Finite integral transforms, which are a specific subset of pseudo – spectral methods are used to reduce the spatial dimensionality of the coupled qP−qS V wave propagation problem in a transversely isotropic (TI) medium to that in one spatial dimension, usually depth, and time. The introduction of an absorbing boundaries, 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 paper, a method based on that presented in Clayton and Engquist (1977) and is employed for the coupled P−S V wave propagation problem in a transversely isotropic medium at the model bottom. The medium considered here is assumed to be radially symmetric and finite Hankel transforms are used to remove the radial coordinate (r). The problem that remains is a coupled problem in depth (z) and time (t). The anisotropic parameters may arbitrarily vary with depth.
View full article as PDF (2.20 Mb)