COMPRESSIVE SENSING
First Claim
1. A computer-implemented method for determining optimal sampling grid during seismic data reconstruction, the method comprising:
- a) constructing an optimization model, via a computing processor, given by minu∥
Su∥
1 s.t. ∥
Ru−
b∥
2≦
σ
wherein S is a discrete transform matrix, b is seismic data on an observed grid, u is seismic data on a reconstruction grid, and matrix R is a sampling operator;
b) defining mutual coherence as
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Abstract
Computer-implemented method for determining optimal sampling grid during seismic data reconstruction includes: a) constructing an optimization model, via a computing processor, given by minu∥Su∥1 s.t. ∥Ru−b∥2≦σ wherein S is a discrete transform matrix, b is seismic data on an observed grid, u is seismic data on a reconstruction grid, and matrix R is a sampling operator; b) defining mutual coherence as
wherein C is a constant, S is a cardinality of Su, m is proportional to number of seismic traces on the observed grid, and n is proportional to number of seismic traces on the reconstruction grid; c) deriving a mutual coherence proxy, wherein the mutual coherence proxy is a proxy for mutual coherence when S is over-complete and wherein the mutual coherence proxy is exactly the mutual coherence when S is a Fourier transform; and d) determining a sample grid r*=arg minr μ(r).
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Citations
6 Claims
-
1. A computer-implemented method for determining optimal sampling grid during seismic data reconstruction, the method comprising:
-
a) constructing an optimization model, via a computing processor, given by minu∥
Su∥
1 s.t. ∥
Ru−
b∥
2≦
σ
wherein S is a discrete transform matrix, b is seismic data on an observed grid, u is seismic data on a reconstruction grid, and matrix R is a sampling operator;b) defining mutual coherence as - View Dependent Claims (2, 3, 4, 5, 6)
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Specification