Methods and computer-readable medium to implement inversion of angle gathers for rock physics reflectivity attributes
The invention relates to methods and computer-readable medium to determine seismic reflectivity attributes indicating the presence of hydrocarbons in earth. In several embodiments, the methods and computer-readable medium perform the steps of computing seismic reflectivity attributes includes inputting data representing reflected seismic waves and a volume of P-wave velocity, transforming the volume of P-wave velocity into a volume of bulk density, transforming the volume of P-wave velocity into a volume of S-wave velocity using amplitude information from the reflected seismic waves, and using the volume of S-wave velocity and the volume of P-wave velocity to compute the reflectivity attribute.
1 . The method in a host of determining a reflectivity attribute indicating the presence of hydrocarbons in earth, comprising:
inputting data representing reflected seismic waves;
inputting a volume of P-wave velocity;
transforming the volume of P-wave velocity into a volume of bulk density;
transforming the volume of P-wave velocity into a volume of S-wave velocity using amplitude information from the reflected seismic waves; and
using the volume of S-wave velocity and the volume of P-wave velocity to compute the reflectivity attribute.
2 . The method of claim 1 , wherein the amplitude information includes an A parameter and a B parameter corresponding to a linear expression for P-wave reflection strength.
3 . The method of claim 2 , wherein the linear expression is as follows:
R
(
ϕ
)
=
A
(
1
+
sin
2
ϕtan
2
ϕ
1
+
γ
)
+
B
sin
2
ϕ
4 . The method of claim 3 , further comprising computing a formula for the A parameter in terms of the P-wave velocity reflectivity and the y parameter as follows:
A
=
Δ
V
P
V
_
P
(
1
+
γ
2
)
5 . The method of claim 3 , further comprising computing a formula for the B parameter in terms of the P-wave velocity reflectivity, the S-wave velocity reflectivity, the volume of P-wave velocity, the volume of S-wave velocity, and the γ parameter as follows:
B
=
1
2
Δ
V
P
V
_
P
(
1
-
4
γ
V
S
2
V
P
2
)
-
4
V
S
2
V
P
2
Δ
V
S
V
_
S
6 . The method of claim 4 , further comprising computing the P-wave velocity reflectivity where γ is a constant value γ′, from the formula for the A parameter as follows:
Δ
V
P
V
_
P
=
A
(
1
+
γ
′
2
)
7 . The method of claim 6 , further comprising computing the bulk density reflectivity from the formula for γ shown in equation (32) as follows:
Δ
ρ
ρ
_
=
γ
′
Δ
V
P
V
_
P
8 . The method of claim 7 , further comprising computing the S-wave velocity reflectivity from the formula for the B parameter as follows:
Δ
V
S
V
_
S
=
1
2
Δ
V
P
V
_
P
(
1
-
4
γ
′
V
S
2
V
P
2
)
-
B
4
V
S
2
V
P
2
9 . The method of claim 2 , further comprising using the A and B parameters to compute a spatially varying γ volume, γ V .
10 . The method of claim 9 , further comprising computing the A and B parameters using γ V .
11 . The method of claim 9 , wherein the spatially varying volume γ V is computed using the ratio of the A and B parameters, B/A.
12 . The method of claim 9 , wherein the spatially varying volume γ V is computed using an iterative procedure.
13 . The method of claim 11 , further comprising using the spatially varying volume γ V to iteratively recompute the A and B parameters.
14 . The method of claim 10 , further comprising computing the P-wave velocity reflectivity where γ is a spatially varying volume γ V , from the formula for the A parameter as follows:
Δ
V
P
V
_
P
=
A
(
1
+
γ
V
2
)
15 . The method of claim 10 , further comprising computing the bulk density reflectivity from the formula for γ shown in equation (32) as follows:
Δρ
ρ
_
=
γ
V
Δ
V
P
V
_
P
16 . The method of claim 10 , further comprising computing the S-wave velocity reflectivity from the formula for the B parameter as follows:
Δ
V
S
V
_
S
=
1
2
Δ
V
P
V
_
P
(
1
-
4
γ
V
V
S
2
V
P
2
)
-
B
4
V
S
2
V
P
2
17 . The method of claim 1 , wherein the volume of S-wave velocity is computed with a single-parameter mudrock line equation.
