# US 10,310,138 B2 · Accelerated Occam inversion using model remapping and Jacobian matrix decomposition

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- Number: US 10,310,138 B2
- Document ID: US10310138B2
- Status: Granted
- Kind: B2
- Application number: 15/239,174
- Filed: 2016-08-17
- Published: 2017-03-16
- Granted: 2019-06-04
- Earliest claimed: 2015-09-15
- Assignees: ExxonMobil Upstream Research Company
- Applicants: Brent D. Wheelock
- Inventors: Brent D. Wheelock
- Web page: https://patentgrep.com/patent/US10310138B2

## CPC

- G01V 20/00: Geomodelling in general
- G01V 3/38: Processing data, e.g. for analysis, for interpretation, for correction
- G01V 11/00: Prospecting or detecting by methods combining techniques covered by two or more of main groups G01V1/00 - G01V9/00
- G06F 17/16: Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)}
- G01V 2210/61: Analysis by combining or comparing a seismic data set with other data
- G01V: GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS (means for indicating the location of accidentally buried, e.g. snow-buried, persons A63B29/02)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

A method including: generating an updated subsurface property model of a subsurface region, with a computer, from an initial estimate of the subsurface property model by performing an iterative inversion, which includes inverting geophysical data to infer the updated subsurface property model, wherein the generating the updated subsurface property model includes linearly remapping the initial estimate of the subsurface property model based on an inverse of a regularization operator, included with the initial estimate of the subsurface property model, into one in which the regularization operator is represented by an identity matrix, performing a unitary matrix decomposition in order to group the identity matrix with sparse matrices output from the unitary matrix decomposition, and performing a search over at least one trade-off parameter to reduce a misfit between simulated data generated from a most recent estimate of the subsurface property model and the geophysical data until a predetermined stopping criteria is satisfied; and generating, with a computer, an image of the subsurface region using the updated subsurface property model.

## Claims

### Claim 1

A method comprising:
generating an updated subsurface property model of a subsurface region, with a computer, from an initial estimate of the subsurface property model by performing an iterative inversion, which includes inverting geophysical data to infer the updated subsurface property model,
wherein the generating the updated subsurface property model includes linearly remapping the initial estimate of the subsurface property model based on an inverse of a regularization operator, included with the initial estimate of the subsurface property model, into one in which the regularization operator is represented by an identity matrix,
performing a unitary matrix decomposition in order to group the identity matrix with sparse matrices output from the unitary matrix decomposition, and
performing a search over at least one trade-off parameter to reduce a misfit between simulated data generated from a most recent estimate of the subsurface property model and the geophysical data until a predetermined stopping criteria is satisfied;
generating, with a computer, an image of the subsurface region using the updated subsurface property model; and
using at least one of the updated subsurface property model or the image of the subsurface region to manage hydrocarbon exploration.

### Claim 2 (depends on 1)

The method of claim 1, wherein the unitary matrix decomposition represents fully, or approximately, a matrix product of a Jacobian matrix.

### Claim 3 (depends on 1)

The method of claim 1, wherein the unitary matrix decomposition is Single Value Decomposition (SVD).

### Claim 4 (depends on 1)

The method of claim 1, wherein the unitary matrix decomposition is randomized SVD.

### Claim 5 (depends on 1)

The method of claim 1, wherein the unitary matrix decomposition is bidiagonalization.

### Claim 6 (depends on 3)

The method of claim 3, wherein the generating includes computing the SVD once for each iteration of the iterative inversion, and performing the search using the computed SVD and one or more trade-off parameters to reduce the misfit.

### Claim 7 (depends on 4)

The method of claim 4, wherein the generating includes computing the randomized SVD once for each iteration of the iterative inversion, and performing the search using the computed SVD and one or more trade-off parameters to reduce the misfit.

### Claim 8 (depends on 3)

The method of claim 3, wherein the generating includes computing the SVD once for each iteration of the iterative inversion, and performing a search using the computed SVD and one or more trade-off parameters to determine a smoothest solution which fits the geophysical data and satisfies a predetermined target misfit relative to the geophysical data.

### Claim 9 (depends on 4)

The method of claim 4, wherein the generating includes computing the randomized SVD once for each iteration of the iterative inversion, and performing a search using the computed SVD and one or more trade-off parameters to determine a smoothest solution which fits the geophysical data and satisfies a predetermined target misfit relative to the geophysical data.

### Claim 10 (depends on 1)

The method of claim 1, wherein managing hydrocarbon exploration comprises drilling a well at a location determined from at least one of the updated subsurface property model or the image of the subsurface region.

### Claim 11 (depends on 1)

The method of claim 1, wherein managing hydrocarbon exploration comprises exploring for hydrocarbons using at least one of the updated subsurface property model or the image of the subsurface region.

### Claim 12 (depends on 1)

The method of claim 1, wherein managing hydrocarbon exploration comprises performing a survey that acquires geophysical data.

### Claim 13 (depends on 1)

The method of claim 1, wherein the iterative inversion is a joint inversion of two or more of electromagnetic data, magnetotelluric data, gravity data, or seismic data.

### Claim 14 (depends on 1)

The method of claim 1, wherein the geophysical data is either controlled source electromagnetic data, seismic data, gravity data, or magnetotelluric data.

### Claim 15 (depends on 1)

The method of claim 1, wherein the iterative inversion is a joint inversion.

### Claim 16 (depends on 15)

The method of claim 15, wherein the joint inversion includes two or more geophysical data sets.

### Claim 17 (depends on 15)

The method of claim 15, wherein the joint inversion includes at least two trade off parameters used to adjust a relative weighting in generating the updated subsurface property model.

### Claim 18 (depends on 1)

The method of claim 1, wherein the sparse matrices are diagonal eigenvalue matrices when the unitary matrix decomposition is SVD or randomized SVD.

### Claim 19 (depends on 1)

The method of claim 1, wherein the sparse matrices are bidiagonal matrices when the unitary matrix decomposition is bidiagonalization.