Stochastic inverse tomography of highly heterogeneous aquifers

Abstract:

Aquifer properties such as permeability are often highly heterogeneous with significant variations occurring at various scales: for example from the kilometer to the centimeter scale and sometimes smaller. For many hydrogeologic applications, an attempt is made to infer the aquifer properties by observing the aquifer’s response to stimulation (e.g., pumping, tracer injection, etc.) at a number of monitoring wells that are sparsely distributed across a field whose length scale is often tens, hundreds, or thousands of meters. Here the scales of observations are defined by the distances between the wells used for stimulation and observation. This disparity in scales of aquifer heterogeneity versus observations makes it difficult, and perhaps impossible, for inverse methods to reproduce the small scale heterogeneities that are present in the actual aquifer. Most inverse methods that are in use produce fields (e.g., permeability fields) that are much smoother than we expect the actual field to be, essentially failing to represent the small scale heterogeneity at all. This failure is important because small scale heterogeneities can have a significant impact on transport (e.g., trapping of tracers/contaminants in small, low-permeability lenses). We present an approach to inverse analysis that is capable of representing these small scale heterogeneities. The approach inverts for a smooth field with a fixed (i.e., it is not part of the inversion) noise added to the smooth field to represent the small scale heterogeneities. We note that although this approach does represent small scale heterogeneities, it does not reproduce the actual small scale heterogeneities that exist in the aquifer. The representation of the small scale heterogeneities is stochastic, and, because of this, we call the method stochastic inverse tomography.