Simulation of lognormal random fields with varying resolution scale and local average for Darcy flow

Abstract

The paper presents a new method for generating isotropic realizations of a random field with varying resolution scales and local block averages in one, two, or three dimensions. The random field has a lognormal distribution as found for the hydraulic conductivity in Darcy's flow in hydrology. We also present a fast method for generating anisotropic realizations of aGaussian random field using superposition of harmonic modes. Both methods are implemented in a software package which is presented. The realizations of the rescaled random field are made up ofupscaled local averages of the underlying random field which are consistentwith the level of resolution and which can be conditioned. The approach is motivated by the need to represent engineering properties aslocal averages and to be able to easily condition the realizations to incorporate known data or to change the resolution within sub-regions. The numerical results show that the method is very efficient computationally.