Abstract
SUMMARY Difference geophysical tomography (e.g. radar, resistivity and seismic) is used increasingly for imaging fluid flow and mass transport associated with natural and engineered hydrologic phenomena, including tracer experiments, in situ remediation and aquifer storage and recovery. Tomographic data are collected over time, inverted and differenced against a background image to produce ‘snapshots’ revealing changes to the system; these snapshots readily provide qualitative information on the location and morphology of plumes of injected tracer, remedial amendment or stored water. In principle, geometric moments (i.e. total mass, centres of mass, spread, etc.) calculated from difference tomograms can provide further 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 parametrization (image pixels) result in tomograms which are subject to artefacts such as smearing or pixel estimates taking on the sign opposite to that expected for the plume under study. Here, we demonstrate a novel parametrization 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 design an inverse problem that (1) is overdetermined and computationally efficient because the image is described by only a few parameters, (2) produces tomograms consistent with expected plume behaviour (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. We demonstrate the approach in a series of numerical examples basedonstraight-raydifference-attenuationradarmonitoringofthetransportofanionictracer, and show that the methodology outlined here is particularly effective when limited data are available.
Highlights
The ability of difference tomography to resolve a plume—or any target—depends on (1) the physics underlying the measurements and approximations made in the forward model for inversion, (2) the survey geometry and acquisition rate, which are commonly limited in geophysical problems, (3) the measurement errors, (4) the parametrization of the inverse problem, (5)
The resolving power of tomography is a well-studied problem (Backus & Gilbert 1968; Menke 1984; Friedel 2003; Sheng & Schuster 2003; Day-Lewis & Lane 2004; Day-Lewis et al 2005), but relatively little attention has been paid in the literature to the particular problem of dynamically imaging plumes
In an application of time-lapse electrical resistivity tomography (ERT) to monitor a fluid tracer in the unsaturated zone, Binley et al (2002) observed a 50 per cent discrepancy between the injected mass and the mass recovered by ERT; this mass-balance error was attributed to variable ERT sensitivity and poor resolution of tracer in portions of the tomogram
Summary
Recent advances in geophysical instrumentation, inversion approaches and software have enabled unprecedented insights into diverse, natural and engineered hydrologic processes including transport of ionic tracers (e.g. Slater et al 1997; Kemna et al 2002; Day-Lewis et al 2003; Vanderborght et al 2005; Cassiani et al 2006; Day-Lewis et al 2006; Singha & Gorelick 2006), infiltration (e.g. Binley et al 2001; Deiana et al 2008; Looms et al 2008a,b; Nimmo et al 2009), submarine groundwater discharge (Swarzenski et al 2006, 2007; Nguyen et al 2009; Henderson et al 2010), aquifer storage and recovery (Singha et al 2007) and in situ engineered aquifer remediation (e.g. Lane et al 2004; Williams et al 2005; Lane et al 2006; Hubbard et al 2008; Chen et al 2009; Williams et al 2009; Johnson et al 2010). The philosophies underlying these parametrizations differ, with some designed to capitalize on the measurement configuration and physics (e.g. natural pixels), and others to take advantage of knowledge of the imaged target (e.g. moments, geometric objects) Underlying these efforts are objectives of (1) reducing the number of inversion parameters, facilitating rapid time-lapse or 3-D imaging (e.g. reducing both acquisition and inversion time), (2) matching the inversion parameters to quantities of engineering or geological relevance (e.g. anomaly centre of mass, magnitude and size), facilitating use of inversion results by non-geophysicists and (3) defining parameters that reduce the need for regularization and prevent the inversion from producing spurious anomalies inconsistent with the structure under study. The method outlined here performs well in the presence of limited data
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