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Publications > Pidlisecky and others, 2010.

A distribution-based parameterization for difference tomographic imaging of solute plumes

A. Pidlisecky (adampid@ucalgary.ca)
Geoscience, University of Calgary, Calgary, AB, Canada

K. Singha (ksingha@psu.edu)
Geosciences, The Pennsylvania State University, State College, PA, USA

F.D. Day-Lewis (daylewis@usgs.gov)
WRD/Office of Groundwater, Branch of Geophysics, U.S. Geological Survey, Storrs, CT, USA

Abstract

Time-lapse geophysical tomography (e.g., cross-well radar, resistivity, and seismic) increasingly is used for imaging fluid flow and mass transport associated with natural and engineered hydrologic phenomena. Tomographic datasets commonly are collected over multiple time intervals and processed to yield 'snapshots' that reveal changes to a system resulting from stimuli (e.g. tracer injections, in-situ remediation, or aquifer storage and recovery). Time-lapse snapshots provide qualitative information on the location and morphology of plumes of injected tracer, remedial amendment, or stored water. However, extracting quantitative information from these snapshots can be challenging. In principle, geometric moments (i.e., total mass, centers of mass, spread, etc.) calculated from difference tomograms can provide quantitative insight into the rates of advection, dispersion, and mass transfer; however, recent work has shown that moments calculated from tomograms are commonly biased, as they are strongly affected by the subjective choice of regularization criteria. Conventional approaches to regularization (Tikhonov) and parameterization (image pixels) result in tomograms that are subject to artifacts such as smearing or pixel estimates taking on the sign opposite to that expected for the plume under study. At the heart of the issues associated with conventional tomographic processing is that the inversion algorithms typically produce a general solution, and are not tailored to the specific problem under consideration. Here, we demonstrate a novel parameterization, specifically developed for imaging plumes associated with hydrologic phenomena. Capitalizing on the mathematical analogy between moment-based descriptors of plumes and the moment-based parameters of probability distributions, we formulate an inverse problem which (1) is overdetermined and computationally efficient because the image is described by only a few parameters (e.g., 8 for the 2D examples here), (2) produces tomograms consistent with expected plume behavior (e.g., changes of one sign relative to the background image), (3) yields parameter estimates that are readily interpreted for plume morphology and offer direct insight into hydrologic processes, and (4) requires comparatively few data to achieve reasonable model estimates. The inversion parameters are related to the plume’s mass, vertical and horizontal centers of mass, vertical and horizontal spreads, rotation from horizontal, and two scaling factors which allow for a truncated distribution. We demonstrate the approach in a series of numerical examples based, for simplicity, on straight-ray difference-attenuation radar monitoring of the transport of an ionic tracer through heterogeneous media, and show that the methodology outlined here is particularly effective when limited data are available.

Final copy as submitted to the American Geophysical Union for publication as: Pidlisecky, A., Singha, K., and Day-Lewis, F.D., 2010, A distribution-based parameterization for difference tomographic imaging of solute plumes, [abs.], in 2010 Fall Meeting, San Francisco, California, 13-17 December 2010, proceedings: American Geophysical Union, Washington, D.C., abstract H13G-08.