System and method for real-time passive seismic event localization
Abstract
A computer-implemented method for seismic event localization includes: generating, with at least one processor, a vectorized snapshot matrix representing wave propagation data at a series of snapshots in time for a subterranean formation; computing a reduced orthonormal column basis matrix based on the vectorized snapshot matrix; constructing a reduced order wave propagation model based on the reduced orthonormal column basis matrix; receiving seismic data collected from a plurality of receivers at the subterranean formation; generating a time-domain coefficient matrix based on back propagation of the received seismic data and the reduced order wave propagation model; reconstructing time-reversed wavefield data based on the time-domain coefficient vector; and generating signals for outputting wavefield or seismic event location information based on the time-reversed wavefield data.
Claims
exact text as granted — not AI-modifiedWhat is claimed is:
1 . A computer-implemented method for seismic event localization, the method comprising:
generating, with at least one processor, a vectorized snapshot matrix representing wave propagation data at a series of snapshots in time for a subterranean formation; computing a reduced orthonormal column basis matrix based on the vectorized snapshot matrix; constructing a reduced order wave propagation model based on the reduced orthonormal column basis matrix; receiving seismic data collected from a plurality of receivers at the subterranean formation; generating a time-domain coefficient matrix based on back propagation of the received seismic data and the reduced order wave propagation model; reconstructing time-reversed wavefield data based on the time-domain coefficient vector; and generating signals for outputting wavefield or seismic event location information based on the time-reversed wavefield data.
2 . The method of claim 1 , wherein computing the reduced orthonormal column basis matrix comprises: singular value decomposition or QR decomposition.
3 . The method of claim 1 , wherein computing the reduced orthonormal column basis matrix is based on multi-dimensional stress-velocity two-way elastic wave equations:
∂
v
x
(
t
)
∂
t
=
1
ρ
∂
τ
xx
(
t
)
∂
x
+
1
ρ
∂
τ
xz
(
t
)
∂
z
+
f
v
x
(
t
)
∂
v
z
(
t
)
∂
t
=
1
ρ
∂
τ
xz
(
t
)
∂
x
+
1
ρ
∂
τ
zz
(
t
)
∂
z
+
f
v
z
(
t
)
∂
τ
xx
(
t
)
∂
t
=
(
λ
+
2
μ
)
∂
v
z
(
t
)
∂
x
+
λ
∂
v
z
(
t
)
∂
z
+
f
p
(
t
)
∂
τ
zz
(
t
)
∂
t
=
(
λ
+
2
μ
)
∂
v
z
(
t
)
∂
z
+
λ
∂
v
x
(
t
)
∂
x
+
f
p
(
t
)
∂
τ
x
z
(
t
)
∂
t
=
μ
(
∂
v
x
(
t
)
∂
z
+
∂
v
z
(
t
)
∂
x
)
,
where τ xx and τ zz are the x and z components of the normal stress fields; τ xz is shear stress field; v x and v z are horizontal and vertical components of particle velocity fields; f v x and f v z are single forces and f p is an external pressure source
4 . The method of claim 1 , wherein generating the vectorized snapshot matrix comprises: simulating wave propagations on a set of spatially discretized partial differential equations; and extracting simulated wave propagation data at each snapshot in the series of snapshots in time.
5 . The method of claim 4 , wherein simulating the wave propagations uses source positions corresponding to locations of physical receivers at the subterranean formation.
6 . The method of claim 4 , wherein the set of spatially discretized partial differential equations include 2-dimensional stress-velocity two-way elastic wave equations.
7 . The method of claim 1 , wherein the wave propagation data is generated with a velocity model associated with the subterranean formation.
8 . The method of claim 1 , wherein the seismic data collected from the plurality of receivers includes pressure data or particle velocity data.
9 . The method of claim 1 , wherein reconstructing the time-reversed wavefield data is based on reconstructing a target area of the subterranean formation.
10 . The method of claim 1 , wherein the vectorized snapshot matrix comprises wave propagation data and absorbing layer values.
11 . A computing system for seismic event localization, the system comprising:
at least one memory and at least one processor configured for: generating a vectorized snapshot matrix representing wave propagation data at a series of snapshots in time for a subterranean formation; computing a reduced orthonormal column basis matrix based on the vectorized snapshot matrix; constructing a reduced order wave propagation model based on the reduced orthonormal column basis matrix; receiving seismic data collected from a plurality of receivers at the subterranean formation; generating a time-domain coefficient matrix based on back propagation of the received seismic data and the reduced order wave propagation model; reconstructing time-reversed wavefield data based on the time-domain coefficient vector; and generating signals for outputting wavefield or seismic event location information based on the time-reversed wavefield data.
12 . The system of claim 11 , wherein computing the reduced orthonormal column basis matrix comprises: singular value decomposition or QR decomposition.
13 . The system of claim 11 , wherein computing the reduced orthonormal column basis matrix is based on multi-dimensional stress-velocity two-way elastic wave equations:
∂
v
x
(
t
)
∂
t
=
1
ρ
∂
τ
xx
(
t
)
∂
x
+
1
ρ
∂
τ
xz
(
t
)
∂
z
+
f
v
x
(
t
)
∂
v
z
(
t
)
∂
t
=
1
ρ
∂
τ
xz
(
t
)
∂
x
+
1
ρ
∂
τ
zz
(
t
)
∂
z
+
f
v
z
(
t
)
∂
τ
xx
(
t
)
∂
t
=
(
λ
+
2
μ
)
∂
v
z
(
t
)
∂
x
+
λ
∂
v
z
(
t
)
∂
z
+
f
p
(
t
)
∂
τ
zz
(
t
)
∂
t
=
(
λ
+
2
μ
)
∂
v
z
(
t
)
∂
z
+
λ
∂
v
x
(
t
)
∂
x
+
f
p
(
t
)
∂
τ
x
z
(
t
)
∂
t
=
μ
(
∂
v
x
(
t
)
∂
z
+
∂
v
z
(
t
)
∂
x
)
,
where τ xx and τ zz are the x and z components of the normal stress fields; τ xz is shear stress field; v x and v z are horizontal and vertical components of particle velocity fields; f v x and f v z are single forces and f p is an external pressure source
14 . The system of claim 11 , wherein generating the vectorized snapshot matrix comprises: simulating wave propagations on a set of spatially discretized partial differential equations; and extracting simulated wave propagation data at each snapshot in the series of snapshots in time.
15 . The system of claim 14 , wherein simulating the wave propagations uses source positions corresponding to locations of physical receivers at the subterranean formation.
16 . The system of claim 14 , wherein the set of spatially discretized partial differential equations include 2-dimensional stress-velocity two-way elastic wave equations.
17 . The system of claim 11 , wherein the wave propagation data is generated with a velocity model associated with the subterranean formation.
18 . The system of claim 11 , wherein the seismic data collected from the plurality of receivers includes pressure data or particle velocity data.
19 . The system of claim 11 , wherein reconstructing the time-reversed wavefield data is based on reconstructing a target area of the subterranean formation.
20 . The system of claim 11 , wherein the vectorized snapshot matrix comprises wave propagation data and absorbing layer values.Join the waitlist — get patent alerts
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