EIT Reconstruction Algorithms: Pitfalls, Challenges and Recent Developments

We review developments, issues and challenges in Electrical Impedance Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT, Manchester 2003. We focus on the necessity for three dimensional data collection and reconstruction, efficient solution of the forward problem and present and future reconstruction algorithms. We also suggest common pitfalls or ``inverse crimes'' to avoid.Comment: A review paper for the 4th Workshop on Biomedical Applications of EIT, Manchester, UK, 200

High-order regularized regression in Electrical Impedance Tomography

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral transform, that maps changes in the electrical properties of a domain to their respective variations in boundary data. Using perturbation theory the transform is approximated to yield a high-order misfit unction which is then used to derive a regularized inverse problem. In particular, we consider the nonlinear problem to second-order accuracy, hence our approximation method improves upon the local linearization of the forward mapping. The inverse problem is approached using Newton's iterative algorithm and results from simulated experiments are presented. With a moderate increase in computational complexity, the method yields superior results compared to those of regularized linear regression and can be implemented to address the nonlinear inverse problem

Ensemble Kalman Filter Assimilation of ERT Data for Numerical Modeling of Seawater Intrusion in a Laboratory Experiment

Seawater intrusion in coastal aquifers is a worldwide problem exacerbated by aquifer overexploitation and climate changes. To limit the deterioration of water quality caused by saline intrusion, research studies are needed to identify and assess the performance of possible countermeasures, e.g., underground barriers. Within this context, numerical models are fundamental to fully understand the process and for evaluating the effectiveness of the proposed solutions to contain the saltwater wedge; on the other hand, they are typically affected by uncertainty on hydrogeological parameters, as well as initial and boundary conditions. Data assimilation methods such as the ensemble Kalman filter (EnKF) represent promising tools that can reduce such uncertainties. Here, we present an application of the EnKF to the numerical modeling of a laboratory experiment where seawater intrusion was reproduced in a specifically designed sandbox and continuously monitored with electrical resistivity tomography (ERT). Combining EnKF and the SUTRA model for the simulation of density-dependent flow and transport in porous media, we assimilated the collected ERT data by means of joint and sequential assimilation approaches. In the joint approach, raw ERT data (electrical resistances) are assimilated to update both salt concentration and soil parameters, without the need for an electrical inversion. In the sequential approach, we assimilated electrical conductivities computed from a previously performed electrical inversion. Within both approaches, we suggest dual-step update strategies to minimize the effects of spurious correlations in parameter estimation. The results show that, in both cases, ERT data assimilation can reduce the uncertainty not only on the system state in terms of salt concentration, but also on the most relevant soil parameters, i.e., saturated hydraulic conductivity and longitudinal dispersivity. However, the sequential approach is more prone to filter inbreeding due to the large number of observations assimilated compared to the ensemble size

Tomographic inversion of time-domain resistivity and chargeability data for the investigation of landfills using a priori information

In this paper, we present a new code for the modelling and inversion of resistivity and chargeability data using a priori information to improve the accuracy of the reconstructed model for landfill. When a priori information is available in the study area, we can insert them by means of inequality constraints on the whole model or on a single layer or assigning weighting factors for enhancing anomalies elongated in the horizontal or vertical directions. However, when we have to face a multilayered scenario with numerous resistive to conductive transitions (the case of controlled landfills), the effective thickness of the layers can be biased. The presented code includes a model-tuning scheme, which is applied after the inversion of field data, where the inversion of the synthetic data is performed based on an initial guess, and the absolute difference between the field and synthetic inverted models is minimized. The reliability of the proposed approach has been supported in two real-world examples; we were able to identify an unauthorized landfill and to reconstruct the geometrical and physical layout of an old waste dump. The combined analysis of the resistivity and chargeability (normalised) models help us to remove ambiguity due to the presence of the waste mass. Nevertheless, the presence of certain layers can remain hidden without using a priori information, as demonstrated by a comparison of the constrained inversion with a standard inversion. The robustness of the above-cited method (using a priori information in combination with model tuning) has been validated with the cross-section from the construction plans, where the reconstructed model is in agreement with the original design

