Interpretation and inversion of low‐frequency head observations

Abstract

An asymptotic expression for transient head variations, valid at low‐frequencies, forms the basis for an efficient scheme for estimating hydraulic conductivity. The critical computational step is equivalent to solving the governing equation for steady state head. Thus, model parameter sensitivities, relating changes in head to changes in hydraulic conductivity, of the fully transient problem can be computed with the equivalent of four steady state head computations. A comparison of model parameter sensitivities computed using the low‐frequency asymptotic approach and sensitivities computed using a purely numerical approach indicates good agreement. An inversion of synthetic hydraulic tomography data indicates that it is possible to estimate overall permeability variations using the technique. In an actual application to truncated crosswell pressure tests from the Raymond field site, we image two high permeability fracture zones, in agreement with a conceptual model of the region. The location of the two fracture zones correlates with the position of transmissive fractures, as measured by borehole conductivity logs.