Flexible scaling model for use in random field simulation of hydraulic conductivity

A new fractal scaling model is proposed for use in aquifer heterogeneity modeling and simulation. The new model, which is obtained by subordination of fractional Brownian motion, provides a unifying framework for scaling models of heterogeneity in that it includes previous scaling models as special cases and can also be tuned continuously between these models. Choosing the subordinator to be a lognormal distribution results in a non-Gaussian scaling model with a moderate degree of variability that matches data better than previous fractal scaling models, thus providing more accurate heterogeneity representations for use in stochastic flow and transport predictions. Two new stochastic simulation algorithms are constructed from the new models, one based on sequential simulation algorithms and the other based on probability field simulation. Both algorithms can be made conditional on available measurements.