`
`UNITED STATES PATENT AND TRADEMARK OFFICE
`
`UNITED STATES DEPARTMENT OF COMMERCE
`United States Patent and Trademark Office
`Addiess. COMMISSIONER FOR PATENTS
`PO Box 1450
`Alexandria, Viigmia 22313-1450
`wwwuspto.gov
`
`APPLICATION
`NUMBER
`
`FILING or
`3710:) DATE
`
`GRP ART
`UNIT
`
`
`
`
`
`F
`
`61/898,960
`
`11/01/2013
`
`FEE REC'D
`
`260
`
`ATTY.DOCKET.NO
`
`42183U801
`
`TOT CLAHVIS IND CLAIMS
`
`28841
`
`ConocoPhiIIips Company
`Legal Department - Intellectual Property Docketlng
`600 North Dairy Ashford (77079-1175)
`PO. Box 4783
`
`Houston, TX 77210-4783
`
`CONFIRMATION NO. 3851
`
`FILING RECEIPT
`
`lllllllllllllllllIllllIllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
`00000006 9 5608
`
`Date Mailed: 11/14/2013
`
`It will not be examined for patentability and will
`Receipt is acknowledged of this provisional patent application.
`become abandoned not later than twelve months after its filing date. Any correspondence concerning the application
`must include the following identification information: the US. APPLICATION NUMBER, FILING DATE, NAME OF
`APPLICANT, and TITLE OF INVENTION. Fees transmitted by check or 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 processes the 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
`
`Power of 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 used for 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 US. 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 the filing 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 not result in a grant of "an international
`patent" and does not eliminate the need of applicants to 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 accordance with 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 made in the United States, the Director of the USPTO must
`issue a license before applicants can apply for a patent in a foreign country. The filing of a US. patent application
`serves as a request for a foreign filing license. The application's filing receipt contains further information and
`guidance as to 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 deadlines for 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 US. Government website, http://www.stopfakes.gov. Part of a Department of Commerce initiative,
`this website includes self-help "toolkits" giving innovators guidance on how to protect intellectual property in specific
`countries such as China, Korea and Mexico. For questions regarding patent enforcement issues, applicants may
`call the US. Government hotline 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 issued in 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 and limitations 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 indicated is 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 license is to be retained by the licensee and may be used at any time on or 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 grant of a license does not in any way lessen the responsibility of a licensee for the security of the subject matter
`as imposed by any Government contract or the provisions of existing laws relating to espionage and the national
`security or the export of technical data. Licensees should apprise themselves of 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" DOES NOT appear on this form. Applicant may still petition for a license under 37 CFR 5.12,
`if a license is desired before the expiration of 6 months from the filing date of the application. If 6 months has lapsed
`from the filing date of this application and the licensee has not received any indication of a secrecy order under 35
`U.S.C. 181, the licensee may foreign 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
`business investment, innovation, and commercialization of new technologies. The US. offers tremendous resources
`and advantages for those who invest and manufacture goods here. Through SelectUSA, our nation works to
`promote and facilitate business investment. SelectUSA provides information assistance to the international investor
`community; serves as an ombudsman for existing and potential investors; advocates on behalf of US. cities, states,
`and regions competing for global investment; and counsels US. economic development organizations 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://www.SelectUSA.gov or call
`+1 -202-482—6800.
`
`page 3 of 3
`
`

`

`PTO/AIN14 (03-13)
`Approved for use through 0181/2014. OMB 0651-0032
`US. Patent and Trademark Office; US. DEPARTMENT OF COMMERCE
`Under the Paperwork Reduction Act of 1995, no persons are required to respond to a collection of information unless it contains a valid OMB control number.
`
`
`
`
`
`Title of Invention
`
`COMPRESSIVE SENSING
`
`The application data sheet is part of the provisional or nonprovisional application for which it 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 pursuant to
`El 37 CFR 5.2 (Paper filers only. Applications that fall under Secrecy Order may not be filed electronically.)
`
`
`Inventor Information:
`
`Inventor
`
`1
`
`Legal Name
`
`
`Prefix Given Name
`Middle Name
`Family Name
`Chengbo
`Residence Information (Select One)
`(9 US Residency 0 Non US Residency 0 Active US Military Service
`
`Suffix
`
`Mailing Address of Inventor:
`
`Address 1
`
`Address 2
`
`1405 W. Hilshire Park Dr.
`
`Postal Code
`
`77055
`
`us
`
`
`Inventor
`2
`
`Legal Name
`
`Prefix Given Name
`
`Middle Name
`
`Sam
`T.
`KAPLAN
`
`
`Suffix
`
`
`
`Mailing Address of Inventor:
`
`Address 1
`
`Address 2
`
`27 Kingwood Rd.
`
`City
`
`Oakland
`
`Postal Code
`
`94619
`
`StatelProvince
`
`CA
`
`us
`
`Inventor
`
`3
`
`Legal Name
`
`Prefix Given Name
`Charles
`
`Middle Name
`T.
`
`Family Name
`MOSHER
`
`Suffix
`
`
`Residence Information (Select One) @ US Residency 0 Non US Residency 0 Active US Military Service
`
`EFS Web 2.2.5
`
`
`
`
`
`Residence Information (Select One) @ US Residency 0 Non US Residency 0 Active US Military Service
`
`City
`
`Oakland
`
`StatelProvince
`
`CA
`
`Country of Residence i
`
`US
`
` _
`
`_
`Application Data Sheet 37 CFR 1.76
`
`
`Attorney Docket Number
`42183USO1
`
`
`
`Application Number
`
`

