# US 9,753,165 B2 · System, machine, and computer-readable storage medium for forming an enhanced seismic trace using a virtual seismic array > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 9,753,165 B2 - Document ID: US9753165B2 - Status: Granted - Kind: B2 - Application number: 14/981,065 - Filed: 2015-12-28 - Published: 2016-05-12 - Granted: 2017-09-05 - Earliest claimed: 2010-02-22 - Assignees: Saudi Arabian Oil Company; The Texas A&M University System - Applicants: Saudi Arabian Oil Company - Inventors: Ibrahim Abdulaziz Alhukail; Luc Ikelle - Web page: https://patentgrep.com/patent/US9753165B2 ## CPC - G01V 1/28: Processing seismic data, e.g. for interpretation or for event detection (G01V1/48 takes precedence) - G01V 1/32: Transforming one recording into another {or one representation into another} - G01V 2210/55: Array focusing; Phased arrays - G01V 2210/57: Trace interpolation or extrapolation, e.g. for virtual receiver; Anti-aliasing for missing receivers - G01V: GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS (means for indicating the location of accidentally buried, e.g. snow-buried, persons A63B29/02) ## Abstract Embodiments of a system are provided for forming enhanced seismic array traces using virtual seismic sensors in addition to the real seismic sensors to form a virtual seismic array. The system receives the signal responses from the real sensors, processes the signal responses from the sensors to define virtual signals using a narrowband decomposition of the complex envelope of the sensor signal responses, calculates second- and fourth-order statistics to derive steering vectors for the array of real sensors, and forms a virtual seismic array in response thereto. Machines, computer program product, and computer-implemented methods are provided for forming enhanced seismic array traces by receiving the array responses from sensors, processing the signals to define virtual sensor signals and a virtual seismic array, and forming an array response for the virtual seismic array to form a seismic trace of enhanced resolution. ## Claims ### Claim 1 A method to generate seismic images of enhanced resolution, the method comprising: physically positioning a plurality of real seismic sensors in an array, the plurality of real seismic sensors comprising a number of real seismic sensors; obtaining a plurality of wideband seismic signals via the plurality of real seismic sensors physically positioned in an array; dividing each of the plurality of wideband seismic signals into one or more narrowband signals; transforming each of the one or more narrowband signals into a complex-value form, the complex-value form comprising phase and amplitude; creating a number of virtual seismic sensors responsive to a second-order covariance matrix and a higher-order covariance matrix of an order higher than the second-order covariance matrix for the one or more narrowband signals; transforming each of the one or more narrowband signals into the time-space domain responsive to the plurality of real seismic sensors and the virtual seismic sensors to form a virtual array of seismic sensors, the virtual array of seismic sensors comprising the plurality of real seismic sensors and the virtual seismic sensors, the virtual array of seismic sensors representing an increased number of seismic sensors comprising a total of the number of real seismic sensors and the number of virtual seismic sensors; combining the one or more transformed narrowband signals to generate reconstructed wideband seismic signals of enhanced resolution; and generating, using the reconstructed wideband seismic signals of enhanced resolution, a seismic image of subsurface geophysical structures having an enhanced resolution corresponding to the increased number of seismic sensors of the virtual array. ### Claim 2 (depends on 1) A method as defined in claim 1, wherein dividing each of the plurality of wideband seismic signals into one or more narrowband signals is responsive to a filter bank that includes a plurality of band-pass filters for separating each of the plurality of wideband seismic signals into one or more components. ### Claim 3 (depends on 1) A method as defined in claim 1, wherein transforming each of the one or more narrowband signals into a complex-value form is responsive to one or more complex envelopes. ### Claim 4 (depends on 1) A method as defined in claim 1, wherein the higher-order covariance matrix is a fourth-order covariance matrix thereby to define a quadricovariance matrix, and wherein the number of the plurality of wideband seismic signals is the number of the plurality of real seismic sensors to the second power. ### Claim 5 (depends on 1) A method as defined in claim 1, wherein the higher-order covariance matrix is a sixth-order covariance matrix thereby to define a hexacovariance matrix, and wherein the number of the plurality of wideband seismic signals is the number of the plurality of real seismic sensors to the third power. ### Claim 6 (depends on 1) A method as defined in claim 1, wherein the plurality of wideband seismic signals are statistically independent. ### Claim 7 (depends on 1) A method as defined in claim 1, wherein combining the one or more transformed narrowband signals to generate reconstructed wideband seismic signals of enhanced resolution comprises, for each of the plurality of wideband seismic signals, combining the one or more transformed narrowband signals corresponding to the one or more narrowband signals of the wideband seismic signal to generate a reconstituted wideband seismic signal of enhanced resolution corresponding to the wideband seismic signal. ### Claim 8 A machine to generate seismic images of enhanced resolution, the machine comprising: one or more processors; one or more input/output units in communication with the one or more processors and further in communication with a plurality of real seismic sensors physically positioned in an array and configured to sense a plurality of wideband seismic signals, the plurality of real seismic sensors comprising a number of real seismic sensors; and non-transitory computer-readable medium positioned in communication with the one or more processors and having one or more computer programs stored thereon including a set of instructions that when executed by the one or more processors cause the one or more processors to perform operations of: obtaining the plurality of wideband seismic signals via the plurality of real seismic sensors physically positioned in the array; dividing each of the plurality of wideband seismic signals into one or more narrowband signals; transforming each of the one or more narrowband signals into a complex-value form, the complex-value form comprising phase and amplitude; creating a number of virtual seismic sensors responsive to a second-order covariance matrix and a higher-order covariance matrix of an order higher than the second-order covariance matrix for the one or more narrowband signals; transforming each of the one or more narrowband