I present a method of obtaining spatially-varying pseudo derivative
operators with application to wave mode separation in anisotropic
media. The main idea is to utilize polarization vectors constructed
in the wavenumber domain using the local medium parameters and then
transform these vectors back to the space domain.
The main advantage of applying the pseudo derivative operators in the
space domain constructed in this way is that they are suitable for
heterogeneous media.
The wave mode separators obtained using this method are
spatially-variable filtering operators and can be used to separate
wavefields in VTI media with an arbitrary degree of anisotropy. This
methodology is applicable for elastic RTM in heterogeneous anisotropic
media.