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Part of the Well Tests for Site Characterization Project

Regularized Inversion of Tomographic Pumping Tests Incorporating Geophysical Data Through Smoothing Splines

by Geoffrey C. Bohling

Eos Trans. AGU, 88(52), Fall Meeting Supplement, Abstract H42B-06, 2007

Although simultaneous analysis of multiple hydraulic tests, or hydraulic tomography, can help reduce the nonuniqueness in aquifer parameter estimates relative to conventional single-test analysis, this inverse problem still needs to be regularized in some sensible fashion to yield plausible parameter estimates. A number of investigators have presented techniques for incorporating geophysical data into hydraulic inverse problems, using the geophysical data to help define a parameter zonation or exploiting quantitative correlations between hydrogeological and geophysical parameter fields. Both of these approaches are complicated by the potentially complex and site-specific relationships between geophysical and hydrogeological properties and the relative scarcity of hydrogeological parameter data from which to estimate these relationships. I present a simple approach to incorporating geophysical information into the analysis of tomographic pumping tests for characterization of the hydraulic conductivity (K) field in an aquifer. The fundamental idea is to augment the objective function for the hydraulic inversion with a regularization term that encourages the estimated K field to reflect the geophysical parameter field(s) in some smooth fashion, but without specifying the exact nature of that relationship in advance of the inversion. In this study, I explore the incorporation of ground penetrating radar data into the inversion of tomographic pumping tests in an alluvial aquifer through a regularization term relating the estimated K distribution to the radar property distributions through a smoothing spline model. The geophysical data considered are vertical profiles of radar velocity and attenuation from zero-offset radar surveys between the two pumping wells used in the hydraulic tomography experiments and a velocity tomogram between these two wells.

Kansas Geological Survey, Geohydrology
Placed online Jan. 23, 2009
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