A FRACTAL-BASED STOCHASTIC INTERPOLATION SCHEME IN SUBSURFACE HYDROLOGY

The need for a realistic and rational method for interpolating sparse data sets is widespread. Real porosity and hydraulic conductivity data do not vary smoothly over space, so an interpolation scheme that pres erves irregularity is desirable. Such a scheme based on the properties of fractional Brownian motion (fBm) and fractional Gaussian noise (fG n) is presented. Following the methodology of Hewett (1986), the autho rs test for the presence of fGn in a set of 459 hydraulic conductivity (K) measurements. The use of rescaled-range analysis strongly indicat ed the presence of fGn when applied to the natural logs of the K data, and the resulting Hurst coefficient (H) was determined to be 0.82. Th is H value was then used along with the methodology of successive rand om additions to generate a fBm K interpolation (realization) in the ve rtical cross section between two wells. The results appeared realistic , and the overall methodology presented herein may serve as an improve d basis for a conditional simulation approach to the study of various transport processes in porous media. It is now known that fGn- and fBm -related processes are among the most common spatial and temporal vari ations found in nature, although a common physical origin, if any, rem ains obscure,