# US 10,310,123 B2 · Seismic reflection full waveform inversion for reflected seismic data

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- Number: US 10,310,123 B2
- Document ID: US10310123B2
- Status: Granted
- Kind: B2
- Application number: 13/787,884
- Filed: 2013-03-07
- Published: 2013-09-12
- Granted: 2019-06-04
- Earliest claimed: 2012-03-09
- Assignees: Cgg Services SAS
- Applicants: Cggveritas Services SA
- Inventors: Sheng Xu; Feng Chen; Gilles Lambare; Yu Zhang
- Web page: https://patentgrep.com/patent/US10310123B2

## CPC

- G01V 1/3808: {Seismic data acquisition, e.g. survey design}
- G01V 1/303: {for determining velocity profiles or travel times}
- G01V 1/38: specially adapted for water-covered areas (G01V1/28 takes precedence)
- 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

A system and method are described herein for generating a velocity model of returned seismic signals for under-ocean floor environments. The system and method generate a series of source signals, receive a corresponding set of direct signals, reflected signals, and refracted signals, solve a velocity model equation using a full waveform inversion function with respect to the received set of direct signals, reflected signals and refracted signals to minimize a least square misfit function by relaxing a dependency on low frequency reflections in the full waveform inversion function. The system and method then generate the velocity model based on the solution to the velocity model equation, and display the velocity model.

## Claims

### Claim 1

A method for exploring under-ocean floor environments, the method comprising:
generating a series of source signals by a seismic source configured to inject the source signals into an under-ocean floor explored structure;
recording direct signals, reflected signals, and refracted signals corresponding to the source signals;
solving a velocity model equation using a full waveform inversion function with respect to the direct signals, reflected signals and refracted signals to minimize a least square misfit function by relaxing a dependency on low frequency reflections in the full waveform inversion function;
generating the velocity model based on the solution to the velocity model equation; and
determining location of a hydrocarbon reservoir in the under-ocean floor explored structure based on strong velocity or anisotropic parameter variations in the velocity model,
wherein the relaxing the dependency on the low frequency reflections includes
splitting an initial velocity model m into a long wavelength component mo and a short wavelength component δm, and
updating the long wavelength component mo while the short wavelength component δm is fixed.

### Claim 2 (depends on 1)

The method according to claim 1, wherein the step of relaxing the dependency on low frequency reflections comprises:
updating the long wavelength component using a local optimization scheme.

### Claim 3 (depends on 1)

The method according to claim 1, wherein the step of relaxing the dependency on low frequency reflections comprises:
implementing a non-linear iterative relaxation process, that includes
obtaining the long wavelength component of the reflected signals,
updating the short wavelength component using the long wavelength component,
fixing the short wavelength component, and
updating the long wavelength component using the fixed short wavelength component
wherein the updated short wavelength component and the updated long wavelength component are then used to generate the updated velocity model.

### Claim 4 (depends on 3)

The method according to claim 3, wherein the step of updating the short wavelength component using the long wavelength component comprises:
evaluating the following expression
∂
δ
⁢
⁢
G
∂
δ
⁢
⁢
m
0
⁢
|
δ
⁢
⁢
m
⁢
(
m
0
)
⁢
(
r
,
ω
,
s
;
x
)
=
ω
2
⁢
⁢
G
0
⁡
(
r
,
ω
;
x
)
⁢
G
0
⁡
(
y
,
ω
;
s
)
where G indicates Green function that is split into a Green function Go depending on mo and a perturbation thereof δG depending on mo and δm, r is receiver position, s is shot position, ω is angular frequency and x is a model-related position.

### Claim 5 (depends on 4)

The method according to claim 4, wherein the step of updating the short wavelength component using the long wavelength component comprises:
using an migration process.

### Claim 6 (depends on 3)

The method according to claim 3, wherein the step of updating the long wavelength component using the fixed short wavelength component comprises:
using a local optimization scheme.

