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A Nonlinear Inversion Method for 3DElectromagnetic Imaging Using Adjoint Fields
 Inverse Problems
, 1999
"... Electromagnetic Imaging is modeled as an inverse problem for the 3D system of Maxwell's equations of which the isotropic conductivity distribution in the domain of interest has to be reconstructed. The main application we have in mind is the monitoring of conducting contaminant plumes out of ..."
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Cited by 13 (1 self)
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Electromagnetic Imaging is modeled as an inverse problem for the 3D system of Maxwell's equations of which the isotropic conductivity distribution in the domain of interest has to be reconstructed. The main application we have in mind is the monitoring of conducting contaminant plumes out of surface and borehole electromagnetic imaging data. The essential feature of the method developed here is the use of adjoint elds for the reconstruction task, combined with a splitting of the data into smaller groups which dene subproblems of the inversion problem. The method works iteratively, and can be considered as a nonlinear generalization of the Algebraic Reconstruction Technique (ART) in xray tomography. Starting out from some initial guess for the conductivity distribution, an update for this guess is computed by solving one forward and one adjoint problem of the 3D Maxwell system at a time. Numerical experiments are performed for a layered background medium in which one or t...
NETWORK APPROXIMATION FOR EFFECTIVE VISCOSITY OF CONCENTRATED SUSPENSIONS WITH COMPLEX GEOMETRY ∗
"... Abstract. We study suspensions of rigid particles (inclusions) in a viscous incompressible fluid. The particles are close to touching one another, so that the suspension is near the packing limit, and the flow at small Reynolds number is modeled by the Stokes equations. The objective is to determine ..."
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Cited by 4 (2 self)
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Abstract. We study suspensions of rigid particles (inclusions) in a viscous incompressible fluid. The particles are close to touching one another, so that the suspension is near the packing limit, and the flow at small Reynolds number is modeled by the Stokes equations. The objective is to determine the dependence of the effective viscosity 〈μ 〉 on the geometric properties of the particle array. We study spatially irregular arrays, for which the volume fraction alone is not sufficient to estimate the effective viscosity. We use the notion of the interparticle distance parameter δ, based on the Voronoi tessellation, and we obtain a discrete network approximation of 〈μ〉, asδ → 0. The asymptotic formulas for 〈μ〉, derived in dimensions two and three, take into account translational and rotational motions of the particles. The leading term in the asymptotics is rigorously justified in two dimensions by constructing matching upper and lower variational bounds on 〈μ〉. While the upper bound is obtained by patching together local approximate solutions, the construction of the lower bound cannot be obtained by a similar local analysis because the boundary conditions at fluidsolid interfaces must be resolved for all particles simultaneously. We observe that satisfying these boundary conditions, as well as the incompressibility condition, amounts to solving a certain algebraic system. The matrix of this system is determined by the total number of particles and their coordination numbers (number of neighbors of each particle). We show that the solvability of this system is determined by the properties of the network graph (which is uniquely defined by the array of particles) as well as by the conditions imposed at the external boundary.
Incremental methods for simple problems in time series: algorithms and experiments
 In Ninth International Database Engineering and Applications Symposium (IDEAS 2005
, 2005
"... A time series (or equivalently a data stream) consists of data arriving in time order. Single or multiple data streams arise in fields including physics, finance, medicine, and music, to name a few. Often the data comes from sensors (in physics and medicine for example) whose data rates continue to ..."
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Cited by 3 (3 self)
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A time series (or equivalently a data stream) consists of data arriving in time order. Single or multiple data streams arise in fields including physics, finance, medicine, and music, to name a few. Often the data comes from sensors (in physics and medicine for example) whose data rates continue to improve dramatically as sensor technology improves and as the number of sensors increases. So fast algorithms become ever more critical in order to distill knowledge from the data. This paper presents our recent work regarding the incremental computation of various primitives: windowed correlation, matching pursuit, sparse null space discovery and elastic burst detection. The incremental idea reflects the fact that recent data is more important than older data. Our StatStream system contains an implementation of these algorithms, permitting us to do empirical studies on both simulated and real data. 1
Low Frequency Electromagnetic Fields in High Contrast Media
"... . Using variational principles we construct discrete network approximations for the Dirichlet to Neumann or Neumann to Dirichlet maps of high contrast, low frequency electromagnetic media. 1 Introduction Imaging of the electrical conductivity and permittivity of a heterogeneous body by means of low ..."
