US 11,892,578 B2
Seismic imaging method, system, and device based on pre-stack high-angle fast Fourier transform
Liyun Fu, Qingdao (CN); Qingqing Li, Qingdao (CN); Qizhen Du, Qingdao (CN); and Zhiwei Wang, Qingdao (CN)
Assigned to China University of Petroleum (EAST CHINA), Qingdao (CN)
Filed by China University of Petroleum (EAST CHINA), Qingdao (CN)
Filed on Sep. 30, 2022, as Appl. No. 17/958,054.
Claims priority of application No. 202210353352.X (CN), filed on Apr. 6, 2022.
Prior Publication US 2023/0034829 A1, Feb. 2, 2023
Int. Cl. G01V 1/28 (2006.01); G01V 1/36 (2006.01)
CPC G01V 1/282 (2013.01) [G01V 1/362 (2013.01); G01V 2210/512 (2013.01); G01V 2210/67 (2013.01)] 4 Claims
OG exemplary drawing
 
1. A seismic imaging method, comprising:
(S100) collecting seismic data comprising seismic source type, seismic source dominant frequency, location of a shot point, maximum tectonic angle, a set temporal sampling interval, a size of a velocity model, and a spatial interval;
(S200) extracting a common shot point gather from the seismic data; converting the common shot point gather to a time-space domain common offset gather according to the location of the shot point and a location of a receiver point; and converting time-space domain common offset seismic data in the time-space domain common offset gather from time-space domain to frequency-wavenumber domain by using Fourier transform to obtain frequency-wavenumber domain common offset seismic data;
(S300) calculating a plurality of wave propagation angles of a plurality of grid points of the velocity model based on the frequency-wavenumber domain common offset seismic data through the following equation:

OG Complex Work Unit Math
wherein θ represents the wave propagation angles; ∂p/∂x represents a partial derivative of a seismic wavefield in x direction; and ∂p/∂z represents a partial derivative of the seismic wavefield in z direction; and
dividing an imaging region into a first region and a second region based on the plurality of wave propagation angles, wherein a wave propagation angle of the first region is smaller than a wave propagation angle of the second region;
(S400) calculating a plurality of optimized constant coefficients corresponding to the first region and the second region according to the following equation:

OG Complex Work Unit Math
wherein J is an objective function; θ represents the wave propagation angle; n is a medium refractive index; a, b and c represent the plurality of optimized constant coefficients; kx represents wavenumber in x direction; kx represents normalized wavenumber in x direction, and kx=kx/k0; k0 represents wavenumber based on background velocity; and φ is a set maximum imaging angle;
(S500) constructing a rational function-approximation dispersion relation based on heterogeneity of a real underground medium; and substituting the rational function-approximation dispersion relation into a frequency-wavenumber domain Fourier wavefield continuation fundamental equation to obtain a frequency-wavenumber domain wavefield continuation equation, expressed as:

OG Complex Work Unit Math
wherein P(kx,z+Δz) represents wavefield information at a depth of z+Δz; kz represents wavenumber in z direction; p(kx,z) represents wavefield information at a depth of z; α is an intermediate parameter variable, represented by

OG Complex Work Unit Math
 i represents an imaginary number; and Δz represents a spatial sampling interval along a depth direction; and
substituting the plurality of optimized constant coefficients obtained in step (S400) into the intermediate parameter variable α of the frequency-wavenumber domain wavefield continuation equation, and processing the frequency-wavenumber domain common offset seismic data by using the frequency-wavenumber domain wavefield continuation equation thereby obtaining a plurality of images at different depths and frequencies;
(S600) integrating the plurality of images to obtain a plurality of integrated images; and transforming the plurality of integrated images to a spatial domain by using inverse Fourier transform to obtain a plurality of common offset imaging profiles; and
(S700) superposing the plurality of common offset imaging profiles to obtain a seismic image.