Method and apparatus for deghosting seismic data

1. A method for deghosting seismic data related to a subsurface of a body of water, the method comprising:

receiving data recorded with seismic detectors that are towed by a vessel, the data being associated with waves travelling from the subsurface to the seismic detectors;

applying with a processing apparatus a migration procedure to the data to determine a first image of the subsurface;

applying with the processing apparatus a mirror migration procedure to the data to determine a second image of the subsurface;

joint deconvoluting with the processing apparatus the first image and the second image for deghosting a reflectivity of the subsurface; and

generating with the processing apparatus a final image of the subsurface based on the deghosted reflectivity of the joint deconvoluting step.

2. The method of claim 1 , wherein the deghosting is performed during an imaging phase and not in a preprocessing phase with a processing apparatus.

3. The method of claim 1 , wherein no datuming step is performed on the data.

4. The method of claim 1 , wherein a travelling angle of the waves propagating from the subsurface to the detectors or from a surface of the water to the detectors is not restricted.

5. The method of claim 1 , wherein the data is three dimensional data and the migration, the mirror migration and the joint deconvolution are three dimensional procedures.

6. The method of claim 1 , wherein the data are collected from streamers having birds that are controlled to achieve a curved profile.

7. The method of claim 1 , wherein the migration procedure comprises:

recursively synthesizing an incident wave D(x, y, z+Δz, t) at a depth z+Δz from a previous incident wave D(x, y, z, t) at depth z.

8. The method of claim 1 , wherein the mirror migration procedure comprises:

recursively synthesizing an up-travelling wave U(x, y, z+Δz, t) at a depth z+Δz from a previous up-travelling wave U(x, y, z, t) at a depth z.

9. The method of claim 1 , wherein the joint deconvoluting comprises:

determining the reflectivity r(x, y, z), a minimum phase transfer function g min (z), and a maximum phase transfer function g max (z) based on equations:

d 1 ( x,y,z )= g min ( z )· r ( x,y,z ), and

d 2 ( x,y,z )= g max ( z )* r ( x,y,z ),

wherein z is a depth of a point relative to the surface of the water, and x and y are coordinates of the point in a plane substantially parallel with the surface of the water.

10. The method of claim 9 , wherein the g min (z) and g max (z) are three dimensional functions.

11. The method of claim 1 , wherein the migration is a depth migration.

12. The method of claim 1 , wherein the migration is a time migration.

13. The method of claim 1 , wherein the joint deconvolution comprises:

calculating a cost function C for determining the reflectivity, wherein the cost function C is given by:

C=Σ (x,y,z)εV {[d 1 ( x,y,z )− g min ( z )* r ( x,y,z )] 2 +[d 2 ( x,y,z )− g max ( z )* r ( x,y,z )] 2 },

where d 1 (x, y, z) is the first image, d 2 (x, y, z) is the second image, g min (z) is a minimum phase transfer function, g max (z) is a maximum phase transfer function, z is a depth of a point relative to the surface of the water, x and y are coordinates of the point in a plane substantially parallel with the surface of the water, and V is a predetermined volume.

14. The method of claim 1 , further comprising:

applying a (τ, p x , p y ) transform to the first image d 1 (x, y, z) and the second image d 2 (x, y, z), to transform the first image d 1 (x, y, z) into D 1 (p x , p y , τ) and the data d 2 (x, y, z) into D 2 (p x , p y , τ).

15. The method of claim 1 , wherein the data includes recordings from hydrophones and geophones.

16. The method of claim 15 , wherein a result of the migration procedure is d 1 (x, y, z) and a result of the mirror migration procedure is d 2 (x, y, z) for hydrophone type receivers and a result of the migration procedure is d 3 (x, y, z) and a result of the mirror migration procedure is d 4 (x, y, z) for geophones.

17. The method of claim 16 , further comprising:

generating the final image using a joint deconvolution of d 1 (x, y, z), d 2 (x, y, z), d 3 (x, y, z), and d 4 (x, y, z) and based on the following equations:

d 1 ( x,y,z )= g h min ( z )* r ( x,y,z );

d 2 ( x,y,z )= g h max ( z )* r ( x,y,z );

d 3 ( x,y,z )= g g min ( z )* c ( z )* r ( x,y,z ); and

d 4 ( x,y,z )= g g max ( z )* c ( z )* r ( x,y,z ),

where g h min and g g min are minimum phase transfer functions, g h max (z) and g g max (z) are maximum phase transfer functions, z is a depth of a point relative to the surface of the water, x and y are coordinates of the point in a plane substantially parallel with the surface of the water, and c(z) is a calibration operator.

