# US 10,310,112 B2 · Processing geophysical data using 3D norm-zero optimization for smoothing geophysical inversion data

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 10,310,112 B2
- Document ID: US10310112B2
- Status: Granted
- Kind: B2
- Application number: 14/667,424
- Filed: 2015-03-24
- Published: 2016-09-29
- Granted: 2019-06-04
- Earliest claimed: 2015-03-24
- Assignees: Saudi Arabian Oil Company
- Applicants: Saudi Arabian Oil Company
- Inventors: Saleh Al-Dossary; Jinsong Wang
- Web page: https://patentgrep.com/patent/US10310112B2

## CPC

- G01V 1/282: {Application of seismic models, synthetic seismograms}
- G01V 1/302: {in 3D data cubes}
- G01V 1/306: {for determining physical properties of the subsurface, e.g. impedance, porosity or attenuation profiles}
- G01V 1/364: {Seismic filtering (G01V1/37 takes precedence)}
- G01V 2210/48: Other transforms
- G01V 2210/66: Subsurface modeling
- G01V: GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS (means for indicating the location of accidentally buried, e.g. snow-buried, persons A63B29/02)

## Abstract

The present disclosure describes methods and systems, including computer-implemented methods, computer program products, and computer systems, for processing geophysical data. One computer-implemented method includes obtaining a set of raw geophysical data, wherein the raw geophysical data include 3-Dimensional (3D) coordinates; grouping, by a data processing apparatus, the set of the raw geophysical data into a plurality of subsets; and processing, by the data processing apparatus, each subset of the raw geophysical data using a 3D norm zero objective energy function to generate a subset of smoothed geophysical data, wherein the smoothed geophysical data is used to build a subsurface model.

## Claims

### Claim 1

A method for estimating subsurface structure of a reservoir based on raw geophysical data of the reservoir, comprising:
obtaining a set of raw geophysical data of the reservoir, wherein the raw geophysical data include 3-dimensional (3D) coordinates;
grouping, by a data processing apparatus, the set of the raw geophysical data into a plurality of subsets, wherein the grouping the set of the raw geophysical data comprises:
determining geometry information for the set of the raw geophysical data;
determining a memory size of a hardware memory that is used for processing one subset of the plurality of subsets of the raw geophysical data, wherein the hardware memory is coupled with the data processing apparatus; and
grouping the set of the raw geophysical data based on the geometry information and the memory size of the hardware memory;
processing, by the data processing apparatus, each subset of the raw geophysical data using a 3D norm zero objective energy function to generate a subset of smoothed geophysical data, wherein the smoothed geophysical data is used to build a subsurface model of the reservoir, wherein the 3D norm zero objective energy function is
obj
=
∑
x
=
1
k
⁢
(
(
d
⁡
(
x
)
-
m
⁡
(
x
)
)
2
+
λ
·
∑
i
=
1
3
⁢
C
⁡
(
∂
m
⁡
(
x
)
∂
x
i
≠
0
)
)
,
where d(x) represents the subset of the raw geophysical data, k represents a number of the raw geophysical data in the subset, i represents a dimension of the raw geophysical data, m(x) represents the subset of the smoothed geophysical data, C( . . . ) represents a counting function, and λ represents a constant weight, and wherein processing each subset of the raw geophysical data comprises iteratively performing the following steps until an iterative condition is met:
computing an auxiliary value by solving a first sub energy function, wherein the first sub energy function is derived from the 3D norm zero objective energy function with a fixed value of an input data;
computing a next input data by solving a second sub energy function, wherein the second sub energy function is derived from the 3D norm zero objective energy function with a fixed auxiliary value; and
increasing a beta value that is included in the first and the second sub energy functions;
generating, by using the smoothed geophysical data, a migration image of the subsurface structure of the reservoir; and
estimating the subsurface structure of the reservoir based on the migration image.

### Claim 2 (depends on 1)

The method of claim 1, wherein the raw geophysical data is at least one of impedance data, velocity data, or porosity data.

### Claim 3 (depends on 1)

The method of claim 1, wherein the geometry information includes a cross line direction of the raw geophysical data.

### Claim 4 (depends on 1)

The method of claim 1, wherein the iteration condition includes at least one of reaching a predetermined number of iterations or a beta value being over a predetermined threshold.