18 . The method of claim 17 , wherein the single-parameter mudrock line parameter is computed using the ratio of the A and B parameters, B/A.
19 . The method of claim 1 , wherein the volume of S-wave velocity equals zero when the P-wave velocity equals the P-wave velocity of water.
20 . The method of claim 17 , wherein the single-parameter mudrock line equation for S-wave velocity is hyperbolic, and takes the form:
V
S
2
=
b
k
2
(
V
P
2
V
W
2
-
1
)
21 . The method of claim 20 , wherein the hyperbolic mudrock line parameter is computed using the ratio of the A and B parameters, B/A.
22 . The method of claim 20 , wherein the hyperbolic mudrock line parameter is computed with an iterative procedure.
23 . The method of claim 2 , wherein the A and B parameters are computed using depth migrated angle gathers.
24 . The method of claim 23 , wherein the depth migrated angle gathers are computed using a shot record one-way wave equation depth migration.
25 . The method of claim 2 , wherein the A and B parameters are computed by a least-squares inversion of angle gathers.
26 . The method of claim 25 , wherein low quality angle gather data is excluded from the least-squares inversion by a quality measure Q computed from the angle gathers.
27 . The method of claim 2 , wherein the B parameter is calibrated to laboratory data.
28 . The method of claim 27 , further comprising determining a scalar which multiplies the ratio of the A and B parameters, B/A, such that B/A matches a predicted r=B/A.
29 . The method of claim 28 , wherein the expression for the predicted r=B/A is as follows:
r
=
1
-
b
2
V
W
2
(
8
+
4
(
1
-
V
W
2
V
P
2
)
γ
)
1
+
γ
30 . A computer-readable medium storing program instructions for determining a reflectivity attribute indicating the presence of hydrocarbons in earth, that cause a host to perform the following steps, comprising:
inputting data representing reflected seismic waves;
inputting a volume of P-wave velocity;
transforming the volume of P-wave velocity into a volume of bulk density;
transforming the volume of P-wave velocity into a volume of S-wave velocity using amplitude information from the reflected seismic waves; and
using the volume of S-wave velocity and the volume of P-wave velocity to compute the reflectivity attribute.
31 . The computer-readable medium of claim 30 , wherein the amplitude information includes an A parameter and a B parameter corresponding to a linear expression for P-wave reflection strength.
32 . The computer-readable medium of claim 31 , wherein the linear expression is as follows:
R
(
ϕ
)
=
A
(
1
+
sin
2
ϕtan
2
ϕ
1
+
γ
)
+
B
sin
2
ϕ
33 . The computer-readable medium of claim 32 , further comprising computing a formula for the A parameter in terms of the P-wave velocity reflectivity and the γ parameter as follows:
A
=
Δ
V
P
V
_
P
(
1
+
γ
2
)
34 . The computer-readable medium of claim 33 , further comprising computing a formula for the B parameter in terms of the P-wave velocity reflectivity, the S-wave velocity reflectivity, the volume of P-wave velocity, the volume of S-wave velocity, and the γ parameter as follows:
B
=
1
2
Δ
V
P
V
_
P
(
1
-
4
γ
V
S
2
V
P
2
)
-
4
V
S
2
V
P
2
Δ
V
S
V
_
S
35 . The computer-readable medium of claim 34 , further comprising computing the P-wave velocity reflectivity where γ is a constant value γ′, from the formula for the A parameter as follows:
Δ
V
P
V
_
P
=
A
(
1
+
γ
′
2
)
36 . The computer-readable medium of claim 35 , further comprising computing the bulk density reflectivity from the formula for γ shown in equation (32) as follows:
Δρ
ρ
_
=
γ
′
Δ
V
P
V
_
P
37 . The computer-readable medium of claim 36 , further comprising computing the S-wave velocity reflectivity from the formula for the B parameter as follows:
Δ
V
S
V
_
S
=
1
2
Δ
V
P
V
_
P
(
1
-
4
γ
′
V
S
2
V
P
2
)
-
B
4
V
S
2
V
P
2
38 . The computer-readable medium of claim 31 , further comprising using the A and B parameters to compute a spatially varying γ volume, γ V .
