Title: Focused time-lapse inversion of radio and audio magnetotelluric data,
Abstract: Geoelectrical techniques are widely used to monitor groundwater processes,
while surprisingly few studies have considered audio (AMT) and radio (RMT)
magnetotellurics for such purposes. In this numerical investigation, we analyze
to what extent inversion results based on AMT and RMT monitoring data can be
improved by (1) time-lapse difference inversion; (2) incorporation of
statistical information about the expected model update (i.e., the model
regularization is based on a geostatistical model); (3) using alternative model
norms to quantify temporal changes (i.e., approximations of l1 and Cauchy norms
using iteratively reweighted least-squares), (4) constraining model updates to
predefined ranges (i.e., using Lagrange Multipliers to only allow either
increases or decreases of electrical resistivity with respect to background
conditions). To do so, we consider a simple illustrative model and a more
realistic test case related to seawater intrusion. The results are encouraging
and show significant improvements when using time-lapse difference inversion
with non l2 model norms. Artifacts that may arise when imposing compactness of
regions with temporal changes can be suppressed through inequality constraints
to yield models without oscillations outside the true region of temporal
changes. Based on these results, we recommend approximate l1-norm solutions as
they can resolve both sharp and smooth interfaces within the same model.