### Claim 5

A system for estimating subsurface structure of a reservoir based on raw geophysical data of the reservoir, comprising:
a memory; and
at least one hardware processor interoperably coupled with the memory and configured to:
obtain a set of raw geophysical data of the reservoir, wherein the raw geophysical data include 3-Dimensional (3D) coordinates;
group, by a data processing apparatus, the set of the raw geophysical data into a plurality of subsets, wherein the at least one hardware processor configured to group the set of the raw geophysical data comprises the at least one hardware processor configured to:
determine geometry information for the set of the raw geophysical data;
determine a memory size of at least a portion of the memory that is used for processing a subset of the raw geophysical data by the data processing apparatus; and
group the set of the raw geophysical data based on the geometry information and the memory size of at least the portion of the memory;
process, by the data processing apparatus, each subset of the raw geophysical data using a 3D norm zero objective energy function to generate a subset of smoothed geophysical data, wherein the smoothed geophysical data is used to build a subsurface model of the reservoir, wherein the 3D norm zero objective energy function is
obj
=
∑
x
=
1
k
⁢
(
(
d
⁡
(
x
)
-
m
⁡
(
x
)
)
2
+
λ
·
∑
i
=
1
3
⁢
C
⁡
(
∂
m
⁡
(
x
)
∂
x
i
≠
0
)
)
,
where d(x) represents the subset of the raw geophysical data, k represents a number of the raw geophysical data in the subset, i represents a dimension of the raw geophysical data, m(x) represents the subset of the smoothed geophysical data, C( . . . ) represents a counting function, and λ represents a constant weight, and wherein the at least one hardware processor configured to process each subset of the raw geophysical data using the 3D norm zero objective energy function comprises the at least one hardware processor configured to iteratively performing the following steps until an iterative condition is met:
computing an auxiliary value by solving a first sub energy function, wherein the first sub energy function is derived from the 3D norm zero objective energy function with a fixed value of an input data;
computing a next input data by solving a second sub energy function, wherein the second sub energy function is derived from the 3D norm zero objective energy function with a fixed auxiliary value; and
increasing a beta value that is included in the first and the second sub energy functions;
generate, by using the smoothed geophysical data, a migration image of the subsurface structure of the reservoir; and
estimate the subsurface structure of the reservoir based on the migration image.

### Claim 6 (depends on 5)

The system of claim 5, wherein the raw geophysical data is at least one of impedance data, velocity data, or porosity data.

### Claim 7 (depends on 5)

The system of claim 5, wherein the geometry information includes a cross line direction of the raw geophysical data.

### Claim 8 (depends on 5)

The system of claim 5, wherein the iteration condition includes at least one of reaching a predetermined number of iterations or a beta value being over a predetermined threshold.

### Claim 9

A non-transitory, computer-readable medium storing computer-readable instructions for estimating subsurface structure of a reservoir based on raw geophysical data of the reservoir, the instructions executable by a computer and configured to:
obtain a set of raw geophysical data of the reservoir, wherein the raw geophysical data include 3-Dimensional (3D) coordinates;
group, by a data processing apparatus, the set of the raw geophysical data into a plurality of subsets, wherein the grouping the set of the raw geophysical data comprises:
determining geometry information for the set of the raw geophysical data;
determining a memory size of a hardware memory that is used for processing one subset of the plurality of subsets of the raw geophysical data, wherein the hardware memory is coupled with the data processing apparatus; and
grouping the set of the raw geophysical data based on the geometry information and the memory size of the hardware memory;
process, by the data processing apparatus, each subset of the raw geophysical data using a 3D norm zero objective energy function to generate a subset of smoothed geophysical data, wherein the smoothed geophysical data is used to build a subsurface model of the reservoir, wherein the 3D norm zero objective energy function is
obj
=
∑
x
=
1
k
⁢
(
(
d
⁡
(
x
)
-
m
⁡
(
x
)
)
2
+
λ
·
∑
i
=
1
3
⁢
C
⁡
(
∂
m
⁡
(
x
)
∂
x
i
≠
0
)
)
,
where d(x) represents the subset of the raw geophysical data, k represents a number of the raw geophysical data in the subset, i represents a dimension of the raw geophysical data, m(x) represents the subset of the smoothed geophysical data, C( . . . ) represents a counting function, and λ represents a constant weight, and wherein processing each subset of the raw geophysical data comprises iteratively performing the following steps until an iterative condition is met:
computing an auxiliary value by solving a first sub energy function, wherein the first sub energy function is derived from the 3D norm zero objective energy function with a fixed value of an input data;
computing a next input data by solving a second sub energy function, wherein the second sub energy function is derived from the 3D norm zero objective energy function with a fixed auxiliary value; and
increasing a beta value that is included in the first and the second sub energy functions;
generate, by using the smoothed geophysical data, a migration image of the subsurface structure of the reservoir; and
estimate the subsurface structure of the reservoir based on the migration image.

### Claim 10 (depends on 9)

The medium of claim 9, wherein the raw geophysical data is at least one of impedance data, velocity data, or porosity data.

### Claim 11 (depends on 9)

The medium of claim 9, wherein the geometry information includes a cross line direction of the raw geophysical data.