Abstract

A Combined Iterative Transform Method for Wave Propagation in Random Media

H.Waubke (Acoustics Research Institute, Austrian Academy of Sciences, Vienna, Austria)

e-mail: holger.waubke@oeaw.ac.at

A method is presented to combine Fourier transform and finite elements for layers with randomly varying shear modulus. Fourier transform is applied to the horizontal direction. The finite element method in transformed space is used for the vertical direction. The assumption of a stochastic process of the shear modulus in the horizontal direction is new. This direction is simplified by the usage of a DFT that gives a periodicity in space. Karhunen-Loeve expansion separates the stochastic process of the shear modulus into a series of random variables and functions. The random variables are the base for the polynomial chaos. The functional dependency on the transform coordinate leads to a loss of orthogonality of the Fourier transform. Instead of a chaos polynomial transform that extends the solution matrix used formerly for a process in vertical direction, an iterative solution is applied, that needs only for the iterative solution of the mean valued deterministic finite element model and a series of load vectors that depend on the stochastic displacement vector. The dependency comes from the change of the non-orthogonal stochastic parts of the system matrix to the load side and its dependency on the displacement vector. Numerical results are presented.

Section : 8