Wavelet analysis of multiscale permeabilities in the subsurface

Abstract

Wavelet analysis is a new mathematical theory and calculation method for separating and sorting structures on different time scales at different times, and on different spatial scales at different locations. This method has been used to identify spatial heterogeneity of geologic structures and to estimate spatial scales of geophysical parameters in the subsurface. We used the integral wavelet transform to analyze the spatial variability of permeability in the alluvial fan deposits in Radioactive Waste Management Site Area 5 of Nevada. The mother wavelet which we used is the “Mexican Hat” function. A wavelet variance is defined to detect the characteristic scales of non‐periodically spaced spatial structures. Results showed heterogeneity of spatial structure in permeability at hierarchical scales and difference of scales between transects in spatially distributed permeability. These multiscale features of spatial variability of permeability provide an explanation for the strong quasi‐periodic behavior in the horizontal and vertical semivariograms. A comparison among wavelets, fractals, and traditional geostatistics is also given.