`

`PTO/AIN14 (03-13)
`Approved for use through 01l31l2014. 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 of information unless it contains a valid OMB control number.
`
` Attorney Docket Number
`42183USO1
`
`Application Data Sheet 37 CFR 1.76
`
`Application Number
`
`Title of Invention
`COMPRESSIVE SENSING
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`HoustonCity US ‘ StatelProvince | TX | Country of Residencel
`
`Mailing Address of Inventor:
`
`Address 1
`
`Address 2
`
`5907 Saratoga Springs Ln.
`
`Postal Code
`
`77041
`
`Country i
`
`US
`
`Inventor
`
`4
`
`Legal Name
`
`
`
`
`Prefix Given Name
`
`Middle Name
`
`Family Name
`
`Residence Information (Select One)
`
`(9 US Residency 0 Non US Residency 0 Active US Military Service
`
`City
`
`Houston
`
`StatelProvince
`
`TX
`
`Country of Residence i
`
`US
`
`Suffix
`
`
`Mailing Address of Inventor:
`
`Address 1
`
`Address 2
`
`514 Cypress Vista
`
`Postal Code
`
`77094
`
`Country i
`
`US
`
`Inventor
`
`5
`
`Legal Name
`
`Prefix Given Name
`
`Middle Name
`
`Family Name
`
`Residence Information (Select One)
`
`(9 US Residency 0 Non US Residency 0 Active US Military Service
`
`City
`
`Houston
`
`StatelProvince
`
`Country ofResidencei
`
`US
`
`Suffix
`
`Mailing Address of Inventor:
`
`Address 1
`
`Address 2
`
`12239 N. Shadow Cove Dr.
`
`Postal Code
`
`77082
`
`Country i
`
`US
`
`Inventor Information blocks may be
`Inventors Must Be Listed - Additional
`All
`generated within this form by selecting the Add button.
`
`Add
`
`Correspondence Information:
`
`Enter either Customer Number or complete the Correspondence Information section below.
`
`For further information see 37 CFR 1.33(a).
`
`|:| An Address is being provided for the correspondence Information of this application.
`
`EFS Web 2.2.6
`
`
`
`

`

`PTO/AIN14 (03-13)
`Approved for use through 0181/2014. 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 of information unless it contains a valid OMB control number.
`
` Attorney Docket Number
`42183USO1
`
`Application Data Sheet 37 CFR 1.76
`
`
`Application Number
`
`Title of Invention
`COMPRESSIVE SENSING
`
`
`
`Customer Number
`
`28841
`
`Email Address
`
`Legal—IP@conocophi||ips.com
`
`Application Information:
`
`Title of the Invention
`
`COMPRESSIVE SENSING
`
`Attorney DocketNumbe— Small Entity Status Claimed
`Application Type
`Provisional
`
`|:|
`
`Total Number of 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)
`
`El
`
`Request Not to PUinSh. I 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 months after filing.
`
`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 attorney in 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
`Number will be used for the Representative Information during processing.
`
`
`
`
`
`Please Select One:
`
`6) Customer Number
`
`Customer Number
`
`28841
`
`
`
`0 US Patent Practitioner O Limited Recognition (37 CFR 11.9)
`
`
`
`
`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
`
`specific reference required by 35 U.S.C. 119(e) or 120, and 37 CFR 1.78.
` Prior Application Status
`
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` Filing Date (YYYY-MM-DD)
`
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`Prior Application Number
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`
`Add
`
`Foreign Priority Information:
`
`EFS Web 2.2.6
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`

`

`PTO/AIN14 (03-13)
`Approved for use through 0181/2014. 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 of information unless it contains a valid OMB control number.
`
` _
`_
`Attorney Docket Number
`42183USO1
`
`Appllcatlon 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
`that is eligible for retrieval under the priority document 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 PBX 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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`
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`
`Add
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`Statement under 37 CFR 1.55 or 1.78 for AIA (First Inventor to File) Transition
`
`Applications
`
`|:|
`
`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 effective filing date on or after March
`
`16, 2013.
`
`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 (JPO), the Korean Intellectual Property Office (KIPO), the World Intellectual Property Office (WIPO),
`and any other intellectual 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 checked if the applicant
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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)-(d) if a copy of the foreign application that satisfies the certified copy requirement of
`37 CFR 1.55 has been filed in the instant patent application; and 3) any US. application—as—filed from which benefit is
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`In accordance with 37 CFR 1.14(c), access may be provided to information concerning the date of filing this Authorization.
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`EFS Web 2.2.6
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`

