# US 9,753,166 B2 · P-wave and S-wave separation of seismic data in the presence of statics and irregular geometry

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- Number: US 9,753,166 B2
- Document ID: US9753166B2
- Status: Granted
- Kind: B2
- Application number: 14/282,268
- Filed: 2014-05-20
- Published: 2015-11-26
- Granted: 2017-09-05
- Earliest claimed: 2014-05-20
- Assignees: Cgg Services SAS
- Applicants: Cgg Services SA
- Inventors: Richard Bale
- Web page: https://patentgrep.com/patent/US9753166B2

## CPC

- G01V 1/284: {Application of the shear wave component and/or several components of the seismic signal}
- G01V 1/303: {for determining velocity profiles or travel times}
- 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

Methods and systems for separating P-S wave field data are described. Slowness values for the PP mode and the PS mode are estimated and are, typically, unequal based on aliased and/or irregularly sampled data. A calculation, in the space-time domain, based on a matrix of equations, generates separated P-wave and S-wave data. The separated P-wave data and S-wave data are output for further imaging.

## Claims

### Claim 1

A method, stored in a memory and executing on a processor, for separating P-wave data and S-wave data in seismic data acquired over a given subsurface of the earth, said method comprising:
receiving the seismic data, wherein the seismic data is recorded with receivers that record vertical component data and horizontal component data;
establishing a forward modelling equation that links the vertical and horizontal component data to the P-wave and S-wave data through a P-wave slowness and an S-wave slowness;
estimating, in a space-time domain, a P-wave slowness value and an S-wave slowness value;
separating, in the processor, the P-wave data and the S-wave data using the estimated P-wave slowness value and S-wave slowness value;
outputting the separated P-wave data and the separated S-wave data; and
generating an image of the subsurface based on the separated P-wave data and the separated S-wave data, wherein the image is indicative of various layers of the earth,
wherein the P-wave slowness value is different from the S-wave slowness value.

### Claim 2 (depends on 1)

The method of claim 1, wherein said P-wave slowness value and said S-wave slowness value are estimated by ray tracing.

### Claim 3 (depends on 1)

The method of claim 1, wherein said P-wave slowness value and said S-wave slowness value are estimated directly from a normal moveout (NMO) equation.

### Claim 4 (depends on 1)

The method of claim 1, wherein said P-wave data and said S-wave data is three-dimensional (3D) shot records.

### Claim 5 (depends on 1)

The method of claim 1, wherein said step of separating is performed by calculating,
[
U
V
U
H
]
⁡
[
R
V
P
⁡
(
p
P
⁢
⁢
P
)
R
V
S
⁡
(
p
P
⁢
⁢
S
)
R
H
P
⁡
(
p
P
⁢
⁢
P
)
R
H
S
⁡
(
p
P
⁢
⁢
S
)
]
-
1
=
[
D
P
D
S
]
where UV is the vertical component data, UH is the horizontal component data, DP is the separated P-wave data, DS is the separated S-wave data, RVP(pPP) is an amplitude factor for PP measured on a vertical geophone, RHP(pPP) is an amplitude factor for PP measured on a horizontal geophone, RVS(pPS) is an amplitude factor for PS measured on a vertical geophone and RHS(pPS) is an amplitude factor for PS measured on a horizontal geophone.

### Claim 6 (depends on 5)

The method of claim 5, wherein said RVP(pPP) term is inverted to correct for emergence angle amplitude decay when only said vertical component is present.

### Claim 7 (depends on 5)

The method of claim 5, wherein said RVP(pPP) term is defined as
-
2
⁢
⁢
γξ
⁡
(
1
-
2
⁢
V
S
2
⁢
p
P
⁢
⁢
P
2
)
R
0
⁡
(
p
P
⁢
⁢
P
)
,
said RHP(pPP) term is defined as
4
⁢
V
P
⁢
p
P
⁢
⁢
P
⁢
ξη
R
0
⁡
(
p
P
⁢
⁢
P
)
,
said RVS(pPS) term is defined as
4
⁢
V
S
⁢
p
P
⁢
⁢
S
⁢
ξη
R
0
⁡
(
p
P
⁢
⁢
S
)
and said RHS(pPS) term is defined as
2
⁢
η
⁡
(
1
-
2
⁢
V
S
2
⁢
p
P
⁢
⁢
S
2
)
R
0
⁡
(
p
P
⁢
⁢
S
)
where γ equals Vp/Vs, ξ equals
(
V
⁢
⁢
s
V
⁢
⁢
p
-
⁢
V
⁢
⁢
s
2
⁢
p
2
)
1
/
2
,
VS equals an S-wave velocity, VP equals a P-wave velocity, pPP is a slowness value for said PP mode, pPS is a slowness value for PS mode, R0 equals(1−2Vs2p2)2+4p2Vs2ξη and η equals (1−Vs2p2)1/2.

