Polynomial chaos expansion vs. Monte Carlo simulation in a stochastic analysis of wave propagation

Abstract

The paper deals with the propagation of a stochastic wave in an elastic medium using the example of a seismic wave in a ground medium. Identification of subsoil parameters is never exact or complete which justifies the use of random field models or random variable models for input data; thus, the response of the subsoil is also random. In this paper and in the context of random variables, the focus is on a sensitivity analysis addressing the question of how the uncertainty of the input data (subgrade parameters) influences the obtained results (displacements). Two different methods of stochastic analysis are presented—the intrusive polynomial chaos approach supported by the Galerkin projection and Monte Carlo simulation—and compared by using an example of wave propagation in the elastic half-plane. Consistency in the results of both approaches has been achieved; however, the calculation efficiencies differ. The advantages and disadvantages of both approaches are discussed. The upper subsoil layer influences the variances of the random solutions much more than does the lower layer.