Seismic data processing using a down-going annihilation operator
A method for processing seismic data, the method including receiving seismic data acquired by at least one receiver over a water-covered subsurface formation; generating, based on the seismic data, a down-going wavefield; generating, based on the seismic data, a partial down-going wavefield with attenuated water-wave; estimating a subsurface reflectivity R using multi-dimensional deconvolution, which equates (1) a convolution of the down-going wavefield with the subsurface reflectivity R to (2) the partial down-going wavefield; and generating an image of the water-covered subsurface formation based on the subsurface reflectivity R.
1 . A method for processing seismic data to improve subsurface imaging, the method comprising:
receiving seismic data acquired by at least one receiver over a water-covered subsurface formation;
generating, based on the seismic data, a down-going wavefield;
transforming the down-going wavefield into a partial down-going wavefield by attenuating a water-wave component;
estimating a subsurface reflectivity R by performing multi-dimensional deconvolution that maps the down-going wavefield to the partial down-going wavefield over an aperture of source locations, wherein the subsurface reflectivity R represents a set of source-side peg-leg multiples;
attenuating multiple reflections in the seismic data using a multiple model derived from the subsurface reflectivity R; and
generating an image of the water-covered subsurface formation using the seismic data with the attenuated multiple reflections.
2 . The method of claim 1 , wherein the down-going wavefield includes only a source ghost and the partial down-going wavefield is free of the source ghost.
3 . The method of claim 1 , wherein both the down-going wavefield and the partial down-going wavefield include a source ghost.
4 . The method of claim 1 , wherein the model of multiples is M d , and the method further comprising:
generating the model M d of multiples in the down-going wavefield or the partial down-going wavefield based on the subsurface reflectivity R;
attenuating the multiples in the down-going wavefield or the partial down-going wavefield based on the model M d of multiples; and
calculating the image based on the down-going wavefield with attenuated multiples.
5 . The method of claim 1 , wherein the model of multiples is M u , and the method further comprising:
extracting an up-going wavefield U from the seismic data;
generating the model M u of multiples in the up-going wavefield U based on the subsurface reflectivity R; and
attenuating the multiples in the up-going wavefield U based on the model M u of multiples.
6 . The method of claim 1 , wherein the multi-dimensional deconvolution is calculated as a summation over plural source locations.
7 . The method of claim 6 , where the source locations are acquired source locations.
8 . The method of claim 6 , where the source locations are reconstructed source locations.
9 . The method of claim 1 , wherein the multi-dimensional deconvolution is calculated in a transform domain, which is different from the time-space domain.
10 . The method of claim 1 , wherein the multi-dimensional deconvolution is calculated with conditioning, muting, or sparseness weights.
11 . The method of claim 1 , wherein the multi-dimensional deconvolution is calculated with one of an inversion via a conjugate gradient solver, a steepest descent solver, and singular value decomposition.
12 . The method of claim 1 , wherein the step of estimating the subsurface reflectivity R includes regularization of the inversion.
13 . The method of claim 1 , wherein the at least one receiver is an ocean bottom sensor.
14 . The method of claim 1 , wherein the down-going wavefield and the partial down-going wavefield are in a space-time domain.
15 . A computing device for processing seismic data to improve subsurface imaging, the computing device comprising:
an interface for receiving seismic data acquired by at least one receiver over a water-covered subsurface formation; and
a processor connected to the interface and configured to,
generate, based on the seismic data, a down-going wavefield;
transform the down-going wavefield into a partial down-going wavefield by attenuating a water-wave component;
estimate a subsurface reflectivity R by performing a multi-dimensional deconvolution that maps the down-going wavefield to the partial down-going wavefield D u over an aperture of source locations, wherein the subsurface reflectivity R represents a set of source-side peg-leg multiples;
attenuate multiple reflections in the seismic data using a multiple model derived from the subsurface reflectivity R; and
generate an image of the water-covered subsurface formation using the seismic data with the attenuated multiple reflections.
16 . The computing device of claim 15 , wherein the down-going wavefield includes only a source ghost and the partial down-going wavefield is free of the source ghost.
17 . The computing device of claim 15 , wherein both the down-going wavefield and the partial down-going wavefield include a source ghost.
18 . The computing device of claim 15 , wherein the model of multiples is M d , and the processor is further configured to:
generate the model M d of multiples in the down-going wavefield or the partial down-going wavefield based on the subsurface reflectivity R;
attenuate the multiples in the down-going wavefield or the partial down-going wavefield based on the model M d of multiples; and
calculate the image based on the down-going wavefield with attenuated multiples.
19 . The computing device of claim 15 , wherein the multi-dimensional deconvolution is calculated as a summation over plural source locations.
20 . The computing device of claim 19 , where the source locations are acquired source locations.