Glorified optics and wave propagation in nonplanar structure

Abstract

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.

Numerical Modeling for Acoustic Scattering of 3-D Spherical Wavefronts:Implications on Near Source Basin Amplification

“…In the past two decades, different numerical methods for studying scattering effects have been developed. These include the 2-D Aki-Larner method (Aki and Lamer, 1970) and its 3-D extension (Ohori• et al, 1990), the finite difference method (FDM) (Boore, 1972), the finite element method (FEM) (Smith, 1975), the glorified optics method (Hong and Helmberger, 1978), the boundary integral equation method (Dravinski, 1983;Khair et al, 1989;Mossessian and Dravinski, 1990) and the Gaussian bean method (Cerveny et al, 1982). Some hybrid methods which combine the merits of two numerical methods have also been developed ( Van den Berg, 1988).…”