39 . The computer-readable medium of claim 38 , further comprising computing the A and B parameters using γ V .
40 . The computer-readable medium of claim 38 , wherein the spatially varying volume γ V is computed using the ratio of the A and B parameters, B/A.
41 . The computer-readable medium of claim 38 , wherein the spatially varying volume γ V is computed using an iterative procedure.
42 . The computer-readable medium of claim 40 , further comprising using the spatially varying volume γ V to iteratively recompute the A and B parameters.
43 . The computer-readable medium of claim 39 , further comprising computing the P-wave velocity reflectivity where γ is a spatially varying volume γ V , from the formula for the A parameter as follows:
Δ
V
P
V
_
P
=
A
(
1
+
γ
V
2
)
44 . The computer-readable medium of claim 39 , further comprising computing the bulk density reflectivity from the formula for γ shown in equation (32) as follows:
Δρ
ρ
_
=
γ
V
Δ
V
P
V
_
P
45 . The computer-readable medium of claim 39 , further comprising computing the S-wave velocity reflectivity from the formula for the B parameter as follows:
Δ
V
S
V
_
S
=
1
2
Δ
V
P
V
_
P
(
1
-
4
γ
V
V
S
2
V
P
2
)
-
B
4
V
S
2
V
P
2
46 . The computer-readable medium of claim 30 , wherein the volume of S-wave velocity is computed with a single-parameter mudrock line equation.
47 . The computer-readable medium of claim 46 , wherein the single-parameter mudrock line parameter is computed using the ratio of the A and B parameters, B/A.
48 . The computer-readable medium of claim 30 , wherein the volume of S-wave velocity equals zero when the P-wave velocity equals the P-wave velocity of water.
49 . The computer-readable medium of claim 46 , wherein the single-parameter mudrock line equation for S-wave velocity is hyperbolic, and takes the form:
V
S
2
=
b
k
2
(
V
P
2
V
W
2
-
1
)
50 . The computer-readable medium of claim 49 , wherein the hyperbolic mudrock line parameter is computed using the ratio of the A and B parameters, B/A.
51 . The computer-readable medium of claim 49 , wherein the hyperbolic mudrock line parameter is computed with an iterative procedure.
52 . The computer-readable medium of claim 31 , wherein the A and B parameters are computed using depth migrated angle gathers.
53 . The computer-readable medium of claim 52 , wherein the depth migrated angle gathers are computed using a shot record one-way wave equation depth migration.
54 . The computer-readable medium of claim 31 , wherein the A and B parameters are computed by a least-squares inversion of angle gathers.
55 . The computer-readable medium of claim 54 , wherein low quality angle gather data is excluded from the least-squares inversion by a quality measure Q computed from the angle gathers.
56 . The computer-readable medium of claim 31 , wherein the B parameter is calibrated to laboratory data.
57 . The computer-readable medium of claim 56 , further comprising determining a scalar which multiplies the ratio of the A and B parameters, B/A, such that B/A matches a predicted r=B/A.
58 . The computer-readable medium of claim 57 , wherein the expression for the predicted r=B/A is as follows:
r
=
1
-
b
2
V
W
2
(
8
+
4
(
1
-
V
W
2
V
P
2
)
γ
)
1
+
γ