PULSE DISTORTION IN CAUSTIC REGIONS

It is well known that there is a phase shift of pi-associated with the propagation of a seismic pulse through a focus. But this simple behaviour is true only if the two points at which the pulse is observed lie sufficiently far from the focus, one on either side. Near the focus matters are more complicated and the shape of the pulse may be severely distorted because of diffraction. To examine this problem we consider a pulse generated by a point source and focused by a spherical reflector. Using a general combined method of ray tracing and diffraction, we compute seismograms for receivers lying both inside and outside the focal region, and determine how the shape of the pulse changes on propagation through the focus. To assist the physical interpretation of the numerical results, we also present relevant exact and asymptotic results for comparison.