In the past a FWF project dealing with the basics of Stochastic Transformation Methods was executed at the ARI. Explicitly the Karhunen Loeve Expansion and the Transformation of a polynomial Chaos were applied in the wave number domain. The procedure is based on the assumption of Gaussian distributed variables. This assumption shall be generalized to arbitrary random variables.
The assumption of a wave number domain limits the model to a horizontally layered half space. This limitation shall be overcome by Wavelets kernels in the transformation instead of Fourier kernels. The aim is the possibility to calculated one sided statistical distributions for the physical parameters and arbitrary boundaries with the new method.