Forward modelling and inversion of multi‐source TEM data

Abstract

We present a practical formulation for forward modeling and inverting time domain data arising from multiple transmitters. The underpinning of our procedure is the ability to factor the forward modeling matrix and then solve our system using direct methods. We first formulate Maxwell's equations in terms of the magnetic field, H to provide a symmetric forward modeling operator. The problem is discretized using a finite volume technique in space and a backward Euler in time. The MUMPS software package is used to carry out a Cholesky decomposition of the forward operator, with the work distributed over an array of processors. The forward modeling is then quickly carried out using the factored operator. The time savings are considerable and they make the simulations of large ground or airborne data sets feasible and greatly increase our abilities to solve the 3D electromagnetic inverse problem in a reasonable time. The ability to use direct methods also greatly enhances our ability to carry out survey design problems.

Comparison of iterative and direct solvers for 3D CSEM modeling

“…For simulations of realistic survey scenarios involving large 3D volumes of complex geometry and large numbers of sources and receivers, and for inverting 3D data sets, it is crucial to have efficient forward solvers. Various frequency-domain (e.g., Schwarzbach et al, 2011;Streich, 2009;Mulder, 2006;Newman and Alumbaugh, 1995) and time-domain (Oldenburg et al, 2008) finite-difference (FD), finite-element (FE) and integral equation (Zhdanov et al, 2006) modeling schemes have been developed. Finitedifference and finite-element discretizations of Maxwell's equations result in large and sparse systems of linear equations.…”

Practical 3D inversion of large airborne time domain electromagnetic data sets

“…Our inversion is based on a Gauss-Newton method (Oldenburg, et al, 2008), in which a model update ∆m is sought by solving (…”

“…The forward modelling and inversion algorithms used in this research are described in Oldenburg, et al (2008). Maxwell's equations are discretised by a 3D finite volume method in space and a backward Euler method in time.…”

Metalliferous mining geophysics — State of the art after a decade in the new millennium

“…Oldenborger and Oldenburg (2008) reported preliminary results on 3D inversion with high contrasts in conductivity. Oldenburg et al (2008) presented a practical formulation for forward modeling and inverting time-domain data that arise from multiple transmitters. Farquharson (2008) modified the typical minimum-structure inversion algorithm to generate blocky, piecewise-constant earth models, using l1-type measurements of the model structure.…”

“…Even on a 1D section, the 3D inversion provides a better image of the conductivity structure. The group at the University of British Columbia (UBC) also made great strides in modeling and inversion and achieved practical inversion of airborne data (Oldenburg et al, 2005;Holtham and Oldenburg, 2008;Oldenburg et al, 2008;Holtham and Oldenburg, 2010).…”