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.