### Claim 8 (depends on 7)

The method of claim 7, wherein the receivers associated with collecting said vertical component data and said horizontal component data are sampled in only one direction.

### Claim 9 (depends on 7)

The method of claim 7, wherein a receiver spacing is irregular.

### Claim 10 (depends on 7)

The method of claim 7, wherein a receiver spacing is sparse.

### Claim 11 (depends on 7)

The method of claim 7, wherein P receiver statics and S receiver statics are conflicting.

### Claim 12

A system for separating P-wave data and S-wave data in acquired seismic, said system comprising:
a seismic dataset having vertical component data and horizontal component data, the seismic dataset being recorded with seismic receivers; and
one or more processors configured to receive the seismic dataset and execute computer instructions and a memory configured to store said computer instructions wherein said one or more processors are configured to:
estimate, in a space-time domain, a P-wave slowness value and an S-wave slowness value using the seismic dataset;
separate the P-wave data and the S-wave data using (i) a forward modelling equation that links the vertical and horizontal component data to the P-wave and S-wave data through a P-wave slowness and an S-wave slowness, and (ii) estimated P-wave slowness value and S-wave slowness value;
output separated P-wave data and S-wave data; and
generate an image of the subsurface based on the separated P-wave data and the separated S-wave data, wherein the image is indicative of various layers of the earth,
wherein the P-wave slowness value is different from the S-wave slowness value.

### Claim 13 (depends on 12)

The system of claim 12, wherein said slowness value estimation component further comprises a ray tracing component for estimating said P-wave slowness value and said S-wave slowness value.

### Claim 14 (depends on 12)

The system of claim 12, wherein said slowness value estimation component further comprises a normal moveout component for estimating said P-wave slowness value and said S-wave slowness value.

### Claim 15 (depends on 12)

The system of claim 12, wherein said P-S wave field dataset is three-dimensional (3D) shot records.

### Claim 16 (depends on 12)

The system of claim 12, wherein said one or more processors are configured to correct emergence angle amplitude decay when only a vertical component is present.

### Claim 17 (depends on 16)

The system of claim 16, wherein said one or more processors are further configured to invert said matrix of equations when horizontal receivers are present and collect a portion of said P-wave data and said S-wave data.

### Claim 18 (depends on 12)

The system of claim 12, wherein said one or more processors are configured to separate the P-wave data and the S-wave data by calculating:
[
U
V
U
H
]
⁡
[
R
V
P
⁡
(
p
P
⁢
⁢
P
)
R
V
S
⁡
(
p
P
⁢
⁢
S
)
R
H
P
⁡
(
p
P
⁢
⁢
P
)
R
H
S
⁡
(
p
P
⁢
⁢
S
)
]
-
1
=
[
D
P
D
S
]
,
where UV is the vertical component data, UH is the horizontal component data, DP is the P-wave data, DS is the S-wave data, RVP(pPP) is an amplitude factor for PP measured on a vertical geophone, RHP(pPP) is an amplitude factor for PP measured on a horizontal geophone, RVS(pPS) is an amplitude factor for PS measured on a vertical geophone and RHS(pPS) is an amplitude factor for PS measured on a horizontal geophone.

### Claim 19 (depends on 18)

The system of claim 18, wherein said RVP(pPP) term is defined as
-
2
⁢
γξ
⁡
(
1
-
2
⁢
V
S
2
⁢
p
P
⁢
⁢
P
2
)
R
0
⁡
(
p
P
⁢
⁢
P
)
,
said RHP(pPP) term is defined as
4
⁢
V
P
⁢
p
P
⁢
⁢
P
⁢
ξη
R
0
⁡
(
p
P
⁢
⁢
P
)
,
said RVS(pPS) term is defined as
4
⁢
V
S
⁢
p
P
⁢
⁢
S
⁢
ξη
R
0
⁡
(
p
P
⁢
⁢
S
)
and said RHS(pPS) term is defined as
2
⁢
η
⁡
(
1
-
2
⁢
V
S
2
⁢
p
P
⁢
⁢
S
2
)
R
0
⁡
(
p
P
⁢
⁢
S
)
where γ equals Vp/Vs, ξ equals
(
V
⁢
⁢
s
V
⁢
⁢
p
-
V
⁢
⁢
s
2
⁢
p
2
)
1
/
2
,
VS equals an S-wave velocity, VP equals a P-wave velocity, pPP is a slowness value for said PP mode, pPS is a slowness value for PS mode, R0 equals(1−2Vs2p2)2+4p2Vs2ξη and η equals (1−Vs2p2)1/2.

### Claim 20 (depends on 12)

The system of claim 12, wherein the acquired seismic data is aliased and irregularly sampled.