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US 2020/0271802 A1Published application
Determining a component of a wave field
AssigneeStatoil Petroleum AS
InventorsSheng XU, Hongbo ZHOU
Life of this patent
Estimating the term…
Abstract
There is described embodiments relating to a method of determining a wave field in an anisotropic subsurface of the Earth. The method includes numerically solving a decoupled quasi-acoustic single wave mode wave equation based on spatially varied anisotropic parameters, to determine the wave field in the anisotropic subsurface.
Claims5
A computer-implemented method, comprising the steps of:
- determining a wave field in an anisotropic subsurface of the Earth so as to improve computational efficiency, comprising:
- numerically solving with a processor a decoupled quasi-acoustic single wave mode wave equation based on spatially varied anisotropic parameters, to determine the wave field in the anisotropic subsurface;
- and
- performing migration of seismic data using said wave field to provide an image of the subsurface,
- wherein the wave equation comprises a spatial differential operator,
- wherein all terms of the wave equation that contain one or more of the anisotropic parameters are separated out from the spatial differential operator, and
- wherein the wave equation comprises a scalar operator, and the step of solving the wave equation comprises using the anisotropic parameters and a gradient of a predetermined wave field to compute the scalar operator,
- wherein the wave equation is
- ∂
- 2
-
- u
- ∂
- t
- 2
- =
- v
- 0
- 2
-
- ∂
- 2
-
- u
- ∂
- z
- 2
- +
- (
- 1
- +
- 2
-
- ɛ
- )
-
- ν
- 0
- 2
-
- ∂
- 2
-
- u
- ∂
- x
- 2
- +
- (
- v
- 0
- 2
-
- ∂
- 2
-
- u
- ∂
- z
- 2
- +
- (
- 1
- +
- 2
-
- ɛ
- )
-
- ν
- 0
- 2
-
- ∂
- 2
-
- u
- ∂
- x
- 2
- )
-
-
- Δ
-
-
- S
- e
- ,
-
- Δ
-
-
- S
- e
- =
- 1
- 2
-
-
- (
- 1
- -
- 8
-
- (
- ɛ
- -
- δ
- )
-
- n
- x
- 2
-
- n
- z
- 2
- (
- (
- 1
- +
- 2
-
- ɛ
- )
-
- n
- x
- 2
- +
- n
- z
- 2
- )
- 2
- -
- 1
- )
- ,
- wherein u is the wave field, t is time, Se is the scalar operator, v0 is a velocity in the subsurface along an axis of symmetry of anisotropy, nx and ny are horizontal phase directions, nz is a vertical phase direction, and wherein ε and δ are the anisotropic parameters.
138 more elements
The method as claimed in 1, which further comprises:
- estimating the predetermined wave field;
- determining the gradient of the predetermined wave field;
- combining the scalar operator with a square of a velocity and the gradient of the predetermined wave field to obtain a combined result;
- and
- using the combined result, determining the component of the wave field.
2 more elements
Dependencies are inferred from the claim text.