Enhanced projection on convex sets for interpolation and deblending

A tangible, non-transitory, machine readable media, comprising instructions configured to cause a processor to:

• control one or more seismic sources positioned on or above a surface region of Earth to emit seismic signals into the subsurface region, wherein the emitted seismic signals travel downward through the Earth and reflect off geological formations within the subsurface region;
• receive, via one or more receivers disposed relative to the surface region of the Earth, reflected seismic signals returned from the subsurface region to obtain a seismic dataset of a seismic survey based on the reflected seismic signals;
• access the seismic dataset that images at least a portion of a predetermined volume of Earth,
• sort the seismic dataset into a time or depth and space domain such that the seismic response by the Earth is coherent in the sorted domain to generate a sorted seismic dataset,
• splitting the seismic dataset in time or depth and space domain into smaller overlapping windows of at least one sub-dataset;
• calculate a multi-dimension Fourier transform spectrum from each sub-dataset to produce multi-dimension Fourier transformed data;
• determine, for each frequency of a set of frequencies of a seismic frequency spectrum, a maximum frequency spectral value corresponding to a particular frequency of the set of frequencies from the multi-dimension Fourier transformed data, wherein the maximum frequency spectral value represents a maximum energy value at the particular frequency;
• select, for each frequency of the set of frequencies of the seismic frequency spectrum, a threshold value corresponding to the particular frequency of the set of frequencies, wherein each selected threshold value for each frequency of the set of frequencies is applied to the Fourier transformed data at the particular frequency to identify samples having an energy magnitude below the threshold value;
• decrement each threshold value of the plurality of threshold values iteratively to generate a decremented threshold value corresponding to each frequency of the set of frequencies;
• generate a modified Fourier transformed dataset, wherein the modified Fourier transformed dataset is modified by setting Fourier samples of the multi-dimension Fourier transform spectrum having an energy magnitude less than the decremented threshold value at each frequency of the set of frequencies to zero;
• inverse transform the modified Fourier transformed dataset to generate a plurality of interpolated traces;
• and
• substitute each interpolated trace of the plurality of interpolated traces into the empty traces of the seismic dataset where no seismic energy is acquired in data acquisition;
• repeat a Fourier transform, thresholding and inverse transform to create a modified sub-dataset as an interpolated seismic sub-dataset;
• merge all overlapping windows of the interpolated seismic sub-dataset to create an interpolated seismic dataset;
• and
• generate a seismic image of the subsurface region of the subsurface from the interpolated seismic dataset to illustrate locations within the subsurface region of the subsurface that include the hydrocarbons and locations within the subsurface region of the subsurface that include subsurface drilling hazards.

A method of seismic exploration above a region of subsurface containing structural or stratigraphic features conducive to determining a presence, migration, or accumulation of hydrocarbons, the method comprising:

• accessing a seismic dataset of a seismic survey that images at least a portion of a predetermined volume of Earth over the region of the subsurface,
• setting a residual to the seismic dataset;
• combing the residual into a common receiver gather;
• splitting the common receiver gather into smaller overlapping windows of at least one sub-dataset;
• calculating a multi-dimension Fourier transform spectrum from each sub-dataset to produce multi-dimension Fourier transformed data;
• determining a plurality of maximum frequency spectral values from the multi-dimension Fourier transformed data, wherein each maximum frequency spectral value of the plurality of maximum frequency spectral values corresponds to a maximum energy value at a particular frequency of a set of frequencies of a seismic frequency spectrum;
• selecting a plurality of threshold values, wherein each threshold value of the plurality of threshold values corresponds to one frequency of the set of frequencies;
• decrementing each threshold value of the plurality of threshold values iteratively to generate a decremented threshold value corresponding to each frequency of the set of frequencies;
• generating a modified Fourier transformed dataset, wherein the modified Fourier transformed dataset is modified by setting Fourier samples of the multi-dimension Fourier transform spectrum having an energy magnitude less than the decremented threshold value at each frequency of the set of frequencies to zero;
• inverse transforming the modified Fourier transformed dataset to generate a plurality of deblended traces;
• merging all windows of the at least one sub-dataset from the inverse Fourier transform to create a deblended common receiver gather;
• updating a primary signal estimate utilizing the deblended gather to generate an updated primary signal estimate;
• updating the residual based upon the updated primary signal estimate to generate an updated residual;
• repeating the primary signal estimate by combing the updated residual and continuing the processing steps above until the residual is sufficiently small;
• outputting the updated primary signal estimate as a deblended result;
• identifying using the deblended result locations within the region of the subsurface that include the hydrocarbons and locations within the region of the subsurface that include subsurface drilling hazards;
• determining a drilling path into the region of the subsurface that intersects the locations that include the hydrocarbons and avoids the locations that include the subsurface drilling hazards;
• and
• drilling a wellbore into the region of the subsurface along the drilling path.