Seismograms from Epstein Transition Zones

Spectral amplitudes and theoretical seismograms in the vicinity of caustic and critical points are evaluated numerically for acoustic waves propagating in Epstein media. The amplitude decay into the region beyond the caustic is compared with the asymptotic results and good agreement is found at high frequency. At low frequencies the partial reflection enhances the amplitudes at sub-critical angles and the amplitude increases with decreasing thickness of the transition zone. For a thin transition and low frequencies a head wave exists whose amplitude is inversely proportional to frequency.