18. A processing device for deghosting seismic data related to a subsurface of a body of water, the processing device comprising:

an interface configured to receive data recorded by detectors that are towed by a vessel, the data being associated with waves travelling from the subsurface to the detectors; and

a processor connected to the interface and configured to,

apply a migration procedure to the data to determine a first image of the subsurface,

apply a mirror migration procedure to the data to determine a second image of the subsurface,

joint deconvolute the first image and the second image for deghosting a reflectivity of the subsurface, and

generate a final image of the subsurface based on the deghosted reflectivity of the joint deconvoluting step.

19. The processing device of claim 18 , wherein the processor is configured to deghost the final image during an imaging phase and not in a preprocessing phase.

20. The processing device of claim 18 , wherein the processor is configured to perform no datuming step on the data.

21. The processing device of claim 18 , wherein the processor is configured to handle the waves propagating from the subsurface to the detectors or from a surface of the water to the detectors with a travelling angle having no restriction.

22. The processing device of claim 18 , wherein the data is three dimensional data and the migration, the mirror migration and the joint deconvolution are three dimensional procedures.

23. The processing device of claim 18 , wherein the data are collected from streamers having birds that are controlled to achieve a curved profile.

24. The processing device of claim 18 , wherein the processor is configured to:

determine the reflectivity r(x, y, z), a minimum phase transfer function g min (z), and a maximum phase transfer function g max (z) based on equations:

d 1 ( x,y,z )= g min ( z )· r ( x,y,z ), and

d 2 ( x,y,z )= g max ( z )* r ( x,y,z ),

wherein z is a depth of a point relative to the surface of the water, and x and y are coordinates of the point in a plane substantially parallel with the surface of the water.

25. The processing device of claim 24 , wherein the g min (z) and g max (z) are three dimensional functions.

26. The processing device of claim 18 , wherein the migration is a depth migration.

27. The processing device of claim 18 , wherein the migration is a time migration.

28. The processing device of claim 18 , wherein the processor is configured to execute the joint deconvolution by:

calculating a cost function C for determining the reflectivity, wherein the cost function C is given by:

C=Σ (x,y,z)εV {[d 1 ( x,y,z )− g min ( z )* r ( x,y,z )] 2 +[d 2 ( x,y,z )− g max ( z )* r ( x,y,z )] 2 },

where d 1 (x, y, z) is the first image, d 2 (x, y, z) is the second image, g min (z) is a minimum phase transfer function, g max (z) is a maximum phase transfer function, z is a depth of a point relative to the surface of the water, x and y are coordinates of the point in a plane substantially parallel with the surface of the water, and V is a predetermined volume.

29. The processing device of claim 18 , wherein the processor is further configured to:

apply a (τ, p x , p y ) transform to the first image d 1 (x, y, z) and the second image d 2 (x, y, z), to transform the first image d 1 (x, y, z) into D 1 (p x , p y , τ) and the data d 2 (x, y, z) into D 2 (p x , p y , τ).

30. The processing device of claim 18 , wherein the data includes recordings from hydrophones and geophones.

31. The processing device of claim 30 , wherein a result of the migration procedure is d 1 (x, y, z) and a result of the mirror migration procedure is d 2 (x, y, z) for hydrophone type receivers and a result of the migration procedure is d 3 (x, y, z) and a result of the mirror migration procedure is d 4 (x, y, z) for geophones.

32. The processing device of claim 31 , wherein the processor is further configured to:

generate the final image using a joint deconvolution of d 1 (x, y, z), d 2 (x, y, z), d 3 (x, y, z), and d 4 (x, y, z) and based on the following equations:

d 1 ( x,y,z )= g h min ( z )* r ( x,y,z );

d 2 ( x,y,z )= g h max ( z )* r ( x,y,z );

d 3 ( x,y,z )= g g min ( z )* c ( z )* r ( x,y,z ); and

d 4 ( x,y,z )= g g max ( z )* c ( z )* r ( x,y,z ),

where g h min and g g min are minimum phase transfer functions, g h max (z) and g g max (z) are maximum phase transfer functions, z is a depth of a point relative to the surface of the water, x and y are coordinates of the point in a plane substantially parallel with the surface of the water, and c(z) is a calibration operator.

33. A non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed, implement a method for deghosting seismic data related to a subsurface of a body of water, the method comprising:

inputting data recorded by detectors that are towed by a vessel, the data being associated with waves travelling from the subsurface to the detectors;

applying a migration procedure to the data to determine a first image of the subsurface;

applying a mirror migration procedure to the data to determine a second image of the subsurface;

joint deconvoluting the first image and the second image for deghosting a reflectivity of the subsurface; and

generating a final image of the subsurface based on the deghosted reflectivity of the joint deconvoluting step.