US2005018538A1PendingUtilityA1
Method of seismic processing for the decomposition of a wavefield into harmonic components and applications to the determination of angular gathers of reflectivity
Priority: May 27, 2003Filed: May 27, 2004Published: Jan 27, 2005
Est. expiryMay 27, 2023(expired)· nominal 20-yr term from priority
Inventors:Robert Soubaras
G01V 1/36G01V 1/28G01V 1/364G01V 2210/20
36
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Claims
Abstract
Method of processing seismic data representative of at least one wavefield, characterized in that local harmonic components of the wavefield are determined at a given point P of the subsurface by implementing a recurrent processing according to which a harmonic of rank n+1, n being a positive integer, is determined as a function of one or more harmonics of rank n or lower to which is applied at least one filtering which depends on at least one local parameter at the point P, this local parameter being chosen from among the components of the wavevector, the frequency of the wavefield, the local velocity, the local anisotropy parameters or any combination of these various parameters.
Claims
exact text as granted — not AI-modified1 : Method of processing seismic data representative of at least one wavefield, characterized in that local harmonic components of the wavefield are determined at a given point P of the subsurface by implementing a recurrent processing according to which a harmonic of rank n+1, n being a positive integer, is determined as a function of one or more harmonics of rank n or lower to which is applied at least one filtering which depends on at least one local parameter at the point P, this local parameter being chosen from among the components of the wavevector, the frequency of the wavefield, the local velocity, the local anisotropy parameters or any combination of these various parameters.
2 : Method according to claim 1 , characterized in that a harmonic of rank n−1, n being a negative integer, is determined as a function of one or more harmonics of rank n or higher to which is applied at least one filtering which depends on at least one local parameter of the subsurface, this local parameter being chosen from among the components of the wavevector, the frequency of the wavefield, the local velocity, the local anisotropy parameters or any combination of these various parameters.
3 : Method according to claim 2 , characterized in that the harmonics are determined through the recurrence:
ŵ n+1 ( P )= h k 0 (P) + ( P )* ŵ n ( P )
for n a positive integer and
ŵ n−1 ( P )= h k 0 (P) − ( P )* ŵ n ( P )
for n a negative integer
where the operation * designates a filtering, or any linear combination implementing the points neighbouring the point P, and
where h + k0 (P) is a filter corresponding to a filtering as a function of the wavenumber vector k such that:
H k 0 + ( k )= e −jθ(k)
and
where h − k0 (k)(P) is a filter corresponding to a filtering as a function of the wavenumber vector k such that:
H k 0 − ( k )= {overscore (H k 0 + (k))}= e jθ(k)
θ(k) being an angular parameter dependent on at least one component of the wavenumber vector and on k 0 =ω/c with ω=2ƒ, f designating the frequency of the wavefield, c its local velocity,
the initial component ŵ 0 (P)) being equal to the transform in the frequency domain of the wavefield at the point P or being a function thereof.
4 : Method according to claim 3 , characterized in that a filter h k 0 (P) carries out a k x filtering:
H k 0 ( k x )={square root}{square root over (1−( k x /k 0 ) 2 )} jk x /k 0
where k x designates the in-surface projection of the wavenumber.
5 : Method according to claim 3 , characterized in that the case where the subsurface may be regarded as an anisotropic medium, a filter h k 0 (P) carries out a filtering
H
(
k
x
,
k
z
)
=
ⅇ
-
j
θ
=
k
z
+
j
k
x
k
z
2
+
k
x
2
where k x and k z respectively designate the in-surface component of the wavenumber and its perpendicular component.
6 : Method according to claim 3 , characterized in that harmonic decompositions are determined at a given point P of the subsurface for a plurality of values of k 0 , these values lying between 2πƒ min /c max and 2πƒ max /c min , ƒ min and ƒ max being the minimum and maximum frequencies of the wave and c min and c max the minimum and maximum velocities of the velocity field in which the wave propagates.
7 : Method according to claim 3 , characterized in that the initial component is:
w 0 ( P )= g k 0 (P) ( P )* w ( P )
where g k 0 (P) is a spatial filter synthesizing the spectrum in k:
G
k
0
(
k
)
=
1
k
0
1
-
(
k
/
k
0
)
2
k here designating the wavevector, or a component of the latter or else a parameter dependent on the latter.
8 : Method of processing seismic data according to which angular components of a wavefield w(P), where P designates a given point of the subsurface, are determined in the frequency domain, characterized in that harmonic components wn(P) of this wavefield are determined by implementing a method according to one of the preceding claims and its angular components are reconstructed as a function of an angle θ which depends physically on at least one component of the wavevector and/or the frequency of the wavefield and/or the local velocity and/or one or more local anisotropy parameters by determining:
W
(
x
,
θ
)
=
∑
n
=
-
∞
+
∞
w
^
n
(
x
)
B
n
(
θ
)
where the function B n (θ) satisfies a recurrence relation, which may be of order higher than 1 and which is dependent on the filter or filters involved in the recurrence processing of the harmonic decomposition.
