Simulation of TwoPhase Random Field by Stochastic Harmonic Functions

Abstract:

In the present paper, a method was proposed to represent the twophase, homogeneous random field. In the first place, the framework of twophase random field was put forward and the homogeneous and isotropic assumption was given as the premise of the work. Then, the stochastic harmonic function (SHF) representation for the Gaussian random field was provided as the intermedia for the twophase random field. With the SHF based random field, the Nataf’s transformation was applied to convert Gaussian random field into the target random field. The Hermite polynomials were used as the numerical solution for the bivariate Gaussian pdf involved in the Nataf’s transformation. Finally, several numerical examples were given to clarify the validity of stochastic harmonic function based twophase random field.

Key words:twophase random field; stochastic harmonic function; Nataf transformation; Hermite polynomials