System, machine, and computer-readable storage medium for forming an enhanced seismic trace using a virtual seismic array

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.

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.