Compressive sensing

Patent metadata

Field	Value
Publication number	US-9632193-B2
Application number	US-201414529690-A
Country	US
Kind code	B2
Filing date	Oct 31, 2014
Priority date	Nov 1, 2013
Publication date	Apr 25, 2017
Grant date	Apr 25, 2017

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 min u ∥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
μ ≤ C S ⁢ m ( log ⁢ ⁢ n ) 6 ,
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 min r μ(r).

First claim

What is claimed is:

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 min u ∥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, σ represents noise level in observed data, and matrix R is a sampling operator;
b) defining mutual coherence as

μ
⁡

(
r
)

=

max

l
≠
0

⁢



r
^

l



=

max

l
≠
0

⁢



∑

k
=
1

n

⁢

r
k

⁢

ω
kl



 wherein r is sampling grid, {circumflex over (r)} 1 are Fourier transform coefficients, ω=exp(−2π√{square root over (−1)}/n), and n is number of elements in r;
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 min r μ(r).

2. The method of claim 1 , wherein the sample grid is determined via randomized greedy algorithm method.

3. The method of claim 2 , wherein the randomized greedy algorithm method finds local minimum.

4. The method of claim 1 , wherein the sample grid is determined via stochastic global optimization method.

5. The method of claim 1 , wherein r * =arg min r μ(r) is non-convex.

6. The method of claim 1 , wherein the mutual coherence proxy is derived using fast Fourier transform.

Assignees

• Conocophillips Co

Inventors

• Li Chengbo
• Kaplan Sam T
• Mosher Charles C
• Brewer Joel D
• Keys Robert G

Classifications

• G01V1/36

  Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy · CPC title

• G01V2210/169

  Sparse arrays · CPC title

• G01V2210/614

  Synthetically generated data · CPC title

• G01V1/003 Primary

  Seismic data acquisition in general, e.g. survey design (G01V1/3808, G01V1/42 take precedence) · CPC title

• G01V2210/60

  Analysis · CPC title