Spartan gaussian random fields for geostatistical applications: Non-constrained simulations on square lattices and irregular grids

Abstract

Spartan spatial random fields (SSRF’s) are special cases of Gibbs random fields designed for simulating processes with correlated spatial variability. The SSRF’s possess a probability distribution that is determined from “interactions” motivated from physical or geometric constraints, as opposed to data-oriented covariance measures. The interactions involve a frugal set of model parameters, which can be estimated from the data at small computational cost. Potential applications of SSRF’s include the interpolation and simulation of environmental, health, and geophysical data sets, as well image compression. In this paper we develop methods for simulating Spartan fields without constraints on regular lattices and irregular grids in two space dimensions. We focus on the FGC Spartan model that includes fluctuations of a scalar field, its gradient and its curvature, according to a Gaussian energy functional. The methods described can be extended to more general SSRF models with Gaussian fluctuations.