3D near-to-surface conductivity reconstruction by inversion of VETEM data using the distorted Born iterative method

Abstract

In this paper, three-dimensional (3D) subsurface imaging by inversion of data obtained from the very early time electromagnetic system (VETEM) is presented. The distorted Born iterative method is used to match the internal nonlinear property of the 3D inversion problem. The frequency explored is from 0.062 to 3.052 MHz, the high end of which is beyond the induction range. No reported 3D approximation works well for this frequency range, thus the 3D stabilized bi-conjugate-gradient fast Fourier transform method is invoked as the forward solver, in which the total current formulation other than the induced current formulation is used to achieve higher stability. With the use of the reciprocity theorem, the Fréchet derivatives are computed rapidly by two calls to the forward solver. Tikhonov regularization is used so that the contribution from small singular values is suppressed to warrant a smooth solution. The selection of regularization parameter follows a heuristic rule as used in the Levenberg-Marquardt algorithm so that the iteration is stable. Processing the whole data set at one time is prohibitively time-consuming and expensive. The localized property of the geophysical problem is exploited to decompose the original large problem into a number of smaller subproblems. The nonlinear inversion is implemented subsequently on each subproblem first. The inverted conductivity profiles are then combined together to arrive at a complete conductivity image under the whole data domain. The proposed method is first tested on synthetic data and then applied to the VETEM data from the Pit 9 complex of the Department of Energy.

Two-Dimensional Microwave Tomographic Algorithm for Radar Imaging Through Multilayered Media

“…In [9][10][11] the reconstruction of the target permittivity distribution is cast as the minimization of a non-quadratic cost function and solved with global or deterministic optimization methods. To improve the computation efficiency, the distorted Born iterative method (DBIM) and Born iterative method (BIM) dealing with intermediate scatterers are developed in [12,13]. BIM and DBIM start with the first-order Born inversion result and are solved iteratively by incrementally correcting the estimated contrast function in every iteration step.…”

Low-frequency dipolar excitation of a perfect ellipsoidal conductor

“…This work is motivated by geophysical applications [1], [2] (mining prospection), [3] (detection of cavity), or other underground detections [4], [5] (UXO -Unexploded Ordnance) [6], where one wants to localize and/or to estimate size, orientation and conductivity of the embedded structure. Generally, an inverse scheme is used to find either a smooth surface of the structure [7] or the parameters of an equivalent object [8], [9] using iterative methods. Most of the proposed solutions use meshing methods for the scattering problem that have to be evaluated at each iteration, resulting in a large time-consuming numerical process.…”

A Controlled-Site Comparison of Microwave Tomography and Time-Reversal Imaging Techniques for GPR Surveys

“…Different TR-based processing techniques are available that can also be applied to GPR problems, including TR-DORT [35], TR-MUSIC [42,52] and TR hybrid methods [53]. Likewise, several augmentations can be made to the MT implementation considered here, including the use of high-order Born approximations and iterative MT reconstructions [54][55][56]. The use of controlled-site data to compare all such options is beyond the scope of the present work and will be the subject of future studies.…”