Optimizing source and receiver locations for acquiring seismic data used in compressive sensing reconstruction
Source and receiver locations are optimized for acquiring seismic data used in compressive sensing reconstruction. A minimized multidimensional mutual coherence map, which includes a mutual coherence value at each (x,y) location in the mutual coherence map, is used to determine the optimal source and receiver locations from available source and receiver locations in respective, uniformly spaced, target survey grids.
1. A method for optimizing source and receiver locations for acquiring data used in compressive sensing reconstruction, which comprises:
a. creating a uniformly spaced target survey grid for available source locations and a uniformly spaced target survey grid for available receiver locations;
b. dividing the target survey grid for available source locations and the target survey grid for available receiver locations into multiple source subgrids and multiple receiver subgrids, respectively;
c. defining a local multidimensional mutual coherence map, representing an MC map, for each source subgrid and each receiver subgrid as a function of a sparsity promoting transform (F) and a multidimensional sampling function (u s );
d. solving each multidimensional sampling function for each respective source subgrid and each respective receiver subgrid using a global optimizer to iteratively minimize predetermined statistics for each respective MC map under predetermined target survey criteria and predetermined target survey constraints wherein the solution for each multidimensional sampling function determines i) local coordinates for each optimal source location in a respective source subgrid and each optimal receiver location in a respective receiver subgrid, and ii) a minimized MC map for each respective source subgrid and each respective receiver subgrid, each minimized MC map including a mutual coherence value at each (x,y) location in the minimized MC map;
e. converting the local coordinates for each optimal source location and each optimal receiver location in a respective source subgrid and a respective receiver subgrid to global acquisition coordinates that each corresponds to a respective grid node on a respective source subgrid or a respective grid node on a respective receiver subgrid; and
f. combining the optimal source and receiver locations in each respective source subgrid and in each respective receiver subgrid, and the corresponding minimized MC map for each respective source subgrid and each respective receiver subgrid, into a new, optimized, source survey with a combined MC map and a new, optimized, receiver survey with a combined MC map.
2. The method of claim 1 , further comprising:
g. displaying the new source survey and the new receiver survey with each respective combined MC map; and
h. determining if the new source survey and the new receiver survey are valid based on the display of each respective combined MC map.
3. The method of claim 2 , further comprising:
identifying at least one invalid survey;
entering new target survey criteria for each invalid survey; and
repeating steps a-h for each invalid survey using the new target survey criteria.
4. The method of claim 2 , further comprising:
identifying at least one valid survey;
entering new target survey constraints for each valid survey; and
repeating steps a-h for each valid survey using the new target survey constraints.
5. The method of claim 1 , wherein the target survey grid for available source locations and the target survey grid for available receiver locations are created using an initial survey for available source locations and an initial survey for available receiver locations, respectively, and the predetermined target survey criteria.
6. The method of claim 1 , wherein each source subgrid and each receiver subgrid represents a respective process area.
7. The method of claim 6 , wherein the number of multiple source subgrids and the number of multiple receiver subgrids are each equal to a predetermined number of process areas used for a domain.
8. The method of claim 1 , wherein the MC map is defined as:
MC
(
x
,
y
)
=
max
Us
′
max
Us
,
U
s
′
<
max
U
s
,
U
s
′
∈
U
s
;
and
wherein U s =Fu s .
9. The method of claim 8 , wherein the predetermined statistics includes one of a minimum value, a mean value and a standard deviation.
10. A non-transitory program carrier device tangibly carrying computer-executable instructions for optimizing source and receiver locations for acquiring data used in compressive sensing reconstruction, the instructions being executable to implement;
a. creating a uniformly spaced target survey grid for available source locations and a uniformly spaced target survey grid for available receiver locations;
b. dividing the target survey grid for available source locations and the target survey grid for available receiver locations into multiple source subgrids and multiple receiver subgrids, respectively;
c. defining a local multidimensional mutual coherence map, representing an MC map, for each source subgrid and each receiver subgrid as a function of a sparsity promoting transform (F) and a multidimensional sampling function (u s );
d. solving each multidimensional sampling function for each respective source subgrid and each respective receiver subgrid using a computer processor and a global optimizer to iteratively minimize predetermined statistics for each respective MC map under predetermined target survey criteria and predetermined target survey constraints wherein the solution for each multidimensional sampling function determines i) local coordinates for each optimal source location in a respective source subgrid and each optimal receiver location in a respective receiver subgrid, and ii) a minimized MC map for each respective source subgrid and each respective receiver subgrid, each minimized MC map including a mutual coherence value at each (x,y) location in the minimized MC map;
e. converting the local coordinates for each optimal source location and each optimal receiver location in a respective source subgrid and a respective receiver subgrid to global acquisition coordinates that each corresponds to a respective grid node on a respective source subgrid or a respective grid node on a respective receiver subgrid; and
f. combining the optimal source and receiver locations in each respective source subgrid and in each respective receiver subgrid, and the corresponding minimized MC map for each respective source subgrid and each respective receiver subgrid, into a new, optimized, source survey with a combined MC map and a new, optimized, receiver survey with a combined MC map.
11. The program carrier device of claim 10 , further comprising:
g. displaying the new source survey and the new receiver survey with each respective combined MC map; and
h. determining if the new source survey and the new receiver survey are valid based on the display of each respective combined MC map.
12. The program carrier device of claim 11 , further comprising:
identifying at least one invalid survey;
entering new target survey criteria for each invalid survey; and
repeating steps a-h for each invalid survey using the new target survey criteria.
13. The program carrier device of claim 11 , further comprising:
identifying at least one valid survey;
entering new target survey constraints for each valid survey; and
repeating steps a-h for each valid survey using the new target survey constraints.
14. The program carrier device of claim 10 , wherein the target survey grid for available source locations and the target survey grid for available receiver locations are created using an initial survey for available source locations and an initial survey for available receiver locations, respectively, and the predetermined target survey criteria.
15. The program carrier device of claim 10 , wherein each source subgrid and each receiver subgrid represents a respective process area.
16. The program carrier device of claim 15 , wherein the number of multiple source subgrids and the number of multiple receiver subgrids are each equal to a predetermined number of process areas used for a domain.
17. The program carrier device of claim 10 , wherein the MC map is defined as:
MC
(
x
,
y
)
=
max
Us
′
max
Us
,
U
s
′
<
max
U
s
,
U
s
′
∈
U
s
;
and
wherein U s =Fu s .
18. The program carrier device of claim 17 , wherein the predetermined statistics includes one of a minimum value, a mean value and a standard deviation.