9 : Method of processing seismic data according to which angular components of a wavefield w(P), where P designates a given point of the subsurface, are determined in the frequency domain, characterized in that harmonic components wn(P) of this wavefield are determined by implementing a method according to one of the preceding claims and its angular components are reconstructed as a function of an angle θ which depends physically on a local parameter chosen from among the components of the wavevector, the frequency of the wavefield, the local velocity, the local anisotropy parameters or any combination of these various parameters, by determining
W
(
x
,
θ
)
=
∑
n
=
-
∞
+
∞
w
^
n
(
n
)
ⅇ
j
n
θ
10 : Method of processing seismic data according to which incident waves and reflected waves are processed at various points on the surface of the ground so as to determine an angle reflectivity gather, characterized by the steps according to which:
for the various points considered, as well as for the various frequencies and the various shots, a local harmonic decomposition of the incident wave and/or a local harmonic decomposition of the reflected wave is/are computed, a local harmonic decomposition of the reflectivity is deduced therefrom for the various points considered and is summed frequency-wise and shot-wise, an angle gather of the reflectivity is deduced from the harmonic decomposition thus obtained after summation.
11 : Method according to claim 10 , characterized in that to determine a gather in terms of opening angle, we compute:
r
ope
(
x
,
z
,
θ
)
=
∑
n
=
-
N
N
(
-
1
)
n
ⅇ
j
n
θ
∑
f
,
m
i
^
n
(
x
,
z
,
f
,
m
)
_
s
^
n
(
x
,
z
,
f
,
m
)
where î n and ŝ n respectively designate the components of the local harmonic decomposition of the incident wave and of the reflected wave.
12 : Method according to claim 10 , characterized in that to determine a gather in terms of local angle of dip of the reflector, we compute:
r
dip
(
x
,
z
,
θ
)
=
∑
n
=
-
N
N
(
-
1
)
n
ⅇ
j
n
θ
∑
f
,
m
i
^
n
(
x
,
z
,
f
,
m
)
s
^
n
(
x
,
z
,
f
,
m
)
13 : Method according to claim 10 , characterized in that to determine a gather in terms of angle of incidence, we compute:
r
inc
(
x
,
z
,
θ
)
=
∑
n
=
-
N
N
ⅇ
j
n
θ
∑
f
,
m
i
^
n
(
x
,
z
,
f
,
m
)
_
s
(
x
,
z
,
f
,
m
)
14 : Method according to claim 10 , characterized in that the reflectivity is normalized as a function of the autocorrelation of the incident wave.
15 : Method according to claim 1 , characterized in that the harmonics are determined through the recurrence:
ŵ n+1 ( P )=h k 0 (P) + ( P )* ŵ n ( P )
for n a positive integer and
ŵ n−1 ( P )= h k 0 (P) − ( P )* ŵ n ( P )
for n a negative integer
where the operation * designates a filtering , or any linear combination implementing the points neighbouring the point P, and
where h + k0 (P) is a filter corresponding to a filtering as a function of the wavenumber vector k such that:
H k n + ( k )= e −jθ(k)
and
where h − k0 (k)(P) is a filter corresponding to a filtering as a function of the wavenumber vector k such that:
H k 0 − ( k )= {overscore (H k 0 + (k))}= e jθ(k)
θ(k) being an angular parameter dependent on at least one component of the wavenumber vector and on k 0 =ω/c with ω=2πƒ, f designating the frequency of the wavefield, c its local velocity, the initial component ŵ 0 (P)) being equal to the transform in the frequency domain of the wavefield at the point P or being a function thereof.
16 : Method according to claim 15 , characterized in that a filter h k 0 (P) carries out a k x filtering:
H k 0 ( k x )={square root}{square root over (1−( k x /k 0 ) 2 )}− jk x /k 0
where k x designates the in-surface projection of the wavenumber.
17 : Method according to claim 15 , characterized in that harmonic decompositions are determined at a given point P of the subsurface for a plurality of values of k 0 , these values lying between 2πƒ min /c max and 2πƒ max /c min , ƒ min and ƒ max being the minimum and maximum frequencies of the wave and c min and c max the minimum and maximum velocities of the velocity field in which the wave propagates.
18 : Method according to claim 17 , characterized in that harmonic decompositions are determined at a given point P of the subsurface for a plurality of values of k 0 , these values lying between 2πƒ min /c max and 2πƒ max /c max , ƒ min and ƒ max being the minimum and maximum frequencies of the wave and c min and c max the minimum and maximum velocities of the velocity field in which the wave propagates.
19 : Method according to claim 5 , characterized in that harmonic decompositions are determined at a given point P of the subsurface for a plurality of values of k 0 , these values lying between 2πƒ min /c max and 2πƒ max /C min , ƒ min and ƒ max being the minimum and maximum frequencies of the wave and c min and c max the minimum and maximum velocities of the velocity field in which the wave propagates.
20 : Method according to claim 4 , characterized in that harmonic decompositions are determined at a given point P of the subsurface for a plurality of values of k 0 , these values lying between 2πƒ min /c max and 2πƒ max /c min , ƒ min and ƒ max being the minimum and maximum frequencies of the wave and c min and c max the minimum and maximum velocities of the velocity field in which the wave propagates.
