Introduction to Spatial Simulation

The SIM2D Procedure

Introduction to Spatial Simulation

The purpose of spatial simulation is to produce a set of partial realizations of a spatial random field (SRF) $Z(s), s \in D \subset \mathcal{R}^2$ in a way that preserves a specified mean $\mu(s)=E[Z(s)]$ and covariance structure C_z(s₁-s₂) = cov(Z(s₁),Z(s₂)).

The realizations are partial in the sense that they occur only at a finite set of locations (s₁, s₂, ... ,s_n). These locations are typically on a regular grid, but they can be arbitrary locations in the plane.

There are a number of different types of spatial simulation and associated computational methods. PROC SIM2D produces simulations for continuous processes in two dimensions. This means that the possible values of the measured quantity Z(s₀) at location s₀ = (x₀,y₀) can vary continuously over a certain range.

An additional assumption, needed for computational purposes, is that the spatial random field Z(s) is Gaussian.

Spatial simulation is different from spatial prediction, where the emphasis is on producing a point estimate at a given grid location. In this sense, spatial prediction is local. In contrast, spatial simulation is global; the emphasis is on the entire realization (Z(s₁), Z(s₂), ... ,Z(s_n)).

Given the correct mean $\mu(s)$ and covariance structure C_z(s₁-s₂), SRF quantities that are difficult or impossible to calculate in a spatial prediction context can easily be approximated by repeated simulations.

Chapter Contents
Previous
Next
Top