AVO imaging condition in elastic reverse time migration
In a general implementation, systems, apparatus, and methods for AVO of imaging condition in ERTM include the described system provides for an efficient and accurate vector wavefield decomposition with a corresponding modified dot-product imaging condition of ERTM by employing a modified AVO algorithm. In some implementations, the phases of source wavelet and multicomponent records are modified using a 1/ω2 filter and the amplitudes of the extrapolated wavefields are scaled using α2 and β2, where ω, α and β are the angular frequency, local P- and S-wave velocities, respectively. The results yield correct phases, amplitudes, and physical units for separated P- and S-mode wavefields. Divergence and curl operators may then be applied to the phase-corrected and amplitude-scaled elastic wavefields to extract vector P- and S-wavefields. With the separated vector wavefields, a modified dot-product imaging condition can be employed to produce PP and PS reflectivity images.
1. A computer-implemented method for amplitude variations with offset (AVO) of imaging condition in elastic reverse time migration (ERTM) executed by one or more processors, the method comprising:
receiving a seismic dataset of a surveyed subsurface, the seismic dataset comprising source wavelet and multicomponent records;
modifying the source wavelet and multicomponent records to extrapolate a compressional (P) wavefield and a shear (S) wavefield;
scaling the extrapolated P and S wavefields using an angular frequency, a local P-wave velocity, and a local S-wave velocity to generate separated vector wavefields;
employing a dot-product imaging condition to generate PP and PS reflectivity images, wherein the dot-product imaging condition is modified by retaining its signs and recomputing its magnitudes using multiplication of the absolute values of the separated vector wavefields; and
evaluating a productivity of the surveyed subsurface according to the generate PP and PS reflectivity images.
2. The computer-implemented method of claim 1 , wherein modifying the source wavelet and multicomponent records includes modifying phases of the source wavelet and multicomponent records using a
1
ω
2
filter.
3. The computer-implemented method of claim 1 , wherein scaling the extrapolated P and S wavefields includes scaling amplitudes of the extrapolated P and S wavefields using the angular frequency, the local P-wave velocity, and the local S-wave velocity to generate separated vector wavefields.
4. The computer-implemented method of claim 1 , wherein the dot-product imaging condition generate PP and PS reflectivity images with substantially accurate angle- dependent amplitudes.
5. The computer-implemented method of claim 1 , wherein the dot-product imaging conditions use the equations:
I
PP
(
x
)
=
∑
x
s
∫
0
T
sgn
PP
(
x
s
,
x
,
t
)
u
s
P
(
x
s
,
x
,
t
)
u
r
P
(
x
s
,
x
,
t
)
dt
∑
x
s
∫
0
T
u
s
P
(
x
s
,
x
,
t
)
2
dt
,
I
PS
(
x
)
=
∑
x
s
∫
0
T
sgn
PS
(
x
s
,
x
,
t
)
u
s
P
(
x
s
,
x
,
t
)
u
r
𝒮
(
x
s
,
x
,
t
)
dt
∑
x
s
∫
0
T
u
s
P
(
x
s
,
x
,
t
)
2
dt
,
where I PP are I PS are images for PP and PS reflectivities, x s and x are source and image point locations, u is the separated vector wavefield, subscripts s and r denote source and receiver sides, superscripts P and S denote P- and S-modes, |⋅| is an absolute value, and T is a record duration, sgn PP and sgn PS are signs for PP and PS images.
6. One or more non-transitory computer-readable storage media coupled to one or more processors and having instructions stored thereon which, when executed by the one or more processors, cause the one or more processors to:
receive a seismic dataset of a surveyed subsurface, the seismic dataset comprising source wavelet and multicomponent records;
modify the source wavelet and multicomponent records to extrapolate a compressional (P) wavefield and a shear (S) wavefield;
scale the extrapolated P and S wavefields using an angular frequency, a local P-wave velocity, and a local S-wave velocity to generate separated vector wavefields;
employ a dot-product imaging condition to generate PP and PS reflectivity images, wherein the dot-product imaging condition is modified by retaining its signs and recomputing its magnitudes using multiplication of the absolute values of the separated vector wavefields; and
evaluate a productivity of the surveyed subsurface according to the generate PP and PS reflectivity images.
