Seismic data least-square migration method and device

1. A method for generating an image of a subsurface explored by a seismic survey based on least square migration and image de-convolution using a matching operator F, the method comprising:

receiving seismic data d acquired for the subsurface during the seismic survey;

computing a first image m of the subsurface based on the seismic data d;

computing a second image h of the subsurface based on the first image m;

applying a transform operation to the first and second images m and h to obtain a first transform of the first image and a second transform of the second image;

calculating the matching operator F by matching the first transform of the first image to the second transform of the second image; and

generating an updated image m updated of the subsurface based on the matching operator F and the first transform of the first image,

wherein the updated image of the subsurface is useable to determine whether oil and/or gas reservoirs are present in the subsurface.

2. The method of claim 1 , wherein the transform operation is a dip decomposition.

3. The method of claim 2 , wherein the dip decomposition decomposes the first and second images m and h, in an image domain, according to dip volumes V i of the subsurface, the first transform of the first image is a first dip decomposed image m i , the second transform of the second image is a second dip decomposed images h i , where “i” is an index, and the method further comprises:

calculating different matching operators F i for each pair of the first and second dip decomposed images m i and h i that have the same index i.

4. The method of claim 3 , further comprising:

calculating an updated image component m updated i for each pair of first and second dip decomposed images m i and h i that have the same index i by applying the different matching operator F i to a corresponding first dip decomposed image m i .

5. The method of claim 4 , further comprising:

constructing the updated image m updated using the updated image components m updated i corresponding to dip volumes V i .

6. The method of claim 1 , wherein the step of computing a second image h comprises:

applying a demigration operator L to the first image m followed by applying a migration operator L H , wherein the migration operator is an adjoint of the demigration operator,

wherein the demigration operator L and the migration operator L H transform an object from an image space to a data space and vice versa, respectively.

7. The method of claim 1 , wherein the step of calculating further comprises:

applying a cost function in an image space, between the first image m and the second image h, to calculate the matching operator F.

8. The method of claim 1 , wherein the seismic data d is in a data space and the first and second images m and h are in image space, which is different from the data space.

9. The method of claim 1 , wherein the transform operation is a Fourier transform, curvelet transform, tau-p transform or wavelet transform.

10. The method of claim 1 , wherein the first transform of the first image is in a same domain as the first image m.

11. The method of claim 1 , wherein the first transform of the first image is in a domain different from the first image m.

12. The method of claim 1 , further comprising:

splitting the seismic d or the first image m into subsets, and calculating plural pre-stack images p i corresponding to the subsets;

stacking a selected pre-stack range from the pre-stack images p i to generate a stack image s;

de-migrating the stack image s and migrating an output of the de-migrating to produce pre-stack re-migrated images n i ;

calculating the matching operator F by matching the pre-stack re-migrated images n i with the stack image s; and

applying the matching operator F to the pre-stack images p i to obtain updated pre-stack images.

13. The method of claim 1 , wherein at least one of the first and second images is denoised prior to calculating the matching operator F.

14. A computing device for generating an image of a subsurface explored by a seismic survey based on least square migration and image de-convolution using a matching operator F, the computing device comprising:

an interface for receiving seismic data d acquired for the subsurface during the seismic survey; and

a processor connected to the interface and configured to,

compute a first image m of the subsurface based on the seismic data d;

compute a second image h of the subsurface based on the first image m;

apply a transform operation to the first and second images m and h to obtain a first transform of the first image and a second transform of the second image;

calculate the matching operator F by matching the first transform of the first image to the second transform of the second image; and

generate an updated image m updated of the subsurface based on the matching operator F and the first transform of the first image

wherein the updated image of the subsurface is useable to determine whether oil and/or gas reservoirs are present in the subsurface.

15. The computing device of claim 14 , wherein the transform operation is a dip decomposition.

16. The computing device of claim 15 , wherein the dip decomposition decomposes the first and second images m and h, in an image domain, according to dip volumes V i of the subsurface, the first transform of the first image is a first dip decomposed image m i , the second transform of the second image is a second dip decomposed images h i , where “i” is an index, and the processor is further configured to:

calculate different matching operators F i for each pair of the first and second dip decomposed images m i and h i that have the same index i.

17. The computing device of claim 16 , wherein the processor is further configured to:

calculate an updated image component m updated i for each pair of first and second dip decomposed images m i and h i that have the same index i by applying the different matching operator F i to a corresponding first dip decomposed image m i .

18. The computing device of claim 17 , wherein the processor is further configured to:

construct the updated image m updated using the updated image components m updated i corresponding to dip volumes V i .

19. The computing device of claim 14 , wherein the processor is further configured to:

apply a demigration operator L to the first image m followed by applying a migration operator L H , wherein the migration operator is an adjoint of the demigration operator,

wherein the demigration operator L and the migration operator L H transform an object from an image space to a data space and vice versa, respectively.

20. A non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed by a processor, implement instructions for generating an image of a subsurface explored by a seismic survey based on least square migration and image de-convolution using a matching operator F, the instructions controlling the processor to:

receive seismic data d acquired for the subsurface during the seismic survey;

compute a first image m of the subsurface based on the seismic data d;

compute a second image h of the subsurface based on the first image m;

apply a transform operation to the first and second images m and h to obtain a first transform of the first image and a second transform of the second image;

calculate the matching operator F by matching the first transform of the first image to the second transform of the second image; and

generate an updated image m updated of the subsurface based on the matching operator F and the first transform of the first image,

wherein the updated image of the subsurface is useable to determine whether oil and/or gas reservoirs are present in the subsurface.