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![]() | Velocity-independent time-domain seismic imaging using local event slopes | ![]() |
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The main advantage of the oriented approach is
speed. The cost of velocity scanning in conventional processing
(excluding the manual picking labor involved) can be estimated roughly
as the number of scanned velocities times the input data
size. The cost increases dramatically in the case of non-hyperbolic
approximations when more than one parameter needs to be picked. The
cost of local slope estimation with the plane-wave destruction method
is roughly the data size times the number of iterations
times
the filter size
. Typically,
and
,
which is approximately equivalent in cost to scanning
velocities. The next step, however, is dramatically different. Since
each data point is mapped directly to the image instead of being
spread into a wide impulse response, we save the factor in cost
proportional to the size (in samples) of the migration impulse
response. The prestack migration result shown in
Figure 11 was accomplished in under 10 seconds on a
single-node PC.
The cost savings will be reduced somewhat if we take into account more than one local slope (crossing reflection events, diffractions, multiple reflections, etc.) The plane-wave destruction algorithm (Fomel, 2002) can be applied for estimating several interfering data slopes simultaneously. In order to take full advantage of it, data decomposition into local slope components may be required. The curvelet transform (Douma and de Hoop, 2006; Herrmann, 2003) suggests a possible data decomposition approach. To extend the method of curvelet imaging developed by Douma (2006), each local slope component would need to be imaged separately by an oriented approach with its contribution stacked into the final image.
Seismic imaging and velocity estimation is inherently an uncertain
process because of limitations in the data acquisition geometry
and signal bandwidth. In the oriented approach, the uncertainty in
the velocity estimation and in the positioning of seismic reflectors
comes directly from the uncertainty in estimating local event
slopes. Such uncertainty is much easier to estimate
and analyze in the oriented rather than in the traditional
approach thanks to the explicit time-domain
imaging equations 18 and 19
that transform uncertainties in the local event slopes
and
directly into uncertainties of the image point
positioning.
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![]() | Velocity-independent time-domain seismic imaging using local event slopes | ![]() |
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