US2020311178A1PendingUtilityA1
Three-dimensional elastic frequency-domain iterative solver for full waveform inversion
Est. expiryAug 25, 2035(~9.1 yrs left)· nominal 20-yr term from priority
G01V 2210/67G06F 30/20G06F 17/11G06F 17/12G06F 17/142G06F 17/16G01V 99/005G01V 20/00
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Claims
Abstract
Certain implementations of a three-dimensional elastic frequency domain iterative solver for full waveform inversion can be implemented as a method in which frequency domain numerical simulation of elastic waves is per formed in three-dimensional (3D) media.
Claims
exact text as granted — not AI-modified1 - 22 . (canceled)
23 . A computer-implemented method comprising:
representing, by data processing apparatus, a three-dimensional (3D) elastic system in compliance form, the 3D elastic system representing 3D land media, the compliance form comprising
Lu
=
[
i
ω
M
(
x
,
y
,
z
)
-
P
∂
∂
x
-
Q
∂
∂
y
-
R
∂
∂
z
]
u
=
f
,
wherein u represents a velocity through the media, wherein M is an operator represented by
M
=
(
ρ
I
3
×
3
0
0
S
6
×
6
)
,
ρ is density, I 3×3 is an identical operator and S 6×6 is a matrix represented by
S
=
[
a
-
b
-
b
0
0
0
-
b
a
-
b
0
0
0
-
b
-
b
a
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
]
,
a is an operator represented by
a
=
λ
+
μ
u
(
2
μ
+
3
λ
)
,
b is an operator represented by
b
=
(
λ
2
μ
(
2
μ
+
3
λ
)
)
,
c is an operator represented by
c
=
(
1
μ
)
,
λ and μ are Lame parameters, S 6×6 is compliance tensor C −1 , P is represented by
P
=
[
0
A
A
T
0
]
,
Q is represented by
Q
=
[
0
B
B
T
0
]
,
R is represented by
R
=
[
0
D
D
T
0
]
,
wherein
A
=
[
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
]
,
wherein
B
=
[
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
]
,
wherein
D
=
[
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
]
;
determining, by the data processing apparatus, parameters corresponding to the media, dimensions of a computational domain to solve the compliance form and condition at a top boundary of the computational domain;
determining, by the data processing apparatus, one-dimensional (1D) background parameters of the media and a preconditioner solve the compliance form within the computational domain;
representing, by the data processing apparatus, an initial problem as a perturbation of the preconditioner;
iteratively performing, by the data processing apparatus, matrix-vector multiplication to solve the compliance form;
determining, by the data processing apparatus, a velocity distribution of the velocity through the media in response to iteratively performing the matrix-vector multiplication.
24 . The computer-implemented method of claim 23 , wherein the 3D land media comprises heterogeneous media.
25 . The computer-implemented method of claim 23 , wherein the 3D land media comprises isotropic media.
26 . The computer-implemented method of claim 23 , wherein the 3D land media comprises a rock formation.
27 . The computer-implemented method of claim 23 , wherein the 3D land media comprises a hydrocarbon reservoir.
28 . The computer-implemented method of claim 23 , wherein determining the preconditioner comprises constructing the preconditioner as an inverse to the operator shown in the following equation:
L
0
=
i
ω
M
0
(
z
)
-
P
∂
∂
x
-
Q
∂
∂
y
-
R
∂
∂
z
,
wherein the operator M 0 has the same structure as the operator M.
29 . The computer-implemented method of claim 28 , wherein a complex damping function is introduced into the operator M 0 .
30 . The computer-implemented method of claim 29 , wherein the complex damping function is represented by the following equations: a 0 (z)={circumflex over (β)}â 0 (z), b 0 (z)={circumflex over (β)}{circumflex over (b)} 0 (z), c 0 (z)={circumflex over (β)}ĉ 0 (z), {circumflex over (β)}=(1+iβ).
31 . The computer-implemented method of claim 23 , wherein representing the initial problem as the perturbation to the preconditioner comprises representing the initial operator L as a combination of L 0 and δL, wherein representing the initial operator L as a combination of L 0 and δL comprises representing the initial operator according to the following equation: δL=−iω[M 0 (z)−M(x,y,z)].
32 . The computer-implemented method of claim 23 , wherein the matrix-vector multiplication is performed by the application of a parallel Fast Fourier Transform (FFT), a banded matrix solver, and an inverse FFT.Join the waitlist — get patent alerts
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