# US 9,435,904 B2 · Method of correcting velocity for complex surface topography

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- Number: US 9,435,904 B2
- Document ID: US9435904B2
- Status: Granted
- Kind: B2
- Application number: 14/134,258
- Filed: 2013-12-19
- Published: 2015-06-25
- Granted: 2016-09-06
- Earliest claimed: 2013-12-19
- Assignees: Chevron U.S.A. Inc.
- Applicants: Maisha Lara Amaru; Cory James Hoelting
- Inventors: Maisha Lara Amaru; Cory James Hoelting
- Web page: https://patentgrep.com/patent/US9435904B2

## CPC

- G01V 1/36: Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy
- G01V 1/282: {Application of seismic models, synthetic seismograms}
- G01V 1/303: {for determining velocity profiles or travel times}
- G01V 20/00: Geomodelling in general
- G01V 2210/622: Velocity, density or impedance
- G01V 2210/66: Subsurface modeling
- G01V 2210/661: Model from sedimentation process modeling, e.g. from first principles
- 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

Embodiments of a method for correcting velocity models for complex topographies are disclosed herein. In general, embodiments of the method utilize velocity corrections based on geomechanical effects to correct a velocity model to take into account complex surface topographies. In particular, embodiments of the method use a nucleus strain theory to determine the velocity corrections. Further details and advantages of various embodiments of the method are described in more detail herein.

## Claims

### Claim 1

A computer-implemented method of correcting a velocity model, the method comprising:
(a) selecting a velocity model of a subsurface region of interest, the subsurface region of interest located proximate to a surface comprising one or more topographic anomalies;
(b) determining an anomalous overburden stress caused by the one or more topographic anomalies;
(c) determining an overburden strain caused by the one or more topographic anomalies;
(d) using a nucleus of strain theory to determine an anomalous stress propagation in the subsurface region of interest by calculating
S
z
⁡
(
r
a
,
i
)
=
-
C
m
R
3
Sz(ra,i)=−Cm/R3
wherein Sz(ra,i)=anomalous stress at a particular subsurface location ri caused by cell “a” in the anomalous topography, R=distance between subsurface cell “i” and a cell “a” in the one or more topographic anomalies with
C
m
=
2
⁢
G
⁢
⁢
V
a
⁢
E
0
⁡
(
r
a
)
4
⁢
π
Cm=2G VaE0 (ra)/4π
where G=shear modulus, Va=volume of a cell in the one or more topographic anomalies, E0(ra)=anomalous overburden strain at location ra;
(e) determining a velocity correction factor from the anomalous stress propagation; and
(f) using the velocity correction factor to generate a corrected velocity model, wherein at least one of (a) through (f) is performed on a computer.

### Claim 2 (depends on 1)

The method of claim 1 wherein the one or more topographic anomalies comprises a seamount, a ridge, a canyon, a valley, or combinations thereof.

### Claim 3 (depends on 1)

The method of claim 1 wherein (b) comprises determining the overburden stress using:
d
⁢
⁢
S
0
⁡
(
z
i
)
=
∑
i
⁢
⁢
(
ρ
flat
-
ρ
orig
)
⁢
g
⁡
(
z
i
-
z
i
-
1
)
where dS0=the anomalous overburden stress, ρflat=the density without the one or more topographic anomalies, ρorig=original density, g=gravitational constant, and zi=depth.

### Claim 4 (depends on 3)

The method of claim 3 wherein the density is calculated using Gardner's equation.

### Claim 5 (depends on 1)

The method of claim 1 wherein (c) comprises determining the overburden strain using:
E
0
⁡
(
r
a
)
=
d
⁢
⁢
S
0
⁡
(
r
a
)
⁢
(
1
+
v
)
⁢
(
1
-
2
⁢
v
)
E
⁡
(
1
-
v
)
where E0=the anomalous overburden strain, dS0=the anomalous overburden stress, E=Young's modulus of a sediment, v=Poisson's ratio of the sediment, and ra=location of a cell in the one or more topographic anomalies.

### Claim 6 (depends on 1)

The method of claim 1 wherein (e) comprises determining the velocity correction factor using:
vint
anom
=
vint
orig
[
(
1
+
S
zz
S
0
)
1
n
-
1
]
where vintanom=interval velocity anomaly correction factor, vintorig=original interval velocity, S0=the overburden stress, Szz=the sum over Sz for all cells in the one or more topographic anomalies, and n=a constant describing a sensitivity of velocity to stress.

### Claim 7 (depends on 6)

The method of claim 6 wherein n equals 3.

### Claim 8 (depends on 1)

The method of claim 1 wherein the surface comprises a seafloor.

