Generation of a Stochastic Binary Field That Fits a Given Heterogeneity Power Spectrum

TL;DR

This paper introduces a new method to generate stochastic binary fields that match a given heterogeneity power spectrum, enabling better modeling of heterogeneous systems in geosciences.

Contribution

A novel constructive procedure to generate binary fields fitting a specified heterogeneity spectrum and to assess the feasibility of binary mixing.

Findings

The method can test the feasibility of binary mixing for a given spectrum.

It constrains properties of mixing components and modal proportions.

Applicable to various geoscience problems.

Abstract

Incomplete binary mixing of two components can form a heterogeneous assemblage in space. The heterogeneity power spectrum of the assemblage can be frequently obtained. However, it is unknown if a stochastic binary field exists to generate the observed spectrum. We propose a novel and powerful constructive procedure for this purpose. The procedure allows us not only to test whether certain binary mixing is feasible but also to tightly constrain the properties of the mixing components and the modal proportion. The method should find wide applications in many branches of geosciences.