Methods for simultaneous source separation
A multi-stage inversion method for deblending seismic data includes: a) acquiring blended seismic data from a plurality of seismic sources; b) constructing an optimization model that includes the acquired blended seismic data and unblended seismic data; c) performing sparse inversion, via a computer processor, on the optimization model; d) estimating high-amplitude coherent energy from result of the performing sparse inversion in c); e) re-blending the estimated high-amplitude coherent energy; and f) computing blended data with an attenuated direct arrival energy.
1. A multi-stage inversion method for deblending seismic data, the method comprising:
a) acquiring, via a plurality of shots fired from at least one vessel, blended seismic data from a plurality of seismic sources using a compressive sensing sampling scheme, the at least one vessel driven at a constant speed while permitting natural causes to affect the constant speed;
b) constructing an optimization model that relates the blended seismic data to unblended seismic data;
c) performing sparse inversion, via a computer processor, on the optimization model to yield a result;
d) estimating high-amplitude coherent energy from the result;
e) re-blending the high-amplitude coherent energy; and
f) computing a deblended seismic data by attenuating at least a portion of the high-amplitude coherent energy from the blended seismic data.
2. The method of claim 1 , wherein steps c) to f) are iteratively repeated until a desired deblended data is computed.
3. The method of claim 1 , wherein the sparse inversion is by nonmonotone alternating direction method.
4. The method of claim 1 , wherein the optimization model is given by b=Mu, wherein b is the blended seismic data, u is the unblended seismic data, and M is a blending operator.
5. The method of claim 1 , wherein performing the sparse inversion provides at least an approximation of the unblended seismic data u.
6. The method of claim 1 , wherein the high-amplitude coherent energy is subtracted from the blended seismic data after performing the re-blending of the high-amplitude coherent energy.
7. The method of claim 1 , where the high-amplitude coherent energy is selected from, the group consisting of: direct arrival energy, ground roll, mud roll, multiples, near-surface scattering, topographic scattering, noise generated by permafrost, platform, surveys nearby, and any combination thereof.
8. The method of claim 1 , wherein the natural causes cause the at least one vessel to have a variable speed.
9. The method of claim 8 , wherein the blended seismic data is acquired via a plurality of vessels.
10. The method of claim 8 , wherein each of the plurality of vessels covers half of a survey area.
11. A multi-stage inversion method for deblending seismic data, the method comprising:
a) acquiring, via a plurality of shots fired from at least one vessel, blended seismic data from a plurality of seismic sources using a compressive sensing sampling scheme, the at least one vessel driven at a constant speed while permitting natural causes to affect the constant speed;
b) constructing an optimization model that relates the blended seismic data to unblended seismic data;
c) performing sparse inversion, via a computer processor, on the optimization model;
d) estimating a high-amplitude noise from the optimization model, the high-amplitude noise selected from the group consisting of: direct arrival energy, ground roll, and mud roll;
e) re-blending the high-amplitude noise;
f) computing deblended data by attenuating at least a portion of the high-amplitude noise from the blended seismic data; and
g) iteratively repeating steps c) to f) until a desired deblended data is computed.
12. The method of claim 11 , wherein the sparse inversion is by nonmonotone alternating direction method.
13. The method of claim 11 , wherein the optimization model is given by b=Mu, wherein b is the blended seismic data, u is the unblended seismic data, and M is a blending operator.
14. The method of claim 11 , wherein performing the sparse inversion provides at least an approximation of the unblended seismic data u.
15. The method of claim 11 , wherein the high-amplitude noise is subtracted from the blended seismic data after performing the re-blending of the high-amplitude noise.
16. A method for jointly deblending and reconstructing seismic data, the method comprising:
acquiring, via a plurality of shots fired from at least one vessel, blended seismic data from a plurality of seismic sources using a compressive sensing sampling scheme, the at least one vessel driven at a constant speed while permitting natural causes to affect the constant speed;
constructing an optimization model that relates the blended seismic data, unblended seismic data, and a restriction operator that maps data from a grid of reconstructed seismic sources to a grid of observed seismic sources;
performing sparse inversion, via a computer processor, on the optimization model, a high-amplitude energy being estimated from the optimization model, the high-amplitude energy being re-blended; and
computing a deblended data by attenuating at least a portion of the high-amplitude energy.
17. The method of claim 16 , wherein the blended seismic data is acquired by a non-uniform shooting pattern.
18. The method of claim 16 , wherein the sparse inversion is by nonmonotone alternating direction method.
19. The method of claim 16 , wherein the optimization model is given by b=MRu, wherein b is the blended seismic data, u is the unblended seismic data, M is a blending operator, and R is the restriction operator.
20. The method of claim 16 , wherein the performing of the sparse inversion provides at least an approximation of the unblended seismic data u.