signals into the time-space domain responsive to the plurality of real seismic sensors and the virtual seismic sensors to form a virtual array of seismic sensors, the virtual array of seismic sensors comprising the plurality of real seismic sensors and the virtual seismic sensors, the virtual array of seismic sensors representing an increased number of seismic sensors comprising a total of the number of real seismic sensors and the number of virtual seismic sensors; combining the one or more transformed narrowband signals to generate reconstructed wideband seismic signals of enhanced resolution; and generating, using the reconstructed wideband seismic signals of enhanced resolution, a seismic image of subsurface geophysical structures having an enhanced resolution corresponding to the increased number of seismic sensors of the virtual array. ### Claim 9 (depends on 8) A machine as defined in claim 8, wherein the machine further comprises a filter bank that includes a plurality of band-pass filters for separating each of the plurality of wideband seismic signals into one or more components, and wherein dividing each of the plurality of wideband seismic signals into one or more narrowband signals is responsive to the filter bank. ### Claim 10 (depends on 8) A machine as defined in claim 8, wherein transforming each of the one or more narrowband signals into a complex-value form is responsive to one or more complex envelopes. ### Claim 11 (depends on 8) A machine as defined in claim 8, wherein the higher-order covariance matrix is a fourth-order covariance matrix thereby to define a quadricovariance matrix, and wherein the number of the plurality of wideband seismic signals is the number of the plurality of real seismic sensors to the second power. ### Claim 12 (depends on 8) A machine as defined in claim 8, wherein the higher-order covariance matrix is a sixth-order covariance matrix thereby to define a hexacovariance matrix, and wherein the number of the plurality of wideband seismic signals is the number of the plurality of real seismic sensors to the third power. ### Claim 13 (depends on 8) A machine as defined in claim 8, wherein the plurality of wideband seismic signals are statistically independent. ### Claim 14 (depends on 8) A machine as defined in claim 8, wherein combining the one or more transformed narrowband signals to generate reconstructed wideband seismic signals of enhanced resolution comprises, for each of the plurality of wideband seismic signals, combining the one or more transformed narrowband signals corresponding to the one or more narrowband signals of the wideband seismic signal to generate a reconstituted wideband seismic signal of enhanced resolution corresponding to the wideband seismic signal. ### Claim 15 Non-transitory computer-readable medium having one or more computer programs stored therein operable by one or more processors to generate seismic images of enhanced resolution, the one or more computer programs comprising a set of instructions that, when executed by the one or more processors, cause the one or more processors to perform the operations of: obtaining a plurality of wideband seismic signals via a plurality of real seismic sensors physically positioned in an array, the plurality of real seismic sensors comprising a number of real seismic sensors; dividing each of the plurality of wideband seismic signals into one or more narrowband signals; transforming each of the one or more narrowband signals into a complex-value form, the complex-value form comprising phase and amplitude; creating a number of virtual seismic sensors responsive to a second-order covariance matrix and a higher-order covariance matrix of an order higher than the second-order covariance matrix for the one or more narrowband signals; transforming each of the one or more narrowband signals into the time-space domain responsive to the plurality of real seismic sensors and the virtual seismic sensors to form a virtual array of seismic sensors, the virtual array of seismic sensors comprising the plurality of real seismic sensors and the virtual seismic sensors, the virtual array of seismic sensors representing an increased number of seismic sensors comprising a total of the number of real seismic sensors and the number of virtual seismic sensors; combining the one or more transformed narrowband signals to generate reconstructed wideband seismic signals of enhanced resolution; and generating, using the reconstructed wideband seismic signals of enhanced resolution, a seismic image of subsurface geophysical structures having an enhanced resolution corresponding to the increased number of seismic sensors of the virtual array. ### Claim 16 (depends on 15) Non-transitory computer-readable medium having one or more computer programs stored therein as defined in claim 15, wherein dividing each of the plurality of wideband seismic signals into one or more narrowband signals is responsive to a filter bank that includes a plurality of band-pass filters for separating each of the plurality of wideband seismic signals into one or more components. ### Claim 17 (depends on 15) Non-transitory computer-readable medium having one or more computer programs stored therein as defined in claim 15, wherein transforming each of the one or more narrowband signals into a complex-value form is responsive to one or more complex envelopes. ### Claim 18 (depends on 15) Non-transitory computer-readable medium having one or more computer programs stored therein as defined in claim 15, wherein the higher-order covariance matrix is a fourth-order covariance matrix thereby to define a quadricovariance matrix, and wherein the number of the plurality of wideband seismic signals is the number of the plurality of real seismic sensors to the second power. ### Claim 19 (depends on 15) Non-transitory computer-readable medium having one or more computer programs stored therein as defined in claim 15, wherein the higher-order covariance matrix is a sixth-order covariance matrix thereby to define a hexacovariance matrix, and wherein the number of the plurality of wideband seismic signals is the number of the plurality of real seismic sensors to the third power. ### Claim 20 (depends on 15) Non-transitory computer-readable medium having one or more computer programs stored therein as defined in claim 15, wherein the plurality of wideband seismic signals are statistically independent. ### Claim 21 (depends on 15) Non-transitory computer-readable medium having one or more computer programs stored therein as defined in claim 15, wherein combining the one or more transformed narrowband signals to generate reconstructed wideband seismic signals of enhanced resolution comprises, for each of the plurality of wideband seismic signals, combining the one or more transformed narrowband signals corresponding to the one or more narrowband signals of the wideband seismic signal to generate a reconstituted wideband seismic signal of enhanced resolution corresponding to the wideband seismic signal.