### Claim 7 (depends on 6)

The method according to claim 6, wherein the step of using the local optimization scheme comprises:
evaluating the following expressions—
R
⁡
(
r
,
ω
;
s
)
=
G
obs
⁡
(
r
,
ω
;
s
)
-
G
cal
⁡
(
r
,
ω
;
s
)
,
⁢
and
∂
C
∂
m
0
⁢
|
δ
⁢
⁢
m
⁢
(
x
)
=
-
∫
∫
d
⁢
⁢
s
⁢
⁢
d
⁢
⁢
r
⁢
∫
d
⁢
⁢
ω
⁢
∂
δ
⁢
⁢
G
∂
m
0
⁡
(
x
)
⁢
|
δ
⁢
⁢
m
*
⁢
(
r
,
ω
,
s
;
x
)
⁢
R
⁡
(
r
,
ω
;
s
)
where Gobs is an observed Green function, Gcal is a calculated Green function, * denotes complex conjugated form of a function and C is a cost function.

### Claim 8

A method for exploring under-ocean floor environments, the method comprising:
generating a series of source signals by a seismic source configured to inject the source signals into an under-ocean floor explored structure;
recording direct signals, reflected signals, and refracted signals corresponding to the source signals;
solving a velocity model equation using a full waveform inversion function with respect to the set of direct signals, reflected signals and refracted signals to minimize a least square misfit function by splitting the full waveform inversion velocity model m into long wavelength components mo of the reflected signals, and short wavelength components δm of the reflected signals;
updating the short wavelength components of the reflected signals, and the long wavelength components of the reflected signals using an iterative relaxation process;
generating an iterative velocity model based on the solution to the velocity model equation that includes the iterated long wavelength components of the reflected signals and the iterated short wavelength components of the reflected signals; and
determining location of a hydrocarbon reservoir in the under-ocean floor explored structure based on strong velocity or anisotropic parameter variations in the velocity model,
wherein the iterative relaxation process includes updating the iterated long wavelength component mo while the short wavelength component δm is fixed.

### Claim 9 (depends on 8)

The method according to claim 8, wherein the updating of the long wavelength components of the reflected signals comprises evaluating the following expression
∂
δ
⁢
⁢
G
∂
m
0
⁢
|
δ
⁢
⁢
m
⁢
(
m
0
,
δ
⁢
⁢
m
)
⁢
(
r
,
ω
,
s
;
x
)
=
ω
2
⁢
∫
d
⁢
⁢
y
⁡
(
∂
G
0
∂
m
0
⁢
(
r
,
ω
;
y
)
⁢
G
⁡
(
y
,
ω
;
s
)
+
G
0
⁡
(
r
,
ω
;
y
)
⁢
∂
G
∂
m
0
⁢
(
y
,
ω
;
s
)
)
⁢
δ
⁢
⁢
m
⁡
(
y
)
where G indicates Green function, r is receiver position, s is shot position, ω is angular frequency and x is a model-related position.

### Claim 10 (depends on 8)

The method according to claim 8, wherein the step of updating the short wavelength component and the long wavelength component in an iterative relaxation process comprises:
obtaining the initial long wavelength component;
obtaining the initial short wavelength component using the initial long wavelength component;
fixing the short wavelength component;
updating the long wavelength component using a local optimization scheme and then fixing the long wavelength component; and
generating the updated velocity model using the updated long wavelength component and short wavelength component in the full waveform inversion function.

### Claim 11 (depends on 10)

The method according to claim 10, wherein the step of obtaining the initial short wavelength component comprises:
using a true amplitude migration process.

### Claim 12 (depends on 8)

The method according to claim 8, wherein the step of using the iterated long wavelength component of the reflected signals and the iterated short wavelength component of the reflected signals to generate an iterative velocity model with improved velocity resolution comprises:
determining a set of residual data by evaluating the following expression—
R(r,ω;s)=Gobs(r,ω;s)−Gcal(r,ω;s);
solving for a gradient of the cost by evaluating the following expression using the determined residual data—
∂
C
∂
m
0
⁢
|
δ
⁢
⁢
m
⁢
(
x
)
=
-
∫
∫
d
⁢
⁢
s
⁢
⁢
d
⁢
⁢
r
⁢
∫
d
⁢
⁢
ω
⁢
∂
δ
⁢
⁢
G
∂
m
0
⁡
(
x
)
⁢
|
δ
⁢
⁢
m
*
⁢
(
r
,
ω
,
s
;
x
)
⁢
R
⁡
(
r
,
ω
;
s
)
;
and
evaluating the following expression to update the velocity model by using the results of the gradient cost function—
∂
δ
⁢
⁢
G
∂
m
0
⁢
|
δ
⁢
⁢
m
⁢
(
m
0
,
δ
⁢
⁢
m
)
⁢
(
r
,
ω
,
s
;
x
)
=
ω
2
⁢
∫
d
⁢
⁢
y
⁡
(
∂
G
0
∂
m
0
⁢
(
r
,
ω
;
y
)
⁢
G
⁡
(
y
,
ω
;
s
)
+
G
0
⁡
(
r
,
ω
;
y
)
⁢
∂
G
∂
m
0
⁢
(
y
,
ω
;
s
)
)
⁢
δ
⁢
⁢
m
⁡
(
y
)
.

