Multiscale electrical impedance tomography

Abstract

[1] Electrical impedance tomography aims to recover the electrical conductivity underground from surface and/or borehole apparent resistivity measurements. This is a highly nonlinear inverse problem, and linearized inverse methods are likely to produce solutions corresponding to local minima of the misfit function to minimize. In the present paper, electrical impedance tomography is addressed through a nonlinear approach, namely, simulated annealing, in order to escape from local minima and to produce conductivity distributions independent of the starting models. Simulated annealing belongs to the Monte Carlo family which needs numerous forward modelings, and particular attention is paid both to the forward numerical solution of the Poisson equation and to the parameterization of the inverse problem, i.e., the way the conductivity distribution is mathematically represented. The 2.5-dimensional forward problem is solved through a multigrid approach which iteratively solves the Poisson equation from large to small scales. In the same spirit, the conductivity model is parameterized in a multiscale way by representing the conductivity distribution with a superimposition of block whose sizes (in suitable units) are integer powers of 2. The multiscale inversion is implemented in a sequential way by first inverting for the conductivity of the coarser blocks and by progressively incorporating finer blocks in the conductivity model. A decision stage based on a sensitivity analysis is performed before incorporating finer blocks in order to optimize the parameterization by not adding unnecessary details into the conductivity model. Both a synthetic example and a field experiment are used to explain the method, and comparisons with a linearized inversion technique are done.

Inversion of polar motion data: Chandler wobble, phase jumps, and geomagnetic jerks

“…[15] Simulated annealing consists in a sequence of Metropolis loops while simultaneously applying a topological transformation to the likelihood L by decreasing a control parameter T traditionally called the temperature [Kirkpatrick et al, 1983;Gibert and Virieux, 1991;Mosegaard and Tarantola, 1995;Pessel and Gibert, 2003]. The transformed likelihood is given by,…”

Joint inversion of gravity and geoelectrical data for groundwater and structural investigation: application to the northwestern part of Sinai, Egypt

“…In the last years the interest in the application of global optimization techniques, for example, genetic algorithm (GA), controlled random search (CRS), SA, etc. to geophysical problems has been increasing and a better convergence to global minimum of the objective functions has been reported by several authors (Kirkpatrick et al 1983;Rothman 1986;Dittmer & Szymansky 1995;Dosso & Oldenburg 1991;Sen & Stoffa 1995;Pessel & Gibert 2003).…”

Identification of sources of potential fields with the continuous wavelet transform: Application to VLF data

“…Both the GBR and GBZ VLF antennas located in Great Britain were used since their northern location ensure good induction effects with a primary field H p perpendicular to the stike of the fault. The VLF tilt Φ was measured every 5 meters along a profile oriented perpendicularly to the fault and where electrical tomography experiments and spontaneous potential measurements have already been done [ Gibert and Pessel , 2001; Pessel and Gibert , 2003].…”