`

`PTO/AlAl14 (03-13)
`Approved for use through 0181/2014. 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 of information unless it contains a valid OMB control number.
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`_
`Appllcatlon Data Sheet 37 CFR 1.76
`
`Attorney Docket Number
`_
`_
`
`42183USO1
`
` _
`
`
`Title of Invention
`
`COMPRESSIVE SENSING
`
`
`0 Person to whom the inventor is obligated to assign.
`0 Person who shows sufficient proprietary interest
`
`Applicant Information:
`
`Providing assignment information in this section does not substitute for compliance with any requirement of part 3 of Title 37 of CFR
`to have an assignment recorded by the Office.
`
`Applicant
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`1
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`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 address of the legal representative who is the applicant under 37 CFR
`1.43; or the name and address of the assignee, person to whom the inventor is under an obligation to assign the invention, or person
`who otherwise shows sufficient proprietary interest in the matter who is the applicant under 37 CFR 1.46. If the applicant is an
`applicant under 37 CFR 1.46 (assignee, person to whom the inventor is obligated to assign, or person who otherwise shows sufficient
`proprietary interest) together with one or more joint inventors, then the joint inventor or inventors who are also the applicant should be
`identified in this section.
`
`@ Assignee
`
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`0 Legal Representative under 35 U.S.C. 117
`
`0 Joint Inventor
`
`If applicant is the legal representative, indicate the authority to file the patent application, the inventor is:
`
`Name of the Deceased or Legally lncapacitated Inventor::|
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`Organizatm Name
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`CONOCOPHILLIPS COMPANY
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`
`Address 2
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`IP Services Group - Attn: Docketing
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`600 N. Dairy Ashford, Bldg. ML-1065
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`
`
`
`
`
`
`
`
`lMichaelSungjoon Pio/ Date (YYYY-MM-DD)Signature 2013-11-01
`
`
`
`
`PTO/AlAl14 (03-13)
`Approved for use through 0181/2014. 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 of information unless it contains a valid OMB control number.
`
` Attorney Docket Number
`42183USO1
`
`Application Data Sheet 37 CFR 1.76
`
`Application Number
`
`Title of Invention
`COMPRESSIVE SENSING
`
`
`
`
`Assignee
`
`1
`
`Complete this section only if non-applicant assignee information is desired to be included on the patent application publication in
`accordance with 37 CFR 1.215(b). Do not include in this section an applicant under 37 CFR 1.46 (assignee, person to whom the
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`63290
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`EFS Web 2.2.5
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`

`

`IN THE UNITED STATES PATENT AND TRADEMARK OFFICE
`
`Docket No. 42183USOl
`
`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. 42183USOl
`
`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.
`
`BACKGROUND OF 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.
`
`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 employed to spatially transform irregularly acquired seismic data to
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`regularly sampled data that is easier to interpret. This regularization can involve a
`
`number or processing techniques such as 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 equations has a desirable solution. A
`
`seismic data reconstruction problem (e.g. Stolt, 2002; Trad, 2003; Liu and Sacchi, 2004;
`
`Abma and Kabir, 2006; Ramirez et al., 2006; Naghizadeh and Sacchi, 2007; Xu et al.,
`
`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
`
`theory can address such issues as, 1) how many observations need to be collected, 2)
`
`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
`
`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. 42183USOI
`
`[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 [1 norm to promote some sparse representation of the reconstructed data. The
`
`£1 norm has become of particular interest due to its relation to the £0 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 £1
`
`and £0 norms, and use of the £1 norm in a convex optimization model (Candes et al.,
`
`2006). At least one theory of compressive sensing indicates that a sparse or compressible
`
`signal can be recovered from a small number of random linear measurements by solving
`
`a convex £1 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 of a traditional regular grid in order to increase bandwidth and reduce cost.
`
`Generally, irregular survey design based on compressive sensing can be summarized by
`
`the following steps: 1) determine a nominal regular grid for survey area, 2) choose a
`
`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 approach is applicable to both
`
`shot and receiver dimensions.
`
`[0006]
`
`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
`
`spacing of nominal grid for reconstruction. If a predefined nominal grid is too coarse, the
`
`reconstructed seismic data may still be aliased; if the predefined nominal grid is 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 survey area,
`
`then it may not be feasible to select a proper nominal grid beforehand.
`
`

`

`Docket No. 42183USOl
`
`BRIEF SUMMARY OF 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 mo