`count of the number of non-zero elements. Theorems provide conditions for exact
`
`recovery of the reconstructed data and which,in part, rely on relationship between the ¢;
`
`and 4) norms, and use of the 4; norm in a convex optimization model (Candesetal.,
`
`2006). At least one theory of compressive sensing indicates that a sparse or compressible
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`signal can be recovered from a small number of random linear measurements by solving
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`a convex /; optimization problem (e.g. Baraniuk, 2007).
`
`[0005]
`
`Compressive sensing can also provide new opportunities for survey design
`
`using an irregular sampling grid (e.g. Hennenfent and Herrmann, 2008; Kaplan et al.,
`
`2012) instead ofa traditional regular grid in order to increase bandwidth and reducecost.
`
`Generally, irregular survey design based on compressive sensing can be summarized by
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`the following steps: 1) determine a nominal regular grid for survey area, 2) choose a
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`subset of locations from this nominal grid in a random or randomly jittered (Hennenfent
`
`and Herrmann, 2008) fashion, 3) acquire seismic data based on chosen locations, and 4)
`
`reconstruct the data back to the original nominal grid. This approachis applicable to both
`
`shot and receiver dimensions.
`
`[0006]
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`In certain cases, compressive sensing using irregular acquisition grids can be
`
`used to recover significantly broader spatial bandwidth than could be obtained using a
`
`regular sampling grid. Recovered bandwidth is primarily determined according to the
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`spacing of nominal grid for reconstruction. If a predefined nominalgrid is too coarse, the
`
`reconstructed seismic data maystill be aliased; if the predefined nominal gridis too fine,
`
`the time and cost savings of irregular versus regular survey design may become
`
`insignificant. In general, if there is a lack of prior information about a given surveyarea,
`
`then it may not be feasible to select a proper nominal grid beforehand.
`
`

`

`Docket No. 42183US01
`
`BRIEF SUMMARYOF THE DISCLOSURE
`
`[0007]
`
`The present invention relates generally to seismic imaging. More particularly,
`
`but not by way of limitation, embodiments of the present invention include tools and
`
`methods for processing seismic data by compressive sensing.
`
`[0008]
`
`Compressive sensing theory is utilized for seismic data reconstruction.
`
`Compressive sensing,
`
`in part,
`
`requires an optimization model.
`
`Two classes of
`
`optimization models, synthesis- and analysis-based optimization models, are considered.
`
`For the analysis-based optimization model, a novel optimization algorithm (SeisADM)is
`
`presented. SeisADM adapts the alternating direction method with a variable-sp