Estimating Transmissivity in One‐Dimensional Heterogeneous Aquifers With Groundwater Head Data: From Time or Frequency Perspectives

Abstract

Time series of groundwater head in a semi‐infinite, one‐dimensional confined aquifer due to variable boundary forcing can be decomposed into two signals: head rise from a sudden boundary increase, and head fluctuation from boundary sinusoidal changes. Analyzed from time and frequency domains, these signals reconstruct the original series via convolution or superposition, offering insights into transmissivity (T). In this study, the time‐domain head data and frequency‐domain fluctuation data are used to estimate T. For a two‐zone aquifer with a pair of T values, the information content on T from the head at a given time is similar to that of the amplitude of the fluctuation at a certain frequency. In addition, the phase shift of the fluctuation also contains non‐redundant information on T. We introduce two concepts, that is, equivalent and interpreted T, to describe representative T, with which homogeneous aquifer can produce the same head/amplitude/phase shift signal and its temporal/frequency derivative as those observed in a heterogeneous aquifer. By applying Fréchet kernels as a spatial weight, we provide a connection between equivalent/interpreted T and the heterogeneous spatial distribution of T. Based on Monte Carlo simulations, we compare the equivalent/interpreted T against the local‐scale geometric mean T. The equivalent T from high‐frequency phase shift produces the better estimation. Finally, we investigate the effectiveness of observations at different frequencies and times for estimating heterogeneous T during a hydraulic tomography survey. The results show the amplitude and phase shift of multi‐frequency fluctuations can better characterize aquifer heterogeneity than head from the time‐domain perspective alone.