### Claim 13

A system for exploring under-ocean floor environments, the system comprising:
a plurality of sources configured to generate a series of source signals and to inject the source signals into an under-ocean floor explored structure;
a plurality of receivers configured to detect and record direct signals, reflected signals, and refracted signals corresponding to the source signals;
a processor configured to solve a velocity model equation using a full waveform inversion function with respect to the direct signals, reflected signals and refracted signals to minimize a least square misfit function by relaxing a dependency on low frequency reflections in the full waveform inversion function, and to generate a velocity model based on the solution to the velocity model equation, and to determine location of a hydrocarbon reservoir in the under-ocean floor explored structure based on strong velocity or anisotropic parameter variations in the velocity model; and
a display configured to display the velocity model,
wherein the relaxing the dependency on the low frequency reflections includes splitting an initial velocity model m into a long wavelength component mo and a short wavelength component δm, and updating the long wavelength component mo while the short wavelength component δm is fixed.

### Claim 14 (depends on 13)

The system according to claim 13, wherein
the processor is further configured to update long wavelength component of the full waveform inversion function generated velocity model affecting the reflected signals when relaxing the dependency on low frequency reflections.

### Claim 15 (depends on 13)

The system according to claim 13, wherein
the processor is further configured to implement a non-linear iterative relaxation process, such that the processor is still further configured to
obtain the long wavelength component of the reflected signals,
update the short wavelength component using the long wavelength component;
fix the short wavelength component;
update the long wavelength component using the fixed short wavelength component, and
generate the updated velocity model using the updated short wavelength component and updated long wavelength component.

### Claim 16 (depends on 15)

The system according to claim 15, wherein, when updating the short wavelength component using the long wavelength component the processor evaluates the following expression—
∂
δ
⁢
⁢
G
∂
δ
⁢
⁢
m
0
⁢
|
δ
⁢
⁢
m
⁢
(
m
0
)
⁢
(
r
,
ω
,
s
;
x
)
=
ω
2
⁢
⁢
G
0
⁡
(
r
,
ω
;
x
)
⁢
G
0
⁡
(
y
,
ω
;
s
)
where G indicates Green function, that is split into a Green function G0 depending on mo and a perturbation thereof δG depending on mo and δm, r is receiver position, s is shot position, ω is angular frequency and x is a model-related position.

### Claim 17 (depends on 16)

The system according to claim 16, wherein
the processor is further configured to use an amplitude migration process to update the short wavelength component using the long wavelength component.

### Claim 18 (depends on 15)

The system according to claim 15, wherein
the processor is further configured to use a local optimization scheme to update the long wavelength component when using the fixed short wavelength component.

### Claim 19 (depends on 18)

The system according to claim 18, wherein
the processor is further configured to use the local optimization scheme by evaluating the following expressions
R
⁡
(
r
,
ω
;
s
)
=
G
obs
⁡
(
r
,
ω
;
s
)
-
G
cal
⁡
(
r
,
ω
;
s
)
,
⁢
and
∂
C
∂
m
0
⁢
|
δ
⁢
⁢
m
⁢
(
x
)
=
-
∫
∫
d
⁢
⁢
s
⁢
⁢
d
⁢
⁢
r
⁢
∫
d
⁢
⁢
ω
⁢
∂
δ
⁢
⁢
G
∂
m
0
⁡
(
x
)
⁢
|
δ
⁢
⁢
m
*
⁢
(
r
,
ω
,
s
;
x
)
⁢
R
⁡
(
r
,
ω
;
s
)
where Gobs is an observed Green function, Gcal is a calculated Green function, * denotes complex conjugated form of a function and R are residuals.

