Generating geophysical images using directional oriented wavefield imaging
The present disclosure describes methods and systems, including computer-implemented methods, computer program products, and computer systems, for generating geophysical images. One computer-implemented method includes receiving a set of seismic data associated with a subsurface region; generating source analytic wavefields and receiver analytic wavefields based on the set of seismic data; decomposing the source analytic wavefields and receiver analytic wavefields; computing directions of propagations for the source analytic wavefields and receiver analytic wavefields; computing, for a plurality of subsurface points, an azimuth angle and a reflection angle for a respective subsurface point based on the directions of propagations; generating for each of the plurality of subsurface points, a weighting function for a respective subsurface point based on the azimuth angle and the reflection angle of the respective subsurface point; and generating a subsurface image using the weighting functions of the plurality of subsurface points.
1. A method for generating subsurface images, comprising:
receiving, by a data processing apparatus, a set of seismic data associated with a subsurface region;
generating, by the data processing apparatus, source analytic wavefields and receiver analytic wavefields based on the set of seismic data;
decomposing the source analytic wavefields and receiver analytic wavefields based on down-going and up-going components of the source analytic wavefields and receiver analytic wavefields;
computing, by the data processing apparatus, directions of propagations for the source analytic wavefields and receiver analytic wavefields based on the decomposed source analytic wavefields and receiver analytic wavefields, wherein the directions of propagations are computed using an optical flow method;
computing, by the data processing apparatus, for a plurality of subsurface points, an azimuth angle and a reflection angle for a respective subsurface point based on the directions of propagations, wherein the reflection angle for the respective subsurface point is calculated according to
cos
θ
=
k
→
·
k
→
r
k
→
k
→
r
,
and the azimuth angle for the respective subsurface point is calculated according to
cos
φ
=
(
k
→
s
×
k
→
r
)
·
(
n
→
×
(
k
→
s
+
k
→
r
)
)
k
→
s
×
k
→
r
n
→
×
(
k
→
s
+
k
→
r
)
,
where θ is the reflection angle, φ is the azimuth angle, {right arrow over (n)} is a unit vector indicating starting direction of the azimuth angle, {right arrow over (k)} is a wavefield vector, {right arrow over (k)} s is a wavefield vector at a source location, and {right arrow over (k)} r is a wavefield vector at a receiver location;
generating, for each of the plurality of subsurface points, a weighting function for the respective subsurface point by using the azimuth angle and the reflection angle of the respective subsurface point, wherein each weighting function represents illumination energy at the respective subsurface point according to the azimuth angle and the reflection angle of the respective subsurface point; and
generating a subsurface image using the weighting functions of the plurality of subsurface points that are constructed using the azimuth angles and the reflection angles of the respective subsurface points.
2. The method of claim 1 , wherein the source analytic wavefields and the receiver analytic wavefields are generated using Green's function.
3. The method of claim 1 , wherein the source analytic wavefields and receiver analytic wavefields are decomposed based on a product of Green's function and a Hilbert transform of the set of seismic data.
4. The method of claim 1 , wherein the subsurface image is generated by stacking weighting functions for the plurality of subsurface points.
