Method of filter generation for seismic migration using Remez algorithm

A method of seismic wavefield depth extrapolation comprising the steps of:

• i) approximating the complex 1D depth extrapolation operator D(k) with an ordinary Fourier cosine series having N coefficients hn;
• ii) setting a desired maximum migration dip angle θ and desired N;
• iii) computing a table of extrapolation filters hn for a range of normalized frequencies ω ⁢ ⁢ Δ ⁢ ⁢ x v ,
• where
• for a given normalized frequency ω ⁢ ⁢ Δ ⁢ ⁢ x v ,
• define a frequency transition band width and
• determine the N coefficients hn for the given normalized frequency ω ⁢ ⁢ Δ ⁢ ⁢ x v
• using a Remez-type approximation where the amplitude is monotonically decreasing in the transition band;
• iv) extrapolating a seismic wavefield for a lateral region at a given depth using the N filter coefficients hn from said table corresponding to the normalized frequency for the lateral region.

A method of migrating seismic data, for converting stacked seismic data into a geologic image, using a parallel computer having a number of processing components, each with local memory, where the seismic data is downwardly continued in the frequency domain for all depth planes of interest, including the steps of:

• i) assigning processing components to respective lateral subgrids of seismic data in x,y depth plane;
• ii) determining a table of extrapolation filters which varies according to lateral (x,y) subgrids of seismic data by approximatingthe extrapolation filters using a Remez-type approximation with an error less than a certain amount;
• iii) loading said table into local memory of each processing component;
• and
• iv) operating said processing components independently to extrapolate the seismic data for the x,y depth plane, each processing component accessing its table in local memory according to the subsurface acoustic velocity in its assigned subgrid.

A parallel computer-implemented method of seismic wavefield depth extrapolation, in furtherance of transforming stacked seismic data into a geologic image, comprising the steps of:

• i) approximating the complex ID depth extrapolation operator D(k) with an ordinary Fourier cosine having N coefficients hn;
• ii) setting a desired maximum migration dip angle Ø and desired N;
• iii) computing a table of extrapolation filters hn for a range of normalized frequencies ω ⁢ ⁢ Δ ⁢ ⁢ x v ,
• where
• for a given normalized frequency ω ⁢ ⁢ Δ ⁢ ⁢ x v ,
• define a frequency transition bandwidth and
• determine the N coefficients hn for the given normalized frequency ω ⁢ ⁢ Δ ⁢ ⁢ x v
• using a Remez-type approximation where the amplitude is monotonically decreasing in the transition band;
• iv) extrapolating a seismic wavefield for a lateral region at a given depth using the N filter coefficients hn from said table corresponding to the normalized frequency for the lateral region.

A method of acquiring and processing seismic data comprising the steps of:

• i) acquiring seismic data;
• ii) applying quality control, filtering and deconvulation on a trace basis to the seismic data;
• iii) estimating the velocity of the subsurface formations;
• iv) performing D dip moveout correction and stacking to the seismic data;
• and
• v) migrating the seismic data, using a parallel computer having a number of processing components, each with local memory, where the seismic data is downwardly continued in the frequency domain for all depth planes of interest, such that a map of formation locations is created, including the steps of:
• a) assigning processing components to respective lateral subgrids of seismic data in an x,y depth plane;
• b) determining a table of extrapolation filters which varies according to lateral (x,y) subgrids of seismic data by approximating the extrapolation filters using a Remez-type approximation with an error less than a certain amount;
• c) loading the table into local memory of each processing component;
• and
• d) operating the processing components independently to extrapolate the seismic data for the x,y depth plane, each processing component accessing its table in local memory according to the subsurface acoustic velocity in its assigned subgrid.