Using Wavelet Analysis to Investigate Statistical Properties in Hydraulic Conductivity and Head Fields

Wavelet analysis involves an integral transform of, for example, a hydraulic conductivity field, using a wavelet as the kernel of the transform. A wavelet is a function that is non-zero only over a finite region; therefore the wavelet transform analyzes only a subset of the data set. The wavelet is shifted to analyze different subsets of the data set, and it is scaled to analyze different scales of the data set. We perform wavelet analysis and calculate the local wavelet energy spectrum (LWES), which provides information about dominant length scales at each position in the domain. We generate sets of bounded, one-dimensional, stationary hydraulic conductivity fields with known statistical properties and we run numerical flow simulations, with constant head boundaries, using these fields. We use wavelet analysis to analyze the dominate scales in both the hydraulic conductivity fields and resulting non-stationary head fields, and we explore the relationships between dominant scales in the hydraulic conductivity field and dominant scales in flow. We develop analytical solutions for the LWES to corroborate these relationships.