Multivariate Geostatistical Grid-Free Simulation of Natural Phenomena

Abstract

Conventional geostatistical simulation methods are implemented in a way that is inherently gridded and sequence dependent. A variant of spectral simulation method is revisited from a linear model of regionalization standpoint to simulate realizations of coregionalized variables that are expressed as a function of the coordinates of the simulation locations, data values, and imposed spatial structure. The resulting grid-free simulation (GFS) methodology expresses a realization at any set of regularly or irregularly distributed nodes. GFS consists of two main steps: unconditional grid-free simulation and dual cokriging-based conditioning. The unconditional multivariate simulation is represented by a linear model of coregionalization, where weights are derived from the covariance function of the modeled system, and random factors are computed as a sum of equally weighted line processes within a turning bands paradigm. These stochastic line processes are expressed as a linear model of regionalization, weights are from the Fourier series decomposition of line covariance functions, and random factors have a cosine function form requiring coordinates of simulation locations and the random phases. The resulting conditionally simulated values are uniquely tied to simulation locations by an analytical form. Newly assimilated data change current realizations only locally within the correlation range. The GFS parameters are carefully chosen from a series of examples, and the associated theory is illustrated with a three-dimensional case study.