### Claim 9

A computer system, comprising:
an interface for receiving a seismic input volume, the seismic input volume comprising a plurality of seismic traces;
a memory resource;
input and output functions for presenting and receiving communication signals to and from a human user;
one or more central processing units for executing program instructions; and program memory, coupled to the central processing unit, for storing a computer program including program instructions that, when executed by the one or more central processing units, cause the computer system to perform a plurality of operations for correcting a velocity model, the plurality of operations comprising:
(a) selecting a velocity model of a subsurface region of interest, the subsurface region of interest located proximate to a surface comprising one or more topographic anomalies;
(b) determining an anomalous overburden stress caused by the one or more topographic anomalies;
(c) determining an overburden strain caused by the one or more topographic anomalies;
(d) using a nucleus of strain theory to determine an anomalous stress propagation in the subsurface region of interest by calculating
S
z
⁡
(
r
a
,
i
)
=
-
C
m
R
3
Sz(ra,i)=−Cm/R3
wherein Sz(ra,i)=anomalous stress at a particular subsurface location ri caused by cell “a” in the anomalous topography, R=distance between subsurface cell “i” and a cell “a” in the one or more topographic anomalies with
C
m
=
2
⁢
G
⁢
⁢
V
a
⁢
E
0
⁡
(
r
a
)
4
⁢
π
Cm=2GVaE0(ra)/4π
where G=shear modulus, Va=volume of a cell in the one or more topographic anomalies, E0(ra)=anomalous overburden strain at location ra;
(e) determining a velocity correction factor from the anomalous stress propagation; and
(f) using the velocity correction factor to generate a corrected velocity model.

### Claim 10 (depends on 9)

The system of claim 9 wherein the one or more topographic anomalies comprises a seamount, a ridge, a canyon, a valley, or combinations thereof.

### Claim 11 (depends on 9)

The system of claim 9 wherein (b) comprises determining the overburden stress using:
d
⁢
⁢
S
0
⁡
(
z
i
)
=
∑
i
⁢
⁢
(
ρ
flat
-
ρ
orig
)
⁢
g
⁡
(
z
i
-
z
i
-
1
)
where dS0=the anomalous overburden stress, ρflat=the density without the one or more topographic anomalies, ρorig=original density, g=gravitational constant, and zi=depth.

### Claim 12 (depends on 11)

The system of claim 11 wherein the density is calculated using Gardner's equation.

### Claim 13 (depends on 9)

The system of claim 9 wherein (c) comprises determining the overburden strain using:
E
0
⁡
(
r
a
)
=
d
⁢
⁢
S
0
⁡
(
r
a
)
⁢
(
1
+
v
)
⁢
(
1
-
2
⁢
v
)
E
⁡
(
1
-
v
)
where E0=the anomalous overburden strain, dS0=the anomalous overburden stress, E=Young's modulus of a sediment, v=Poisson's ratio of the sediment, and ra=location of a cell in the one or more topographic anomalies.

### Claim 14 (depends on 9)

The system of claim 9 wherein (e) comprises determining the velocity correction factor using:
vint
anom
=
vint
orig
[
(
1
+
S
zz
S
0
)
1
n
-
1
]
where vintanom=interval velocity anomaly correction factor , vintorig=original interval velocity, S0=the overburden stress, Szz=the sum over Sz for all cells in the one or more topographic anomalies, and n=a constant describing a sensitivity of velocity to stress.

### Claim 15 (depends on 14)

The system of claim 14 wherein n equals 3.

### Claim 16 (depends on 9)

The system of claim 9 wherein the surface comprises a seafloor.

### Claim 17

A computer-implemented method of correcting a velocity model, the method comprising:
(a) selecting a velocity model of a subsurface region of interest, the subsurface region of interest located proximate a surface comprising one or more topographic anomalies;
(b) using a nucleus of strain theory to determine a velocity correction factor for the one or more topographic anomalies by calculating
S
z
⁡
(
r
a
,
i
)
=
-
C
m
R
3
Sz(ra,i)=−Cm/R3
wherein Sz(ra,i)=anomalous stress at a particular subsurface location ri caused by cell “a” in the anomalous topography, R=distance between subsurface cell “i” and a cell “a” in the one or more topographic anomalies with
C
m
=
2
⁢
G
⁢
⁢
V
a
⁢
E
0
⁡
(
r
a
)
4
⁢
π
Cm=2GVaE0(ra)/4π
where G=shear modulus, Va=volume of a cell in the one or more topographic anomalies, E0(ra)=anomalous overburden strain at location ra; and
(c) using the velocity correction factor to generate a corrected velocity model, wherein at least one of (a) through (c) is performed on a computer.

### Claim 18 (depends on 17)

The method of claim 17 wherein the surface comprises a seafloor.