Equivalent Hydraulic Conductivity of Heterogeneous Aquifers Estimated by Multi-Frequency Oscillatory Pumping

Aquifers are a vital part of our water cycle and modeling groundwater flow is paramount for a number of environmental applications. Modeling requires the estimation of aquifer properties, which is mostly achieved by field pumping tests. Oscillatory pumping tests involve repeated pumping and injection of aquifer water, which generates a periodic head signal. We investigate the estimation of equivalent hydraulic conductivity ((Formula presented.)) in an oscillatory pumping test with a multi-frequency excitation. Synthetic head data are generated from numerical simulations of pumping in heterogeneous aquifers and an inverse method is applied to estimate (Formula presented.). The method involves a Fast Fourier Transform (FFT) analysis for obtaining the spatial distribution of head amplitude and then matching the amplitudes using a semi-analytical solution of a homogeneous aquifer with conductivity (Formula presented.). We investigate the dependence of (Formula presented.) on pumping frequency in view of the previous literature, which has found increasing values for higher frequencies. We did not find this increase in (Formula presented.) with frequency and minor variations which were observed appear to be a result of numerical error. The result implies that oscillatory pumping field tests can be used for (Formula presented.) estimation without any corrections for frequency dependence.