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Cited by 2 (1 self)
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. Using variational principles we construct discrete network approximations for the Dirichlet to Neumann or Neumann to Dirichlet maps of high contrast, low frequency electromagnetic media. 1 Introduction Imaging of the electrical conductivity and permittivity of a heterogeneous body by means of lowfrequency electrical or electromagnetic field measurements is an inverse problem, often called "impedance tomography", "electromagnetic induction tomography", "magnetotellurics" and so on. Applications arise in many areas, for example in medicine with diagnostic imaging, in nondestructive testing, in oil recovery, in subsurface flow monitoring, in underground contaminant detection, etc. In this paper we will focus attention on imaging heterogeneous media with large variations in the magnitude of their electrical properties. This is relevant in many geophysical applications where the conductivity can vary over several orders of magnitude. For example, a dry rock matrix is insulating compared...
ASYMPTOTIC APPROXIMATION OF THE DIRICHLET TO NEUMANN MAP OF HIGH CONTRAST CONDUCTIVE MEDIA
, 2013
"... Abstract. We present an asymptotic study of the Dirichlet to Neumann map of high contrast composite media with perfectly conducting inclusions that are close to touching. The result is an explicit characterization of the map in the asymptotic limit of the distance between the particles tending to ze ..."
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Abstract. We present an asymptotic study of the Dirichlet to Neumann map of high contrast composite media with perfectly conducting inclusions that are close to touching. The result is an explicit characterization of the map in the asymptotic limit of the distance between the particles tending to zero.
Error of the network approximation for densely packed
, 2001
"... composites with irregular geometry ..."
Discussion Reply to comment on “Electrical Tomography of La Soufrière of Guadeloupe Volcano: Field experiments, 1D inversion and
, 2007
"... We thank Linde and Revil for their comment [1] (hereafter referred to as L&R) which gives us the opportunity to provide more details about our ..."
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We thank Linde and Revil for their comment [1] (hereafter referred to as L&R) which gives us the opportunity to provide more details about our
Crosssection electrical resistance tomography of La Soufrière of Guadeloupe lava dome
"... The electrical resistivity distribution at the base of La Soufrière of Guadeloupe lava dome is reconstructed by using transmission electrical resistivity data obtained by injecting an electrical current between two electrodes located on opposite sides of the volcano. Several pairs of injection elect ..."
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The electrical resistivity distribution at the base of La Soufrière of Guadeloupe lava dome is reconstructed by using transmission electrical resistivity data obtained by injecting an electrical current between two electrodes located on opposite sides of the volcano. Several pairs of injection electrodes are used in order to constitute a data set spanning the whole range of azimuths, and the electrical potential is measured along a cable covering an angular sector of ≈ 120 ◦ along the basis of the dome. The data are inverted to perform a slice electrical resistivity tomography (SERT) with specific functions implemented in the EIDORS open source package dedicated to electrical impedance tomography applied to medicine and geophysics. The resulting image shows the presence of highly conductive regions separated by resistive ridges. The conductive regions correspond to unconsolidated material saturated by hydrothermal fluids. Two of them are associated with partial flank collapses and may represent large reservoirs that could have played an important role during past eruptive events. The resistive ridges may represent massive andesite and are expected to constitute hydraulic barriers. Key words: Electrical properties – tomography – image processing – Volcanic hazards and risks 1
Small Interparticle Distance of the Effective Properties of a HighContrast Random Dispersed Composite
"... We consider a highcontrast twophase composite such as a ceramic/polymer composite or a fiberglass composite. Our objective is to determine the dependence of the effective conductivity A ̂ (or the effective dielectric constant or the effective shear modulus) of the composite on the random location ..."
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We consider a highcontrast twophase composite such as a ceramic/polymer composite or a fiberglass composite. Our objective is to determine the dependence of the effective conductivity A ̂ (or the effective dielectric constant or the effective shear modulus) of the composite on the random locations of the inclusions (ceramic particles or fibers) when the concentration of the inclusions is high. We consider a twodimensional model and show that the continuum problem can be approximated by a discrete random network (graph). We use variational techniques to provide rigorous mathematical justification for this approximation. In particular, we have shown asymptotic equivalence of the effective constant A ̂ for the discrete and continuum models in the limit when the relative interparticle distance goes to zero. We introduce the geometrical interparticle distance parameter using Voronoi tessellation, and emphasize the relevance of this parameter due to the fact that for irregular (nonperiodic) geometries it is not uniquely determined by the volume fraction of the inclusions.