5. The method of claim 1 , wherein the set of seismic data comprise time-domain common shot gather.
6. A non-transitory computer-readable medium storing instructions which, when executed, cause a computing device to perform operations comprising:
receiving, by a data processing apparatus, a set of seismic data associated with a subsurface region;
generating, by the data processing apparatus, source analytic wavefields and receiver analytic wavefields based on the set of seismic data;
decomposing the source analytic wavefields and receiver analytic wavefields based on down-going and up-going components of the source analytic wavefields and receiver analytic wavefields;
computing, by the data processing apparatus, directions of propagations for the source analytic wavefields and receiver analytic wavefields based on the decomposed source analytic wavefields and receiver analytic wavefields, wherein the directions of propagations are computed using an optical flow method;
computing, by the data processing apparatus, for a plurality of subsurface points, an azimuth angle and a reflection angle for a respective subsurface point based on the directions of propagations, wherein the reflection angle for the respective subsurface point is calculated according to
cos
θ
=
k
→
·
k
→
r
k
→
k
→
r
,
and the azimuth angle for the respective subsurface point is calculated according to
cos
φ
=
(
k
→
s
×
k
→
r
)
·
(
n
→
×
(
k
→
s
+
k
→
r
)
)
k
→
s
×
k
→
r
n
→
×
(
k
→
s
+
k
→
r
)
,
where θ is the reflection angle, φ is the azimuth angle, {right arrow over (n)} is a unit vector indicating starting direction of the azimuth angle, {right arrow over (k)} is a wavefield vector, {right arrow over (k)} s is a wavefield vector at a source location, and {right arrow over (k)} r is a wavefield vector at a receiver location;
generating, for each of the plurality of subsurface points, a weighting function for the respective subsurface point by using the azimuth angle and the reflection angle of the respective subsurface point, wherein each weighting function represents illumination energy at the respective subsurface point according to the azimuth angle and the reflection angle of the respective subsurface point; and
generating a subsurface image using the weighting functions of the plurality of subsurface points that are constructed using the azimuth angles and the reflection angles of the respective subsurface points.
7. The non-transitory computer-readable medium of claim 6 , wherein the source analytic wavefields and the receiver analytic wavefields are generated using Green's function.
8. The non-transitory computer-readable medium of claim 6 , wherein the source analytic wavefields and receiver analytic wavefields are decomposed based on a product of Green's function and a Hilbert transform of the set of seismic data.
9. The non-transitory computer-readable medium of claim 6 , wherein the subsurface image is generated by stacking weighting functions for the plurality of subsurface points.
10. The non-transitory computer-readable medium of claim 6 , wherein the set of seismic data comprise time-domain common shot gather.
11. A device, comprising:
at least one hardware processor;
a non-transitory computer-readable storage medium coupled to the at least one hardware processor and storing programming instructions for execution by the at least one hardware processor, wherein the programming instructions instruct the at least one hardware processor to:
receive, by the at least one hardware processor, a set of seismic data associated with a subsurface region;
generate, by the at least one hardware processor, source analytic wavefields and receiver analytic wavefields based on the set of seismic data;
decompose the source analytic wavefields and receiver analytic wavefields based on down-going and up-going components of the source analytic wavefields and receiver analytic wavefields;
compute, by the at least one hardware processor, directions of propagations for the source analytic wavefields and receiver analytic wavefields based on the decomposed source analytic wavefields and receiver analytic wavefields, wherein the directions of propagations are computed using an optical flow method;
compute, by the at least one hardware processor, for a plurality of subsurface points, an azimuth angle and a reflection angle for a respective subsurface point based on the directions of propagations, wherein the reflection angle for the respective subsurface point is calculated according to
cos
θ
=
k
→
·
k
→
r
k
→
k
→
r
,
and the azimuth angle for the respective subsurface point is calculated according to
cos
φ
=
(
k
→
s
×
k
→
r
)
·
(
n
→
×
(
k
→
s
+
k
→
r
)
)
k
→
s
×
k
→
r
n
→
×
(
k
→
s
+
k
→
r
)
,
where θ is the reflection angle, φ is the azimuth angle, {right arrow over (n)} is a unit vector indicating starting direction of the azimuth angle, {right arrow over (k)} is a wavefield vector, {right arrow over (k)} s is a wavefield vector at a source location, and {right arrow over (k)} r is a wavefield vector at a receiver location;
generate, for each of the plurality of subsurface points, a weighting function for the respective subsurface point by using the azimuth angle and the reflection angle of the respective subsurface point, wherein each weighting function represents illumination energy at the respective subsurface point according to the azimuth angle and the reflection angle of the respective subsurface point; and
generate a subsurface image using the weighting functions of the plurality of subsurface points that are constructed using the azimuth angles and the reflection angles of the respective subsurface points.
12. The device of claim 11 , wherein the source analytic wavefields and the receiver analytic wavefields are generated using Green's function.
13. The device of claim 11 , wherein the source analytic wavefields and receiver analytic wavefields are decomposed based on a product of Green's function and a Hilbert transform of the set of seismic data.
14. The device of claim 11 , wherein the subsurface image is generated by stacking weighting functions for the plurality of subsurface points.