On shear-wave triplication in transversely isotropic media

The exact solution to the problem of qSV triplication in homogenous transversely isotropic media has been long known, but the result is algebraically complex and is seldom applied in practice. We present an appropriate approximation (not assuming weak qSV-anisotropy) that simplifies the conditions for the onset of off-axis triplication as anisotropy is increased, identifying the anisotropy parameter σ as the controlling parameter. It follows that commonly reported surface-seismic P-wave move-out measurements imply that many formations in the earth's sedimentary crust support off-axis qSV triplications. For typical Vp/Vs velocity ratios and a horizontally stratified earth, however, off-axis qSV triplications appear to only occur for shear-wave incidence angles too far from the vertical to be sampled by surface-seismic converted-wave survey geometries.