The study of wave motion in a bounded elastic medium using a Monte Carlo ray tracing approach.

Abstract

Computer algorithms are developed and the solutions of the displacement-field components are plotted for three different locations of the receiver for each model. Numerical results are compared with the generalized ray analyses conducted by Pao and Pao et al. for the same geometry and the load conditions.

In this investigation, the displacement response of a bounded elastic medium is analyzed using a ray-tracing method coupled to a Monte-Carlo technique. The medium is an elastic, homogeneous, and isotropic solid bounded by six arbitrarily inclined stress-free plane surfaces. The wave-front curvature transformations due to the mode conversions at the free surfaces are derived. For sampling the reflected rays at the free surface, the Russian-roulette algorithm is utilized.

Numerical calculations are given for the following three models: (a) A two-dimensional plate with stress-free boundaries. The force is an impulsive dilatational wave located at the point (0,0). (b) A two-dimensional plate with stress-free boundaries. The force is a unit normal stress acting at the point (0,15) of the free surface. The force and the receiver are located at the opposite sides of the plate. (c) A two-dimensional plate with stress-free boundaries. The force is a unit normal stress acting at the point (0,15) of the free surface. The force and the receiver are located at the upper surface of the plate.