Identification of the permeability distribution in soil by hydraulic tomography

Abstract

A tomographical method is presented that allows the reconstruction of the structure of soil layers between two boreholes. If the soil is water saturated, the transient field equation for pore water pressure S(x) delta tu(x,t)- Del .(k(x) Del u(x,t))=Q can be used to reconstruct the soil structure from its permeability k(x). The transient potential field u(x, t) is controlled by hydraulic dipoles (point source and point sink). The positions of source and sink are varied over both boreholes. Pore water pressure observations are used as data for the inverse problem. Uniqueness problems are discussed. The forward problem is discretized in a FE algorithm, the inverse problem solved by a standard output least-squares method.

Estimation of heterogeneous aquifer parameters using centralized and decentralized fusion of hydraulic tomography data

“…A relatively recent alternative method for estimating the spatial distribution of aquifer parameters at a high resolution is hydraulic tomography (HT) (Gottlieb and Dietrich, 1995;Butler Jr. et al, 1999;Yeh and Liu, 2000;Berg and Illman, 2011). In HT, an aquifer is stressed at different locations and the responses to these stresses at a network of observation wells are inverted to map the parameters spatially.…”

Three‐dimensional numerical inversion of pneumatic cross‐hole tests in unsaturated fractured tuff: 1. Methodology and borehole effects

“…Whereas they were able to reproduce quite accurately the spatial pattern of synthetic permeabilities, they were less successful in reproducing their magnitudes. The same was true about a study by Gottlieb and Dietrich [1995] We analyze the pneumatic cross-hole test data in two ways: (1) by considering pressure records from individual borehole monitoring intervals one at a time, while treating the rock as being spatially uniform, and (2) by considering pressure records from multiple tests and borehole monitoring intervals simultaneously, while treating the rock as being randomly heterogeneous. The first approach yields a series of equivalent air permeabilities and air-filled porosities for rock volumes having length scales ranging from meters to tens of meters, represented nominally by the distances between corresponding injection and monitoring intervals.…”

“…More recently, the concept of hydraulic tomography has been explored by Bohling [1993], Tosaka et al [1993], Gottlieb and Dietrich [1995] [see also Gottlieb, 1992], Masumoto et al [1995,1996,1998], Butler et al [1999], and Yeh and Liu [2000]. Tosaka et al [1993] used an inverse model to analyze simultaneously a series of transient cross-hole tests in two-and threedimensional synthetic media.…”

Joint interpretation of sequential pumping tests in unconfined aquifers

“…They include numerical studies [e.g., Gottlieb and Dietrich, 1995;Yeh and Liu, 2000;Bohling et al, 2002;Yeh, 2005, 2006;Fienen et al, 2008;Ni and Yeh, 2008;Castagna and Bellin, 2009;Xiang et al, 2009;Liu and Kitanidis, 2011], followed by laboratory sandbox studies [e.g., Liu et al, 2002;Brauchler et al, 2003;Illman et al, 2007;Liu et al, 2007;Illman et al, 2008;Yin and Illman, 2009;Illman et al, 2010;Berg and Illman, 2011a;Illman et al, 2012] and then experimental field studies [e.g. Bohling et al, 2007;Li et al, 2007;Straface et al, 2007;Cardiff et al, 2009;Illman et al, 2009;Berg and Illman, 2011b;Brauchler et al, 2011;Huang et al, 2011].…”