21 : Method according to claim 16 , characterized in that harmonic decompositions are determined at a given point P of the subsurface for a plurality of values of k 0 , these values lying between 2πƒ min /c max and 2πƒ max /c min ,ƒ min and ƒ max being the minimum and maximum frequencies of the wave and c min and c max the minimum and maximum velocities of the velocity field in which the wave propagates.
22 : Method according to claim 15 , characterized in that harmonic decompositions are determined at a given point P of the subsurface for a plurality of values of k 0 , these values lying between 2πƒ min /c max and 2πƒ max /c min , ƒ min and ƒ max being the minimum and maximum frequencies of the wave and c min and c max the minimum and maximum velocities of the velocity field in which the wave propagates.
23 : Method according to claim 4 , characterized in that the initial component is:
w 0 ( P )= g k 0 (P) ( P )* w ( P )
where g k 0 (P) is a spatial filter synthesizing the spectrum in k:
G
k
0
(
k
)
=
1
k
0
1
-
(
k
/
k
0
)
2
k here designating the wavevector, or a component of the latter or else a parameter dependent on the latter.
24 : Method according to claim 5 , characterized in that the initial component is:
w 0 ( P )= g k 0 (P) ( P )* w ( P )
where g k 0 (P) is a spatial filter synthesizing the spectrum in k:
G
k
0
(
k
)
=
1
k
0
1
-
(
k
/
k
0
)
2
k here designating the wavevector, or a component of the latter or else a parameter dependent on the latter.
25 : Method according to claim 15 , characterized in that the initial component is:
w 0 ( P )= g k 0 (P) ( P )* w ( P )
where g k 0 (P) is a spatial filter synthesizing the spectrum in k:
G
k
0
(
k
)
=
1
k
0
1
-
(
k
/
k
0
)
2
k here designating the wavevector, or a component of the latter or else a parameter dependent on the latter.
26 : Method according to claim 16 , characterized in that the initial component is:
w 0 ( P )= g k 0 (P) ( P )* w ( P )
where g k 0 (P) is a spatial filter synthesizing the spectrum in k:
G
k
0
(
k
)
=
1
k
0
1
-
(
k
/
k
0
)
2
k here designating the wavevector, or a component of the latter or else a parameter dependent on the latter.
27 : Method according to claim 15 , characterized in that the initial component is:
w 0 ( P )= g k 0 (P) ( P )* w ( P )
where g k 0 (P) is a spatial filter synthesizing the spectrum in k:
G
k
0
(
k
)
=
1
k
0
1
-
(
k
/
k
0
)
2
k here designating the wavevector, or a component of the latter or else a parameter dependent on the latter.
28 : Method according to claim 6 , characterized in that the initial component is:
w 0 ( P )= g k 0 (P) ( P )* w ( P )
where g k 0 (P) is a spatial filter synthesizing the spectrum in k:
G
k
0
(
k
)
=
1
k
0
1
-
(
k
/
k
0
)
2
k here designating the wavevector, or a component of the latter or else a parameter dependent on the latter.
29 : Method according to claim 19 , characterized in that the initial component is:
w 0 ( P )= g k 0 (P) ( P )* w ( P )
where g k 0 (P) is a spatial filter synthesizing the spectrum in k:
G
k
0
(
k
)
=
1
k
0
1
-
(
k
/
k
0
)
2
k here designating the wavevector, or a component of the latter or else a parameter dependent on the latter.
30 : Method according to claim 20 , characterized in that the initial component is:
w 0 ( P )= g k 0 (P) ( P )* w ( P )
where g k 0 (P) is a spatial filter synthesizing the spectrum in k:
G
k
0
(
k
)
=
1
k
0
1
-
(
k
/
k
0
)
2
k here designating the wavevector, or a component of the latter or else a parameter dependent on the latter.
31 : Method according to claim 21 , characterized in that the initial component is:
w 0 ( P )= g k 0 (P) ( P )* w ( P )
where g k 0 (P) is a spatial filter synthesizing the spectrum in k:
G
k
0
(
k
)
=
1
k
0
1
-
(
k
/
k
0
)
2
k here designating the wavevector, or a component of the latter or else a parameter dependent on the latter.
32 : Method according to claim 22 , characterized in that the initial component is:
w 0 ( P )= g k 0 (P) ( P )* w ( P )
where g k 0 (P) is a spatial filter synthesizing the spectrum in k:
G
k
0
(
k
)
=
1
k
0
1
-
(
k
/
k
0
)
2
k here designating the wavevector, or a component of the latter or else a parameter dependent on the latter.
33 : Method according to claim 11 , characterized in that the reflectivity is normalized as a function of the autocorrelation of the incident wave.
34 : Method according to claim 12 , characterized in that the reflectivity is normalized as a function of the autocorrelation of the incident wave.
35 : Method according to claim 13 , characterized in that the reflectivity is normalized as a function of the autocorrelation of the incident wave.Join the waitlist — get patent alerts
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