Demultiple using up/down separation of towed variable-depth streamer data

1. A method for processing recorded data acquired using a variable-depth streamer, the method comprising:

receiving the recorded data acquired using the variable-depth streamer;

applying wavefield separation to the recorded data using a processor, at a locus of the variable-depth streamer, to obtain an up-going wavefield and a down-going wavefield at the locus of the variable-depth streamer;

extrapolating the up-going wavefield and the down-going wavefield from the locus of the variable-depth streamer to a predetermined datum, different from the locus of the variable-depth streamer;

calculating multiples by removing the extrapolated down-going wavefield at the predetermined datum from the extrapolated up-going wavefield at the predetermined datum;

removing the multiples from the extrapolated up-going wavefield at the predetermined datum to obtain a primary dataset, which is then migrated or extrapolated to another datum; and

generating an image of a geological formation under the seabed using (1) the primary dataset, and/or (2) the multiples.

2. The method of claim 1 , wherein the predetermined datum is the seabed.

3. The method of claim 1 , wherein

the extrapolated up-going wavefield and the extrapolated down-going wavefield at the predetermined datum are obtained using a wavefield separation based on a tau-p model thereof.

4. The method of claim 1 , wherein the extrapolation uses information on a water velocity dependence on depth.

5. The method of claim 1 , wherein the extrapolated up-going wavefield and the extrapolated down-going wavefield at the predetermined datum are obtained using a sparse inversion method.

6. The method of claim 1 , wherein the calculating of the multiples includes determining a matching filter that minimizes a difference between the extrapolated up-going wavefield and the extrapolated down-going wavefield at the predetermined datum.

7. The method of claim 1 , wherein the calculating of the multiples is an iterative process.

8. The method of claim 7 , wherein the iterative process uses at least two different methods to identify the multiples.

9. The method of claim 1 , wherein the calculating of the multiples includes:

transforming in a spectral domain the extrapolated up-going wavefield and the extrapolated down-going wavefield at the predetermined datum; and

dividing the transformed up-going wavefield to the transformed down-going wavefield.

10. The method of claim 1 , further comprising:

extrapolating the multiples to another datum.

11. The method of claim 1 , further comprising:

migrating the multiples separately from the primary dataset, to another datum.

12. An apparatus for seismic data processing, the apparatus comprising:

an input-output interface configured to receive recorded data acquired using a variable-depth streamer; and

a data processing unit configured

to apply wavefield separation to the recorded data, at a locus of the variable-depth streamer, to obtain an up-going wavefield and a down-going wavefield at the locus of the variable-depth streamer;

to extrapolate the up-going wavefield and the down-going wavefield from the locus of the variable-depth streamer to a predetermined datum, different from the locus of the variable-depth streamer;

to calculate multiples by removing the extrapolated down-going wavefield at the predetermined datum from the extrapolated up-going wavefield at the predetermined datum, and

to generate an image of a geological formation under the seabed using (1) a primary dataset obtained by removing the multiples from the extrapolated up-going wavefield at the predetermined datum, and/or (2) the multiples

wherein the data processing unit is configured to perform one or more of the following operations to generate the image:

extrapolating the multiples to another datum;

extrapolating the primary dataset to the another datum; and

migrating the primary dataset and the multiples separately, to the another datum.

13. The apparatus of claim 12 , wherein the predetermined datum is the seabed.

14. A method for exploring a geological formation under the seabed, the method comprising:

receiving data recorded using a variable-depth streamer;

processing the recorded data to generate an image of the geological formation using a processor,

wherein the processing includes,

applying wavefield separation to the recorded data, at a locus of the variable-depth streamer, to obtain an up-going wavefield and a down-going wavefield at the locus of the variable-depth streamer,

extrapolating the up-going wavefield and the down-going wavefield from the locus of the variable-depth streamer to a predetermined datum, different from the locus of the variable-depth streamer,

calculating multiples based on the extrapolated up-going wavefield and the extrapolated down-going wavefield at the predetermined datum, the up-going wavefield and the down-going wavefields at the locus of the variable-depth streamer being derived using an inversion and/or minimization method,

removing the multiples from the extrapolated up-going wavefield at the predetermined datum to obtain a primary dataset, which is then migrated or extrapolated to another datum, and

generating an image of the geological formation under the seabed using (1) the primary dataset, and/or (2) the multiples.

15. A non-transitory computer-readable medium configured to store executable codes which when executed by a computer perform a method for processing recorded data acquired using a variable-depth streamer, the method comprising:

receiving the recorded data acquired using the variable-depth streamer;

applying wavefield separation to the recorded data, at a locus of the variable-depth streamer, to obtain an up-going wavefield and a down-going wavefield at the locus of the variable-depth streamer;

extrapolating the up-going wavefield and the down-going wavefield from the locus of the variable-depth streamer to a predetermined datum, different from the locus of the variable-depth streamer;

calculating multiples by removing the extrapolated down-going wavefield at the predetermined datum from the extrapolated up-going wavefield at the predetermined datum;

removing the multiples from the extrapolated up-going wavefield at the predetermined datum to obtain a primary dataset, which is then migrated or extrapolated to another datum; and

generating an image of a geological formation under the seabed using (1) the primary dataset, and/or (2) the multiples.