We present a new technique, based on the Direct Solution Method (DSM)
[Geller et al., 1990; Hara et al., 1991; Geller and Ohminato, 1994], f
or calculating SH (toroidal) synthetic seismograms for spherically sym
metric, isotropic, media. No asymptotic approximations are used and th
e synthetics, which fully include both body and surface waves, can be
computed for a broad range of frequencies. Our algorithm accurately ha
ndles sources that require discontinuities in the vertically dependent
part of the displacement. We use matrix operators that minimize the n
umerical error of the solutions. An example synthetic profile is prese
nted for a 600km deep source in the IASP91 model for the period range
4-5000s.