Detection of Leaks in Underground Storage Tanks Using Electrical Resistance Methods

Ramirez, Abelardo; Daily, William; Binley, Andrew; LaBrecque, Douglas; Roelant, David

doi:10.4133/jeeg1.3.189

Cited by 146 publications

(76 citation statements)

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“…The inverse conductivity problem has applications in subsurface flow monitoring and remediation [25,27,56,64], underground contaminant detection [26,57], nondestructive evaluation [30,77,78], and a medical imaging technique known as electrical impedance tomography (EIT) (see [24] for a review article on EIT). In EIT the domain Ω is often a cross-section of the body, such as a patient's chest.…”

Section: Introductionmentioning

confidence: 99%

Direct Reconstructions of Conductivities from Boundary Measurements

Mueller¹,

Siltanen²

2003

SIAM J. Sci. Comput.

116

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Abstract. The problem of reconstructing an unknown electric conductivity from boundary measurements has applications in medical imaging, geophysics, and nondestructive testing. A. Nachman [Ann. of Math. (2), 143 (1996), pp. 71-96.] proved global uniqueness for the two-dimensional inverse conductivity problem using a constructive method of proof. Based on this proof, Siltanen, Mueller, and Isaacson [Inverse Problems, 16 (2000), pp. 681-699] presented a new numerical reconstruction method that solves the nonlinear problem directly without iteration. The method was verified with nonnoisy rotationally symmetric examples. In this paper the method is extended by introducing a new regularization scheme, which is analyzed theoretically and tested on symmetric and nonsymmetric numerical examples containing computer simulated noise.

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Section: Introductionmentioning

confidence: 99%

Direct Reconstructions of Conductivities from Boundary Measurements

Mueller¹,

Siltanen²

2003

SIAM J. Sci. Comput.

116

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“…In all the experiments we used synthetic data generated by the formula (1.7) to which we added noise. In [27], the authors discuss the issue of measurement accuracy in real data gathering experiments. The level of noise expected in real data, given the present modern equipment is approximately 1%.…”

Section: Numerical Resultsmentioning

confidence: 99%

A multiscattering series for impedance tomography in layered media

Borcea

Ortiz

1999

Inverse Problems

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Abstract. We introduce an inversion algorithm for tomographic images of layered media. The algorithm is based on a multiscattering series expansion of the Green function that, unlike the Born series, converges unconditionally. Our inversion algorithm obtains images of the medium that improves iteratively as we use more and more terms in the multiscattering series. We present the derivation of the multiscattering series, formulate the inversion algorithm and demonstrate its performance through numerical experiments.

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“…The insufficiency of the ERT data to resolve the subsurface is commonly supplied (regularized) by the assumptions of model smoothness (e.g. Labrecque et al, 1996;Fridel, 2003) or blockiness (e.g. Loke et al, 2003).…”

Section: Introductionmentioning

confidence: 99%

“…Binley and Kemna, 2005), engineering geophysics (e.g. Ramirez et al, 1996) or mining exploration (e.g. Oldenburg et al, 1997).…”

Section: Introductionmentioning

confidence: 99%

Constrained electrical resistivity tomography Bayesian inversion using inverse Matérn covariance matrix

2017

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Bayesian inversion using maximum a posteriori (MAP) estimator is a quantitative approach that has been successfully applied to the electrical resistivity tomography inverse problem. In most approaches, model covariance parameters are generally chosen stationary and isotropic, which assumes statistical homogeneity of studied field.However, the statistical properties of resistivity within the Earth are, in reality, location depend due to spatially varying processes that control the bulk resistivity of rocks, such as water content, porosity, clay content, etc. In order to take into account the spatial variability of the resistivity field, we propose to use the non-stationary Matérn covariance family that is defined through linear stochastic partial differential equations. Two types of prior information are considered, structure orientation and spatially increasing range with increasing depth. The latter is applied successfully on the first synthetic model which aims at retrieving the depth of bedrock and the shape of conductive lens. In the second synthetic example, a conductive dyke model embedded into four layers is used to study the performance of structure orientation. Finally, the proposed approach is used to invert real data measured over an extensively characterized sandy-to-silty aquifer. Structure orientation of this aquifer was firstly determined by applying structure tensor calculated using gradients of gpr image. The introduction of this information gives a resistivity model that is more compatible with the aquifer structure.

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Detection of Leaks in Underground Storage Tanks Using Electrical Resistance Methods

Cited by 146 publications

References 0 publications

Direct Reconstructions of Conductivities from Boundary Measurements

Direct Reconstructions of Conductivities from Boundary Measurements

A multiscattering series for impedance tomography in layered media

Constrained electrical resistivity tomography Bayesian inversion using inverse Matérn covariance matrix

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