Inversion of multiconfiguration complex EMI data with minimum gradient support regularization: A case study

Frequency-domain electromagnetic instruments allow the collection of data in different configurations, that is, varying the intercoil spacing, the frequency, and the height above the ground. Their handy size makes these tools very practical for near-surface characterization in many fields of applications, for example, precision agriculture, pollution assessments, and shallow geological investigations. To this end, the inversion of either the real (in-phase) or the imaginary (quadrature) component of the signal has already been studied. Furthermore, in many situations, a regularization scheme retrieving smooth solutions is blindly applied, without taking into account the prior available knowledge. The present work discusses an algorithm for the inversion of the complex signal in its entirety, as well as a regularization method that promotes the sparsity of the reconstructed electrical conductivity distribution. This regularization strategy incorporates a minimum gradient support stabilizer into a truncated generalized singular value decomposition scheme. The results of the implementation of this sparsity-enhancing regularization at each step of a damped Gauss-Newton inversion algorithm (based on a nonlinear forward model) are compared with the solutions obtained via a standard smooth stabilizer. An approach for estimating the depth of investigation, that is, the maximum depth that can be investigated by a chosen instrument configuration in a particular experimental setting is also discussed. The effectiveness and limitations of the whole inversion algorithm are demonstrated on synthetic and real data sets

Magnetic, electrical, and GPR waterborne surveys of moraine deposits beneath a lake: A case history from Turin, Italy

Bathymetry and bottom sediment types of inland water basins provide meaningful information to estimate water reserves and possible connections between surface and groundwater. Waterborne geophysical surveys can be used to obtain several independent physical parameters to study the sediments. We explored the possibilities of retrieving information on both shallow and deep geological structures beneath a morainic lake by means of waterborne nonseismic methods. In this respect, we discuss simultaneous magnetic, electrical, and groundpenetrating radar (GPR) waterborne surveys on the Candia morainic lake in northerly Turin (Italy).We used waterborne GPR to obtain information on the bottom sediment and the bathymetry needed to constrain the magnetic and electrical inversions. We obtained a map of the total magnetic field (TMF) over the lake from which we computed a 2D constrained compact magnetic inversion for selected profiles, along with a laterally constrained inversion for one electrical profile. The magnetic survey detected some deep anomalous bodies within the subbottom moraine. The electrical profiles gave information on the more superficial layer of bottom sediments. We identify where the coarse morainic material outcrops from the bottom finer sediments from a correspondence between high GPR reflectivity, resistivity, and magnetic anomalie

Lipschitz stability for the electrostatic inverse boundary value problem with piecewise linear conductivities

We consider the electrostatic inverse boundary value problem also known as electrical impedance tomography (EIT) for the case where the conductivity is a piecewise linear function on a domain $\Omega\subset\mathbb{R}^n$ and we show that a Lipschitz stability estimate for the conductivity in terms of the local Dirichlet-to-Neumann map holds true.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1405.047

Nonlinear magnetotransport shaped by Fermi surface topology and convexity in WTe2

The nature of Fermi surface defines the physical properties of conductors and many physical phenomena can be traced to its shape. Although the recent discovery of a current-dependent nonlinear magnetoresistance in spin-polarized non-magnetic materials has attracted considerable attention in spintronics, correlations between this phenomenon and the underlying fermiology remain unexplored. Here, we report the observation of nonlinear magnetoresistance at room temperature in a semimetal WTe2, with an interesting temperature-driven inversion. Theoretical calculations reproduce the nonlinear transport measurements and allow us to attribute the inversion to temperature-induced changes in Fermi surface convexity. We also report a large anisotropy of nonlinear magnetoresistance in WTe2, due to its low symmetry of Fermi surfaces. The good agreement between experiments and theoretical modeling reveals the critical role of Fermi surface topology and convexity on the nonlinear magneto-response. These results lay a new path to explore ramifications of distinct fermiology for nonlinear transport in condensed-matter