|
|
|
| Interferometric imaging condition for wave-equation migration | |
|
Next: Appendix B
Up: Appendix A
Previous: Appendix A
Consider a medium whose behavior is completely defined by the acoustic
velocity, i.e. assume that the density
is
constant and the velocity
fluctuates around a homogenized
value
according to the relation
|
(12) |
where the parameter characterizes the type of random fluctuations
present in the velocity model, and denotes their strength.
Consider the covariance orientation vectors
defining a coordinate system of arbitrary orientation in space. Let
be the covariance range parameters in the
directions of , and , respectively.
We define a covariance function
|
(16) |
where
is a distribution shape parameter and
|
(17) |
is the distance from a point at coordinates
to the
origin in the coordinate system defined by
.
Given the IID Gaussian noise field
, we obtain the random
noise
according to the relation
|
(18) |
where are wavenumbers associated with the spatial
coordinates , respectively. Here,
are Fourier transforms of the covariance function and the noise
,
denotes Fourier transform, and
denotes inverse Fourier transform. The
parameter controls the visual pattern of the field, and
control the size and orientation of a
typical random inhomogeneity.
|
|
|
| Interferometric imaging condition for wave-equation migration | |
|
Next: Appendix B
Up: Appendix A
Previous: Appendix A
2013-08-29