Geophysical Institute of the ASCR

Comparison of synthetics calculated by the QI approximation of the
coupling ray theory and by the Fourier pseudospectral method
A possible test of accuracy of an approximate method is comparison of its results with results of
a more accurate method on models, at which both methods are applicable. The approximate method in
our case is the quasi-isotropic (QI) approximation, see Pšenčík and Dellinger (2001) of the coupling
ray theory (see, e.g., Bulant et al., 2004). The QI approximation was designed to study S-wave
propagating in inhomogeneous weakly anisotropic media, in which neither the ray theory for isotropic
media nor the ray theory for anisotropic media work properly. The QI approximation is also expected
to work in directions, in which S-wave phase velocities are close to each other, it is in singular
directions of S waves and in their vicinities. In these directions, the standard ray theory fails. The
Fourier method is assumed to be the more accurate method. It does not suffer from limitations of the
ray methods. It can be, for example, applied, in singular directions of S waves.
Fig. 30. Comparison of QI (red) and Fourier (black) seismograms generated by a vertical point force in a VSP
experiment in a vertically inhomogeneous HTI model with the axis of symmetry deviating from the vertical plane
containing the source and the borehole.
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