Accelerating full wavefield inversion with nonstationary point-spread functions

Patent metadata

Field	Value
Publication number	US-10036818-B2
Application number	US-201414330767-A
Country	US
Kind code	B2
Filing date	Jul 14, 2014
Priority date	Sep 6, 2013
Publication date	Jul 31, 2018
Grant date	Jul 31, 2018

Abstract

Method for reducing computational time in inversion of geophysical data to infer a physical property model ( 91 ), especially advantageous in full wavefield inversion of seismic data. An approximate Hessian is pre-calculated by computing the product of the exact Hessian and a sampling vector composed of isolated point diffractors ( 82 ), and the approximate Hessian is stored in computer hard disk or memory ( 83 ). The approximate Hessian is then retrieved when needed ( 99 ) for computing its product with the gradient ( 93 ) of an objective function or other vector. Since the approximate Hessian is very sparse (diagonally dominant), its product with a vector may therefore be approximated very efficiently with good accuracy. Once the approximate Hessian is computed and stored, computing its product with a vector requires no simulator calls (wavefield propagations) at all. The pre-calculated approximate Hessian can also be reused in the subsequent steps whenever necessary.

First claim

The invention claimed is:

1. An iterative method for inverting measured geophysical data to infer a subsurface model of one or more physical properties, comprising:
(a) using a subsurface property model, computing an objective function measuring misfit between model-simulated data and the measured geophysical data, wherein the model-simulated data are generated using a computer;
(b) computing a gradient of the objective function with respect to parameters of the subsurface property model;
(c) preconditioning the gradient by multiplying at least one vector by an approximation of a Hessian matrix, said Hessian matrix resulting from an operator of second derivatives with respect to parameters of the subsurface property model operating on the objective function, wherein the approximation of the Hessian matrix is a plurality of columns, but less than all, sampled from the Hessian matrix, and the approximation of the Hessian matrix is stored in a computer readable storage medium;
(d) using the preconditioned gradient to update the subsurface property model;
(e) repeating (a)-(d) at least once using the updated subsurface property model, wherein the approximation of the Hessian matrix is recomputed in some iterations of the steps (a)-(d) or in all iterations of steps (a)-(d); and
(f) generating a subsurface image from a final updated subsurface property model from step (e) that was obtained with the approximation of the Hessian matrix, wherein the subsurface image identifies a location of structure in earth's subsurface that returned waves to receivers that recorded the geophysical data, and
wherein (a)-(f) are implemented with a computer.

2. The method of claim 1 , wherein the at least one vector is the gradient of the objective function, and the preconditioned gradient is given by H −1 g, where H is the approximation of the Hessian matrix and g is the gradient of the objective function.

3. The method of claim 1 , wherein the one or more physical properties are two physical properties, being a first parameter and a second parameter, and the gradient g of the objective function can be expressed as

g
=

(

g
1

g
2

)

,

where g 1 and g 2 are the gradients with respect to the first and the second parameter, respectively, and the at least one vector are basis vectors s 1 and s 2 , defined as follows:

s
1

=

(

-

g
1

0

)

,

s
2

=

(

0

-

g
2

)

,

where 0 denotes a vector consisting of zeros; and the preconditioned gradient (g new ) is given by
g new =−αs 1 −βs 2 ,

where α and β are obtained by solving the following 2×2 matrix equation:

(

s
1
T

⁢

Hs
1

s
1
T

⁢

Hs
2

s
2
T

⁢

Hs
1

s
2
T

⁢

Hs
2

)

⁢

(

α

β

)

=

-

(

g
T

⁢

s
1

g
T

Assignees

• Tang Yaxun
• Lee Sunwoong
• Exxonmobil Upstream Res Co

Inventors

• Tang Yaxun
• Lee Sunwoong

Classifications

• G01V2210/66

  Subsurface modeling · CPC title

• G01V1/28 Primary

  Processing seismic data, e.g. for interpretation or for event detection (G01V1/48 takes precedence) · CPC title

• G06F2111/10

  Numerical modelling · CPC title

• G06F2217/16

  Physics · mapped topic

• G06F17/5009

  Physics · mapped topic