Estimation and simulation of lognormal random fields

Abstract

This paper describes several techniques for estimating and simulating lognormal random fields. The lognormal maximum entropy estimator is presented and compared with simple lognormal kriging. Conditional simulation is performed using the turning bands method combined with simple lognormal kriging. For Gaussian random fields, kriging and the maximum entropy estimator are shown to be equivalent. For lognormal random fields, however, simple lognormal kriging and the lognormal maximum entropy estimator differ. Conditional simulation via simulated annealing is also demonstrated but with generally unsatisfactory results. A hybrid approach involving the turning bands method and simple lognormal kriging yields satisfactory results in the sense that it generates conditional simulations that consistently reproduce conditional marginal distributions.