### Claim 20

A system for exploring under-ocean floor environments, the system comprising:
a plurality of sources configured to generate a series of source signals and to inject the source signals into an under-ocean floor explored structure;
a plurality of receivers configured to detect and record direct signals, reflected signals, and refracted signals corresponding to the source signals;
a processor configured to
solve a velocity model equation using a full waveform inversion function with respect to the direct signals, reflected signals and refracted signals to minimize a least square misfit function,
split the full waveform inversion velocity model m into long wavelength components mo of the reflected signals, and short wavelength components δm of the reflected signals,
update the short wavelength components of the reflected signals, and the long wavelength components of the reflected signals using an iterative relaxation process,
generate an iterative velocity model based on the solution to the velocity model equation that includes the iterated long wavelength components of the reflected signals and the iterated short wavelength components of the reflected signals, and
determine location of a hydrocarbon reservoir in the under-ocean floor explored structure based on strong velocity or anisotropic parameter variations in the velocity model; and
a display configured to display the velocity model,
wherein the iterative relaxation process includes updating the iterated long wavelength component mo while the short wavelength component δm is fixed.

### Claim 21 (depends on 20)

The system according to claim 20, wherein, when updating of the long wavelength components of the reflected signals, the processor evaluates the following expression
∂
δ
⁢
⁢
G
∂
m
0
⁢
|
δ
⁢
⁢
m
⁢
(
m
0
,
δ
⁢
⁢
m
)
⁢
(
r
,
ω
,
s
;
x
)
=
ω
2
⁢
∫
d
⁢
⁢
y
⁡
(
∂
G
0
∂
m
0
⁢
(
r
,
ω
;
y
)
⁢
G
⁡
(
y
,
ω
;
s
)
+
G
0
⁡
(
r
,
ω
;
y
)
⁢
∂
G
∂
m
0
⁢
(
y
,
ω
;
s
)
)
⁢
δ
⁢
⁢
m
⁡
(
y
)
where G indicates Green function that is split into a Green function G0 depending on mo and a perturbation thereof δG depending on mo and δm, r is receiver position, s is shot position, ω is angular frequency and x is a model-related position.

### Claim 22 (depends on 20)

The system according to claim 20, wherein
the processor is further configured to
obtain the initial long wavelength component,
obtain the initial short wavelength component using the initial long wavelength component,
fix the short wavelength component,
update the long wavelength components using a local optimization scheme and then fixing the long wavelength component, and
generate the updated velocity model using the updated long wavelength component and short wavelength component in the full waveform inversion function.

### Claim 23 (depends on 22)

The system according to claim 22, wherein
the processor is further configured to use a true amplitude migration process when obtaining the initial short wavelength component.

### Claim 24 (depends on 20)

The system according to claim 20, wherein
the processor is further configured to determine a set of residual data by evaluating the following expression
R(r,ω;s)=Gobs(r,ω;s)−Gcal(r,ω;s),
and wherein the processor is still further configured to obtain a gradient of the cost function by using the determined residual data and evaluating the following expression—
∂
C
∂
m
0
⁢
|
δ
⁢
⁢
m
⁢
(
x
)
=
-
∫
∫
d
⁢
⁢
s
⁢
⁢
d
⁢
⁢
r
⁢
∫
d
⁢
⁢
ω
⁢
∂
δ
⁢
⁢
G
∂
m
0
⁡
(
x
)
⁢
|
δ
⁢
⁢
m
*
⁢
(
r
,
ω
,
s
;
x
)
⁢
R
⁡
(
r
,
ω
;
s
)
,
where Gobs is an observed Green function, Gcal is a calculated Green function, * denotes complex conjugated form of a function and C is a cost function, and
wherein the processor is still further configured to update the velocity model by using the results of the gradient cost function and evaluating the following expression—
∂
δ
⁢
⁢
G
∂
m
0
⁢
|
δ
⁢
⁢
m
⁢
(
m
0
,
δ
⁢
⁢
m
)
⁢
(
r
,
ω
,
s
;
x
)
=
ω
2
⁢
∫
d
⁢
⁢
y
⁡
(
∂
G
0
∂
m
0
⁢
(
r
,
ω
;
y
)
⁢
G
⁡
(
y
,
ω
;
s
)
+
G
0
⁡
(
r
,
ω
;
y
)
⁢
∂
G
∂
m
0
⁢
(
y
,
ω
;
s
)
)
⁢
δ
⁢
⁢
m
⁡
(
y
)
where G indicates Green function, r is receiver position, s is shot position, ω is angular frequency and x is a model-related position.