Deviated well survey geometry can also be processed using the finite-difference method by applying the recorded wavefields as boundary conditions for the grid points corresponding to the receiver locations at the well.
The acoustic migration scheme presented in this paper can be readily extended to elastic reverse-time crosswell migration. In that case, we need to solve the elastic wave equation (Chang and McMechan, 1987).
In processing crosswell seismic data, a thorny problem is that of removing the aliased tube waves. I found two methods in the literature for removing aliased coherent noise such as tube waves. One method given by Zhang et al. (1992), first applies spatial interpolation and then does dip filtering to remove the aliased tube waves. The other scheme given by Turner (1990), applies notch filters directly in the domain of the original data to remove the aliased tube waves. After the aliased tube waves are removed, the data corresponding to the original receiver locations are again interpolated by the 2-D Fourier transform method, with the temporal and depth intervals chosen to satisfy the numerical grid dispersion relation. I assume that the reflection signals are well sampled in the field survey and that only tube waves are aliased.
Another problem is the handling of multi-component wavefields. The seismic source generates both P and S waves. If the field data is hydrophone data, it contains both P and S waves (Beydoun et al., 1989). This data can be dip filtered into P and S wave components. Then each component is processed independently as an acoustic wave. I assume that wave mode conversion is weak, so that the direct P wave excites P wave diffractions, and the direct S wave excites S wave diffractions. The other option is to transform the hydrophone data into a vector particle-displacement field (Cunha Filho, 1992) - vertical and horizontal components - and then feed the vector particle-displacement field data into an elastic migration scheme. If the field data are geophone vector particle-displacement multi-component data, then the data are directly fed into an elastic migration scheme to generate multi-component images.