Seismic adaptive focusing
A method for use in seismic exploration comprises: accessing a set of seismic data representative of a subterranean geological formation and a subsurface attribute model of the subterranean geological formation; performing a wavefield extrapolation on the seismic data in the subsurface attribute model; applying the time-shift extended imaging condition to the extrapolated wavefields; forming shot-indexed, time shift gathers for each image pixel of the subsurface attribute model from the conditioned extrapolated wavefields; adaptively focusing the gathers; and stacking the adaptively focused gathers; and imaging the subterranean geological formation from the stacked, adaptively focused gathers. The method may, in some aspects, be realized by a computing apparatus programmed to perform the method or as a set of instructions encoded on a non-transitory program storage medium that, when executed by a computing apparatus, perform the method.
1. A method for use in seismic exploration, comprising:
accessing a set of seismic data representative of a subterranean geological formation and a subsurface attribute model of the subterranean geological formation;
performing a wavefield extrapolation on the seismic data in the subsurface attribute model;
applying a time-shift extended imaging condition to the extrapolated wavefields;
forming shot-indexed, time shift gathers for each image pixel of the subsurface attribute model from the conditioned extrapolated wavefields;
adaptively focusing the gathers using a processor, the adaptive focusing comprising determining for each trace in the gather the amount of time shift to apply to yield a zero time lag for that trace and applying the determined time shift to each respective trace;
stacking the adaptively focused gathers using the processor; and
imaging the subterranean geological formation from the stacked, adaptively focused gathers using the processor.
2. The method of claim 1 , wherein executing the adaptive focusing further comprises weighting each trace by a weight that is a decreasing function of a magnitude of a determined time shift for a given trace.
3. The method of claim 2 , wherein the weighting function is:
w
(
x
,
s
)
∝
1
[
τ
i
(
x
,
s
)
+
1
]
2
wherein
x is the spatial coordinate;
s is the shot index; and
τ is the determined time shift for the given trace.
4. The method of claim 1 , wherein executing the adaptive focusing further comprises weighting each trace by a weight that is a decreasing function of the magnitude of a magnitude of a determined time shift for a given trace.
5. The method of claim 4 , wherein the weighting function is:
w
(
x
,
s
)
∝
1
[
τ
i
(
x
,
s
)
+
1
]
2
wherein:
x is the spatial coordinate;
s is the shot index; and
τ is the determined time shift for the given trace.
6. The method of claim 1 , wherein determining for each trace in the gather the amount of time shift includes:
determining the amount of the time shifts from a plurality of low frequency ended images; and
assigning those low frequency time shifts to the respective traces.
7. The method of claim 1 , wherein adaptively focusing the gathers includes iteratively adaptively focusing the gathers before stacking.
8. A computing apparatus programmed to perform a method for use in seismic exploration, the computing apparatus comprising: a processor; bus system; a storage; and a software component residing on the storage that, when invoked by the processor over the bus system, performs a method comprising:
accessing a set of seismic data representative of a subterranean geological formation and, a subsurface attribute model of the subterranean geological formation;
performing a wavefield extrapolation on the seismic data in the subsurface attribute model;
applying a time-shift extended imaging condition to the extrapolated wavefields;
forming shot-indexed, time shift gathers for each image pixel of the subsurface attribute model from the conditioned extrapolated wavefields;
adaptively focusing the gathers;
stacking the adaptively focused gathers; and
imaging the subterranean geological formation from the stacked, adaptively focused gathers.
9. The computing apparatus of claim 8 , wherein executing the adaptive focusing comprises: determining for each trace in the gather the amount of time shift to apply to yield a zero time lag for that trace; and applying the determined time shift to each respective trace.
10. The computing apparatus of claim 8 , wherein executing the adaptive focusing further comprises weighting each trace by a weight that is a decreasing function, of a magnitude of a determined time shift for a given trace.
11. The computing apparatus of claim 10 , wherein the weighting function is:
w
(
x
,
s
)
∝
1
[
τ
i
(
x
,
s
)
+
1
]
2
wherein:
x is the spatial coordinate;
s is the shot index; and
τ is the determined time shift for the given trace.
12. The computing apparatus of claim 9 , wherein determining for each trace in the gather the amount of time shift includes:
determining the amount of the time shifts from a plurality of low frequency extended images; and
assigning those low frequency time shifts to the respective traces.
13. The computing apparatus of claim 8 , wherein adaptively focusing the gathers includes iteratively adaptively focusing the gathers before stacking.
14. A non-transitory program storage medium encoded with instructions that, when executed by a processor, perform a method for use in seismic exploration, the method comprising:
accessing a set of seismic data representative of a subterranean geological formation and a subsurface attribute model of the subterranean geological formation;
performing a wavefield extrapolation on the seismic data in the subsurface attribute model;
applying a time-shift extended imaging condition to the extrapolated wavefields;
forming shot-indexed, time shift gathers for each image pixel of the subsurface attribute model from the conditioned extrapolated wavefields;
adaptively focusing the gathers;
stacking the adaptively focused gathers; and
imaging the subterranean geological formation from the stacked, adaptively focused gathers.
15. The program storage medium of claim 14 , wherein executing the adaptive focusing comprises:
determining for each trace in the gather the amount of time shift to apply to yield a zero time lag for that trace; and
applying the determined time shift to each respective trace.
16. The program storage medium of claim 15 , wherein executing the adaptive focusing further comprises weighting each trace by a weight that is a decreasing function of the magnitude of a magnitude of a determined time shift for a given trace.
17. The program storage medium of claim 16 , wherein the weighting function is:
w
(
x
,
s
)
∝
1
[
τ
i
(
x
,
s
)
+
1
]
2
wherein:
x is the spatial coordinate;
s is the shot index; and
τ is the determined time shift for the given trace.
18. The program storage medium of claim 14 , wherein executing the adaptive focusing further comprises weighting each trace by a weight that is a decreasing function of the magnitude of a magnitude of a deter mined time shift for a given trace.
19. The program storage medium of claim 18 , wherein the weighting function is:
w
(
x
,
s
)
∝
1
[
τ
i
(
x
,
s
)
+
1
]
2
wherein:
x is the spatial coordinate;
s is the shot index; and
τ is the determined time shift for the given trace.
20. The program storage medium of claim 15 , wherein determining for each trace in the gather the amount of time shift includes:
determining the amount of the time shifts from a plurality of low frequency extended images; and
assigning those low frequency time shifts to the respective traces.