Inversion of time domain three-dimensional electromagnetic data

We present a general formulation for inverting time domain electromagnetic data to recover a 3-D distribution of electrical conductivity. The forward problem is solved using finite volume methods in the spatial domain and an implicit method (Backward Euler) in the time domain. A modified Gauss–Newton strategy is employed to solve the inverse problem. The modifications include the use of a quasi-Newton method to generate a pre-conditioner for the perturbed system, and implementing an iterative Tikhonov approach in the solution to the inverse problem. In addition, we show how the size of the inverse problem can be reduced through a corrective source procedure. The same procedure can correct for discretization errors that inevidably arise. We also show how the inverse problem can be efficiently carried out even when the decay time for the conductor is significantly larger than the repetition time of the transmitter wave form. This requires a second processor to carry an additional forward modelling. Our inversion algorithm is general and is applicable for any electromagnetic field  ( E , H , d B / dt )  measured in the air, on the ground, or in boreholes, and from an arbitrary grounded or ungrounded source. Three synthetic examples illustrate the basic functionality of the algorithm, and a result from a field example shows applicability in a larger-scale field example.