Time-lapse geophysical measurements are widely used to monitor the
movement of water and solutes through the subsurface. Yet commonly used
deterministic least squares inversions typically suffer from relatively
poor mass recovery, spread overestimation, and limited ability to
appropriately estimate nonlinear model uncertainty. We describe herein a
novel inversion methodology designed to reconstruct the
three-dimensional distribution of a tracer anomaly from geophysical data
and provide consistent uncertainty estimates using Markov chain Monte
Carlo simulation. Posterior sampling is made tractable by using a
lower-dimensional model space related both to the Legendre moments of
the plume and to predefined morphological constraints. Benchmark results
using cross-hole ground-penetrating radar travel times measurements
during two synthetic water tracer application experiments involving
increasingly complex plume geometries show that the proposed method not
only conserves mass but also provides better estimates of plume
morphology and posterior model uncertainty than deterministic inversion
results.