Glorified optics and wave propagation in nonplanar structure

Waves propagating in varying nonplanar structure can produce many interesting phenomena, such as focusing, caustics, and triplications. A high-frequency technique based on the first-motion approximation, referred to as glorified optics, has been developed to generate synthetic seismograms for these types of problems. The technique, in its simplest form, uses the spreading rate of a beam with transmission and reflection coefficients along each possible ray path. The time behavior of each arrival is either that of the original pulse or its Hilbert transform depending on the position of caustics. The geophysically interesting structure of a soft basin over a half-space is investigated in detail by this method. Synthetic seismograms appropriate for various locations are compared with the results of finite difference and finite element methods. The technique appears rich in insight and should prove very useful in modeling problems.