2.5D forward and inverse modeling for interpreting low-frequency electromagnetic measurements

Abstract

We present 2.5D fast and rigorous forward and inversion algorithms for deep electromagnetic (EM) applications that include crosswell and controlled-source EM measurements. The forward algorithm is based on a finite-difference approach in which a multifrontal LU decomposition algorithm simulates multisource experiments at nearly the cost of simulating one single-source experiment for each frequency of operation. When the size of the linear system of equations is large, the use of this noniterative solver is impractical. Hence, we use the optimal grid technique to limit the number of unknowns in the forward problem. The inversion algorithm employs a regularized Gauss-Newton minimization approach with a multiplicative cost function. By using this multiplicative cost function, we do not need a priori data to determine the so-called regularization parameter in the optimization process, making the algorithm fully automated. The algorithm is equipped with two regularization cost functions that allow us to reconstruct either a smooth or a sharp conductivity image. To increase the robustness of the algorithm, we also constrain the minimization and use a line-search approach to guarantee the reduction of the cost function after each iteration. To demonstrate the pros and cons of the algorithm, we present synthetic and field data inversion results for crosswell and controlled-source EM measurements.

The Effect of Antenna Incident Field Distribution on Microwave Tomography Reconstruction

“…The utilized incident field distribution in the inversion algorithm will be the same incident field distribution that has been used to collect that scattering data set. Specifically, Sections 4.1 and 4.3 use the multiplicative-regularized Gauss-Newton inversion (MR-GNI) algorithm [23,24] to invert the data sets. Section 4.2, on the other hand, deals with shape and location reconstruction using the binary implementation of the MR-GNI algorithm as presented in [25].…”

Identification of subsurface structures using electromagnetic data and shape priors

“…The main aim with the research presented in this paper is to develop a computationally efficient inversion methodology for CSEM data that is able to preserve prior information about geological strata, and we will therefore apply a model-based representation (see, e.g., [2][3][4][5][6][7][8][9]) of the unknown electric conductivity field. Alternatively, a pixel-based representation (see, e.g., [10][11][12][13]) could have been used, although the tendency for smoothing out the resulting conductivity field makes it less attractive. Additionally, large computational costs are associated with running second-order gradient-based optimization algorithms with a pixel-based representation, due to the large number of parameters.…”

Electromagnetic imaging of three-dimensional dielectric objects with Newton minimization

“…Another approach is to solve an inverse-scattering problem in the frequency domain [2]. This method has a wide range of applications, e.g., underground resource detection [3]. If the investigated problem has such a geometry that is invariant in one direction, the three-dimensional (3-D) inverse-scattering problem can be transformed into a two-dimensional problem.…”