Probability Field Simulation: A Retrospective

The practical advantages and theoretical disadvantages of P-field simulation are reviewed in the light of more than a decade of application and research since it was first introduced. A case study example highlights the enduring attractions of the algorithm: its flexibility and speed. When first introduced, probability field simulation was well-suited to certain types of problems that were not well handled by other simulation algorithms available. In particular, it adapted well to the situation where a priori local distributions were available. As it rapidly gained practical acceptance, largely because of its speed, “P-field” simulation was also dismissed by some as a procedure lacking a proper theoretical foundation — more of a clever algorithmic trick than a properly conceived approach to stochastic spatial simulation. In the past decade, the advantages and shortcomings of the procedure have been illuminated through continued widespread application and theoretical research. This paper begins with an overview of the theoretical background and the usual practical implementation of P-field simulation. It then discusses theoretical concerns and assesses their practical implications. A mining case study example illustrates two enduring strengths of P-field simulation: flexibility and speed. 2 Overview and implementation Let F [u; z] denote the cumulative distribution function (cdf) at location u of an attribute Z. Any simulated value, zsim, represents a specific quantile of this local cdf: the z-value at which F [u; z] reaches a probability p(u): zsim = F −1 [u; p(u)] (1) The p values are not spatially independent; this would preclude reproduction of almost any desired spatial autocorrelation in Z .I nstead, thep values must be regarded as a realization of a random function P (u), and simulated with an appropriate pattern of spatial continuity.