The separation of wave-modes for heterogeneous TI models requires
non-stationary spatial filtering with large operators (operators of
samples in each dimension are used in this chapter), which is
computationally expensive. The cost is directly proportional to the
size of the model and to the size of each operator. Furthermore, in a
simple implementation, the storage for the separation operators of the
entire model is proportional to the size of the model and to the size
of each operator. Suppose that a 3D elastic TTI model is
characterized by the model parameters
,
, Thomsen
parameters
and
, and symmetry axis tilt angle
and azimuth angle
. For a 3D model of
grid points, if
one assumes that all operators have a size of
samples, the storage for the operators is
grid
points
samples/independent operator
independent operators/grid point
Bytes/sample
TB. This is not feasible in ordinary processing. However,
since there are relatively few medium parameters, i.e.,the
ratio,
,
, and angles
and
, which determine the properties of the operators, one can
construct a look-up table of operators as a function of these
parameters, and search the appropriate operators at every location in
the model when doing wave-mode separation. For example, suppose one
knows that
,
,
, and the symmetry axis tilt angle
and azimuth angle
, one can sample the
ratio at every
,
and
at every
, and the angles at every
. In this case, one only
needs a storage of
combinations of medium parameters
sample/independent
operator
independent operators/combination of medium
parameters
Bytes/sample
GB; this is more manageable,
although it is still a large volume to store.