7. The computer-readable storage media of claim 6 , wherein modify the source wavelet and multicomponent records includes modify phases of the source wavelet and multicomponent records using a
1
ω
2
filter.
8. The computer-readable storage media of claim 6 , wherein scale the extrapolated P and S wavefields includes scale amplitudes of the extrapolated P and S wavefields using the angular frequency, the local P-wave velocity, and the local S-wave velocity to generate separated vector wavefields.
9. The computer-readable storage media of claim 6 , wherein the dot-product imaging condition generate PP and PS reflectivity images with substantially accurate angle-dependent amplitudes.
10. The computer-readable storage media of claim 6 , wherein the dot-product imaging conditions use the equations:
I
PP
(
x
)
=
∑
x
s
∫
0
T
sgn
PP
(
x
s
,
x
,
t
)
u
s
P
(
x
s
,
x
,
t
)
u
r
P
(
x
s
,
x
,
t
)
dt
∑
x
s
∫
0
T
u
s
P
(
x
s
,
x
,
t
)
2
dt
,
I
PS
(
x
)
=
∑
x
s
∫
0
T
sgn
PS
(
x
s
,
x
,
t
)
u
s
P
(
x
s
,
x
,
t
)
u
r
𝒮
(
x
s
,
x
,
t
)
dt
∑
x
s
∫
0
T
u
s
P
(
x
s
,
x
,
t
)
2
dt
,
where I PP are I PS are images for PP and PS reflectivities, xs and x are source and image point locations, u is the separated vector wavefield, subscripts s and r denote source and receiver sides, superscripts P and S denote P- and S-modes, |⋅| is an absolute value, and T is a record duration, sgn PP and sgn PS are signs for PP and PS images.
11. A system, comprising:
one or more processors; and
a computer-readable storage device coupled to the one or more processors and having instructions stored thereon which, when executed by the one or more processors, cause the one or more processors to:
receive a seismic dataset of a surveyed subsurface, the seismic dataset comprising source wavelet and multicomponent records;
modify the source wavelet and multicomponent records to extrapolate a compressional (P) wavefield and a shear (S) wavefield;
scale the extrapolated P and S wavefields using an angular frequency, a local P-wave velocity, and a local S-wave velocity to generate separated vector wavefields;
employ a dot-product imaging condition to generate PP and PS reflectivity images, wherein the dot-product imaging condition is modified by retaining its signs and recomputing its magnitudes using multiplication of the absolute values of the separated vector wavefields; and
evaluate a productivity of the surveyed subsurface according to the generate PP and PS reflectivity images.
12. The system of claim 11 , wherein modify the source wavelet and multicomponent records includes modify phases of the source wavelet and multicomponent records using a
1
ω
2
filter.
13. The system of claim 11 , wherein scale the extrapolated P and S wavefields includes scale amplitudes of the extrapolated P and S wavefields using the angular frequency, the local P-wave velocity, and the local S-wave velocity to generate separated vector wavefields.
14. The system of claim 11 , wherein the dot-product imaging condition generate PP and PS reflectivity images with substantially accurate angle-dependent amplitudes.
15. The system of claim 11 , wherein the dot-product imaging conditions use the equations:
I
PP
(
x
)
=
∑
x
s
∫
0
T
sgn
PP
(
x
s
,
x
,
t
)
u
s
P
(
x
s
,
x
,
t
)
u
r
P
(
x
s
,
x
,
t
)
dt
∑
x
s
∫
0
T
u
s
P
(
x
s
,
x
,
t
)
2
dt
,
I
PS
(
x
)
=
∑
x
s
∫
0
T
sgn
PS
(
x
s
,
x
,
t
)
u
s
P
(
x
s
,
x
,
t
)
u
r
𝒮
(
x
s
,
x
,
t
)
dt
∑
x
s
∫
0
T
u
s
P
(
x
s
,
x
,
t
)
2
dt
,
where I PP are I PS are images for PP and PS reflectivities, xs and x are source and image point locations, u is the separated vector wavefield, subscripts s and r denote source and receiver sides, superscripts P and S denote P- and S-modes, |⋅| is an absolute value, and T is a record duration, sgn PP and sgn PS are signs for PP and PS images.