An efficient, three-dimensional, anisotropic, fractional Brownian motion and truncated fractional Levy motion simulation algorithm based on successive random additions
Fluid flow and solute transport in the subsurface are known to be strongly influenced by the heterogeneity of aquifers. To simulate aquifer properties, such as logarithmic hydraulic conductivity (ln(K)) variations, fractional Brownian motion (fBm) and truncated fractional Levy motion (fLm) were suggested previously. In this paper, an efficient three-dimensional successive random additions (SRA) algorithm is presented to construct spatial ln(K) distributions. A convenient conditioning procedure using the inverse-distance-weighting method as a data interpolator, which forces the generated fBm or truncated fLm realization to go through known data points, is included also. The proposed method coded in the FORTRAN language, and a complementary code for verifying fractal structure in fBm realizations based on dispersional analysis, are validated carefully through numerical tests. These software packages allow one to go beyond the stationary stochastic process hydrology of the 1980s to the new geo-statistics of nonstationary stochastic processes with stationary increments, as embodied by the stochastic fractals fBm, fLm and their associated increments fGn and fLn. (C) 2002 Elsevier Science Ltd. All rights reserved.
fractional brownian motion fractional levy motion hydraulic conductivity conditioning anisotropy