Method and apparatus for seismic imaging processing with enhanced geologic structure preservation
A method for seismic processing includes steps of seismic signal forward propagation and seismic data back propagation. The subsurface medium image is created after correlating and summarizing forward and backward propagation results. To address migration footprint and noise due to the incomplete data acquisition aperture and migration approximation in the migration operator, the iteration inversion strategy incorporates tensor flow calculated from seismic image. A regularization operator based on structure tensor of image is applied to seismic image inversion.
1. A method for seismic processing, comprising:
positioning a plurality of seismic receivers at different locations in a survey region;
generating seismic vibrations in a subterranean area of the survey region using seismic sources positioned in the subterranean area;
receiving seismic data acquired from the plurality of seismic receivers based on the seismic vibrations in the subterranean area generated by the seismic sources;
creating an image model by migration in time or in depth using a two-way acoustic wave equation from the seismic data; and
updating the image model,
wherein the step of updating the image model further comprises the substeps of:
calculating forward wave propagation using the two-way acoustic wave equation to create synthetic data using a current image model;
comparing the synthetic data and the received seismic data;
when a difference between the synthetic data and the received seismic data exceeds a pre-determined value, calculating a total variation regularization operator and a structure tensor regularization operator using the current image model;
computing wavefield back-propagation and constructing a new gradient with the calculated structure tensor operator and the total variation regularization operator; and
obtaining an update of the current image model,
wherein the total variation regularization operator is
∇
T
V
(
m
)
=
-
∇
·
(
∇
m
❘
"\[LeftBracketingBar]"
∇
m
❘
"\[RightBracketingBar]"
)
,
m is the current image model,
wherein the structure tensor regularization operation is ∇STS(m)=div(H∇m), H is a structure tensor based diffusion function and div is divergence operator,
wherein the substep of computing wavefield back-propagation and constructing a new gradient with the calculated structure tensor operator and the total variation regularization operator is performed by calculating a derivative of
∂
J
∂
m
,
J=∥Gm−d∥ 2 +½ ∥TV ( m )∥ p+ ½∥ STS ( m )∥ p , and
wherein ∥·∥ represents L2 norm, d is the received seismic data, and p is a norm that ranges from 1 to 2.
2. The method of claim 1 , wherein the substep of obtaining an update of the current image model is obtained by solving the equation
J=∥Gm−d∥ 2 +½ ∥TV ( m )∥ p+ ½∥ STS ( m )∥ p.
3. The method of claim 1 , wherein the positioning of the plurality of seismic receivers at different locations in the survey region including positioning one or more sensors in the wellbore.
4. A computing apparatus, comprising:
one or more processors; and
a memory system comprising one or more non-transitory, computer-readable media storing instructions that, when executed by at least one of the one or more processors, cause the computing system to perform operations, the operations comprising:
receiving seismic data acquired from a plurality of seismic receivers in response to seismic vibrations generated by a plurality of seismic sources positioned in a subterranean area;
creating an image model by migration in time or in depth using a two-way acoustic wave equation from the seismic data; and
updating the image model,
wherein the step of updating the image model further comprises the substeps of:
calculating forward wave propagation using the two-way acoustic wave equation to create synthetic data using a current image model;
comparing the synthetic data and the received seismic data;
when a difference between the synthetic data and the received seismic data exceeds a pre-determined value, calculating a total variation regularization operator and a structure tensor regularization operator using the current image model;
computing wavefield back-propagation and constructing a new gradient with the calculated structure tensor operator and the total variation regularization operator; and
obtaining an update of the current image model,
wherein the total variation regularization operator is
∇
TV
(
m
)
=
-
∇
·
(
∇
m
❘
"\[LeftBracketingBar]"
∇
m
❘
"\[RightBracketingBar]"
)
,
m is the current image model,
wherein the structure tensor regularization operation is ∇STS(m)=div(H∇m), H is a structure tensor based diffusion function and div is divergence operator,
wherein the substep of computing wavefield back-propagation and constructing a new gradient with the calculated structure tensor operator and the total variation regularization operator is performed by calculating a derivative of
∂
J
∂
m
,
J=∥Gm−d∥ 2 +½ ∥TV ( m )∥ p+ ½∥ STS ( m )∥ p , and
wherein ∥·∥ represents L2 norm, d is the received seismic data, and p is a norm that ranges from 1 to 2.
5. The computing apparatus of claim 4 , wherein the sub step of obtaining an update of the current image model is carried out by solving the equation
J=∥Gm−d∥ 2 +½ ∥TV ( m )∥ p+ ½∥ STS ( m )∥ p.
6. A non-transitory, computer-readable medium storing instructions that, when executed by at least one processor of a computing apparatus, cause the computing system to perform operations, the operations comprising:
receiving seismic data acquired from a plurality of seismic receivers in response to seismic vibrations generated by a plurality of seismic sources positioned in a subterranean area;
creating an image model by migration in time or in depth using a two-way acoustic wave equation from the seismic data; and
updating the image model,
wherein the step of updating the image model further comprises the substeps of:
calculating forward wave propagation using the two-way acoustic wave equation to create synthetic data using a current image model;
comparing the synthetic data and the received seismic data;
when a difference between the synthetic data and the received seismic data exceeds a pre-determined value, calculating a total variation regularization operator and a structure tensor regularization operator using the current image model;
computing wavefield back-propagation and constructing a new gradient with the calculated structure tensor operator and the total variation regularization operator; and
obtaining an update of the current image model,
wherein the total variation regularization operator is
∇
TV
(
m
)
=
-
∇
·
(
∇
m
❘
"\[LeftBracketingBar]"
∇
m
❘
"\[RightBracketingBar]"
)
,
m is me current image model,
wherein the structure tensor regularization operation is ∇STS(m)=div(H∇m), H is a structure tensor based diffusion function and div is divergence operator,
wherein the substep of computing wavefield back-propagation and constructing a new gradient with the calculated structure tensor operator and the total variation regularization operator is performed by calculating a derivative of
∂
J
∂
m
,
J=∥Gm−d∥ 2 +½ ∥TV ( m )∥ p+ ½∥ STS ( m )∥ p , and
wherein ∥·∥ represents L2 norm, d is the received seismic data, and p is a norm that ranges from 1 to 2.
7. The medium of claim 6 , wherein the substep of obtaining an update of the current image model is carried out by solving the equation
J=∥Gm−d∥ 2 +½ ∥TV ( m )∥ p+ ½∥ STS ( m )∥ p.