A Stochastic Approach to Tracer Tomography

Abstract:

Hydraulic and tracer tomography have evolved as a family of promising hydrogeological field investigation techniques to assess spatial variability of hydraulic parameters. Tomography uses a set of different source-receiver combinations to spatially resolve heterogeneity in an aquifer, which would not be possible using standard field methods such as single well pumping tests. While hydraulic tomography is based on hydraulic pressure variations, tracer tomography uses the tracer travel time from a source (point injection) to a receiver (sampling point) to determine hydraulic properties. Implementation of tracer tests in the field is more challenging than hydraulic testing, and thus the potential of tracers for tomographic aquifer reconstruction is much less explored. Moreover, detailed simulation of solute transport during inversion is computationally demanding and strategies are needed to overcome this bottleneck. The proposed new methodology addresses shortcomings of available inversion procedures, such as simplified conceptual assumptions, limited application windows, and high computational demand. It is based on the use of pilot points, which are widely applied for calibration of highly parameterized groundwater models. These points are, however, not treated as pre-defined, fixed variables. Our proposed implementation dynamically adjusts the number and coordinates of the pilot points during iterative inversion. This yields a self-adaptive procedure that is tailored to the specific structures reconstructed in a tomogram. For the description of tracer transport, the use of an expressive, computationally efficient proxy is suggested. This proxy makes use of travel time calculations based solely on steady state and a path-finding algorithm that strongly speeds up the inversion procedure. This concept is embedded in a stochastic inversion framework, from which an ensemble of inverted models, which honor all available hydraulic and solute transport data, is derived. The proposed methodology is capable of integrating complex and soft geological knowledge, and various types of field observations. Its viability is demonstrated on both a synthetic example and a tomographic field test in a sedimentary aquifer.