Isotropic and transversely isotropic media: absorbing bottom boundary conditions
P. F. Daley
When using pseudo – spectral methods to reduce to the spatial dimensionality of the 2.5D coupled qP-qSv wave propagation problem in an isotropic or transversely isotropic (TI) medium to that in one spatial dimension and time, the introduction of an absorbing boundary, at least, at the model bottom is useful in the removal of spurious arrivals. The top model boundary is usually wanted in the numerical calculations and reflections from the model sides may be removed by a judicious choice of model parameters, which does not significantly increase the run time. In this report, a method similar to that presented in Clayton and Engquist (1977, 1980) and is derived for the coupled P-Sv wave propagation problem in a transversely isotropic medium. Finite Hankel transforms are used to remove the radial coordinate (r) in what is assumed to be a radially symmetric medium. The problem that remains is a coupled problem in depth(z), where the anisotropic parameters may arbitrarily vary, in depth and time(t).