Space-time boundary reflections in elastic media
Kristopher A. Innanen
In 2017 potential monitoring applications of an unusual but perfectly real type of seismic reflection, namely that from time-boundaries (and mixed space-time boundaries), were discussed. The idea is simply that reflections occur from jumps in medium properties, and this holds for jumps along the time coordinate axis just as surely as for jumps along one of the space coordinate axes. Time boundary reflections are intrinsically “normal incidence” scattering events. Analysis was carried out in order to plausibly discuss oblique time-boundary reflections; these were argued to be possible only if the boundary had both space and time components. In this short note we further this interpretation by demonstrating that if elastic waves (P- or S-) encounter pure time boundaries, no conversion occurs. However, if the boundary includes spatial variations as will as time variations, becoming, as it were, oblique time reflections, conversions do occur.