Wave-field reconstruction using a reflection from a variable sea surface

1. A method for seismic exploration of a subsurface formation under the seafloor, the method comprising:

receiving input seismic data recorded with seismic sensors configured to detect seismic waves traveling through the subsurface formation;

obtaining wave-height data using the input seismic data;

processing up-going energy and down-going energy following a reflection at the sea-surface extracted from the input seismic data corresponding to one of the sensors and using a linear operator modified to take into account the wave-height data; and

generating an image of the subsurface formation using the up-going energy or the down-going energy or a combination of the input seismic data and one of the up-going or down-going energy,

wherein the image enables detecting a hydrocarbon reservoir in the subsurface formation.

2. The method of claim 1 , wherein the down-going energy is subsequently reflected or refracted in the subsurface formation and then recorded by another seismic sensor.

3. The method of claim 1 , wherein the up-going energy and/or the down-going energy is representative of a wave-field at hypothetical receiver positions, not at a position of an input trace.

4. The method of claim 1 , wherein the linear operator contains separate terms representing primary and ghost energy.

5. The method of claim 1 , wherein the linear operator includes a reverse model transform.

6. The method of claim 1 , wherein the linear operator is a multiple prediction operator, and the method further comprising:

modifying the multiple prediction operator using the wave-height data,

convolving, with a computing device, the modified operator with the seismic data to generate modified seismic data; and

generating the image of the subsurface formation using the modified seismic data.

7. The method of claim 6 , wherein the multiple prediction operator predicts multiples associated with the input seismic data.

8. The method of claim 1 , wherein the input seismic data is single or multi-component data.

9. The method of claim 1 , wherein the obtaining of the wave-height data comprises:

calculating a height of a wave that describes a top surface of the body of water, for each seismic sensor.

10. The method of claim 9 , wherein the step of calculating a height of the wave comprises:

extrapolating the input seismic data to align primary and ghost wave fields;

cross-correlating the aligned primary and ghost wave fields; and

calculating the height of the wave using a lag obtained at the step of cross-correlating.

11. The method of claim 9 , wherein the step of calculating a height of the wave comprises:

calculating up-going and down-going wave fields using a deghosting method;

aligning the up-going and down-going fields using a wave field extrapolation method using a horizontal top surface;

cross-correlating the aligned up-going and down-going wave fields; and

calculating the height of the wave using a lag obtained at the cross-correlating step.

12. The method of claim 9 , wherein the input data is filtered, and the data before and after filtering are cross-correlated to determine a wave height.

13. The computing device of claim 1 , wherein the linear operator is a multiple prediction operator, and the processor is further configured to:

modify the multiple prediction operator using the wave-height data,

convolve, with a computing device, the modified operator with the seismic data to generate modified seismic data; and

generate the image of the subsurface formation using the modified seismic data.

14. The computing device of claim 13 , wherein the multiple prediction operator predicts multiples associated with the input seismic data.

15. A computing device for seismic exploration of a subsurface formation, the computing device comprising:

an interface for receiving input seismic data recorded with seismic sensors configured to detect seismic waves traveling through the subsurface formation, and wave-height data obtained from the input seismic data; and

a processor connected to the interface and configured to,

process up-going energy at a receiver and down-going energy following a reflection at the sea-surface extracted from the input seismic data and using a linear operator modified to take into account the wave-height data, and

generate an image of the subsurface formation using the up-going energy or the down-going energy or a combination of the input seismic data and one of the up-going or down-going energy,

wherein the image enables detecting a hydrocarbon reservoir in the subsurface formation.

16. The computing device of claim 15 , wherein the down-going energy is subsequently reflected or refracted in the subsurface formation and then recorded by another seismic sensor.

17. The computing device of claim 15 , wherein the up-going energy and/or the down-going energy is representative of a wave-field at hypothetical receiver positions, not at a position of an input trace.

18. The computing device of claim 15 , wherein the linear operator contains separate terms representing primary and ghost energy.

19. The computing device of claim 15 , wherein the linear operator includes a reverse model transform.

20. A non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed by a processor, implement instructions for seismic exploration of a subsurface formation under the seafloor, the instructions comprising:

receiving input seismic data recorded with seismic sensors configured to detect seismic waves traveling through the subsurface formation;

obtaining wave-height data using the input seismic data;

processing up-going energy at a receiver and down-going energy following a reflection at the sea-surface from the input seismic data and using a linear operator modified to take into account the wave-height data; and

generating an image of the subsurface formation using the up-going energy or the down-going energy or a combination of the input seismic data and one of the up-going or down-going energy,

wherein the image enables detecting a hydrocarbon reservoir in the subsurface formation.