A statistical approach to the inverse problem of aquifer hydrology: 2. Case study

Neuman, Shlomo P.; Fogg, Graham E.; Jacobson, E.A.

doi:10.1029/wr016i001p00033

Cited by 63 publications

(13 citation statements)

References 9 publications

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“…This procedure opens exciting perspective in geohydrology like, for example, to determine hydraulic conductivity around a pumping well. Indeed, if one knows the pressure distribution everywhere during a pumping test, well established inverse groundwater modeling allows to determine the distribution of the hydraulic conductivity and storativity around the borehole [e.g., Cooley , 1977, 1979; Neuman and Yakowitz , 1979; Neuman et al , 1980; Yeh and Yoon , 1981; Kitanidis and Vomvoris , 1983; Yeh et al , 1983; Loaiciga and Marino , 1987]. However, the piezometric surface is usually not well constrained due to a lack of observation wells.…”

Section: Introductionmentioning

confidence: 99%

Principles of electrography applied to self‐potential electrokinetic sources and hydrogeological applications

Revil

Naudet

Nouzaret

et al. 2003

Water Resources Research

172

160

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[1] The electrical potential field passively recorded at the ground surface of the Earth (and termed self-potential) can be analyzed to determine the shape and the depth of the piezometric surface. The coupling between hydraulic flow and electrical current density is electrokinetic in nature. The electrokinetic coupling coefficient entering into the integral equation relating the depth of the water table to self-potential signals is analyzed for various types of porous materials. It is simply related to the electrical conductivity of the pore water. In steady state conditions each element of the water table can be seen as an elementary dipole with an inclination locally perpendicular to the water table and strength proportional to the water table elevation. Then, we propose three methods to obtain the shape and range of possible depths of the water table from the study of the selfpotential distribution recorded at the ground surface. The nonuniqueness of the solution is removed if one knows either the electrokinetic coupling coefficient or the water table at one location and under the assumption of the spatial homogeneity of the electrokinetic coupling coefficient. Two field cases are discussed to show the success of the proposed methods for estimating the shape and depth of the water table at two different scales of investigations. They concern the study of self-potential signals associated with the shape of the water table in the vicinity of a pumping well and in the flank of the Kilauea volcano.INDEX TERMS: 1832 Hydrology: Groundwater transport; 5109 Physical Properties of Rocks: Magnetic and electrical properties; 5139 Physical Properties of Rocks: Transport properties; 5114 Physical Properties of Rocks: Permeability and porosity; KEYWORDS: self-potential, hydraulic charge, water table, electrokinetic, streaming potential, tomography Citation: Revil, A., V. Naudet, J. Nouzaret, and M. Pessel, Principles of electrography applied to self-potential electrokinetic sources and hydrogeological applications, Water Resour.

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Section: Introductionmentioning

confidence: 99%

Principles of electrography applied to self‐potential electrokinetic sources and hydrogeological applications

Revil

Naudet

Nouzaret

et al. 2003

Water Resources Research

172

160

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show abstract

“…The corresponding inverse problem may be ill-posed due to a lack of sufficient information about the state of the system (pressure, flux) and the presence of errors (measurement, interpretation and computation). It can therefore yield nonunique and unstable parameter estimates [Neuman, 1973;Neuman and Yakowitz, 1979;Neuman et al, 1980;Neuman, 1980;Neuman, 1986a, 1986b].…”

Section: Parameterization and Inverse Approachmentioning

confidence: 99%

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

Vesselinov¹,

Neuman²,

Illman³

2001

Water Resources Research

Self Cite

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“…Among them, one must first mention the work by Neuman and Carrera. After the first steps taken in 1973, and some additional attempts (Neuman and Yakowitz, 1979;Neuman et al, 1980), the year 1980 was a turning point in Neuman's work. At that point, after Marsily (1978), he adopted, in his optimization algorithm, the calculation of the gradient of the objective function based on the adjoint method proposed by Chavent (1971Chavent ( , 1975.…”

Section: Maximum Likelihoodmentioning

confidence: 97%

Four decades of inverse problems in hydrogeology

Marsily¹,

Delhomme²,

Coudrain³

et al. 2000

Theory, Modeling, and Field Investigation in Hydrogeology: A Special Volume in Honor of Shlomo P. Neumans 60th Birthday

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We review the main stages of the evolution of ideas and methods for solving the inverse problem in hydrogeology; i.e., the identification of the transmissivity field in single-phase flow from piezometric data, in mainly steady-state and, occasionally, transient flow conditions. We first define the data needed to solve an inverse problem in hydrogeology, then describe the numerous approaches that have been developed over the past 40 years to solve it, emphasizing the major contributions made by Shlomo P. Neuman. Finally, we briefly discuss fitting processes that start by defining the unknown field as geological images (generated by Boolean or geostatistical methods).The early attempts at solving the inverse problem were direct, i.e., the transmissivity field was directly determined by using stream lines of the flow and inverting the flow equation along these lines. Faced with the poor results obtained in this manner, hydrogeologists have tried many different ways of minimizing the balance error representing an integral of the mass-balance error for each mesh for a given transmissivity field. These attempts were accompanied by constraints imposed on the transmissivity field in order to avoid instabilities.The idea then emerged that the unknown field should reproduce the local observations of the pressure at the measurement points instead of minimizing a balance error. Second, it should also satisfy a condition of plausibility, which means that the transmissivity field obtained through the inverse solution should not deviate too far from an a priori estimate of the real transmissivity field. This a priori notion led to the inclusion of a Bayesian approach resulting in the search for an optimal solution by maximum likelihood, as expounded later.Simultaneously, the existence of locally measured values in the transmissivity field (obtained by pumping tests) allowed geostatistical methods to be used in the formulation of the problem; the result of this innovation was that three major approaches came into being: (1) the definition of the a priori transmissivity field by kriging; (2) the method of cokriging;(3) the pilot point method. Furthermore, geostatistics made it possible to pose the inverse problem in a stochastic framework and to solve an ensemble of possible and equally probable fields, each of them equally acceptable as a solution.

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A statistical approach to the inverse problem of aquifer hydrology: 2. Case study

Cited by 63 publications

References 9 publications

Principles of electrography applied to self‐potential electrokinetic sources and hydrogeological applications

Principles of electrography applied to self‐potential electrokinetic sources and hydrogeological applications

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

Four decades of inverse problems in hydrogeology

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