An approximate inversion algorithm for time-domain electromagnetic surveys

Time-domain electromagnetic surveys typically comprise numerous soundings, and any useful interpretation procedure must be rapid enough to cope with the subsequent large amounts of data. Even though geological targets invariably display a degree of three-dimensionality, it is often possible to obtain information about their structure from an Earth model constructed from the results of one-dimensional inversions of each sounding. We derive from this process an approximate inversion procedure. The observations from all soundings are averaged to generate a representative data-set which is then inverted using a rigorous one-dimensional algorithm to produce a layered background model. As by-products of the inversion, the sensitivities for the background model are available, as well as the value of the trade-off parameter in the objective function being minimized. Model updates, which do not involve re-calculating the full sensitivities, are then carried out for each sounding. Each update requires only the solution of a small matrix equation, and a few forward modellings. Two or three updates generally result in a marked decrease in the objective function, and hence an improvement in the model for that sounding. The technique is illustrated with synthetic data generated from a three-dimensional model, and with field data collected in Venezuela. The inversion procedure is tailored to produce piecewise-constant models, and to use a robust measure of data misfit. For the field example, rigorous one-dimensional inversions provide the model for comparison. The approximate inversion is shown to provide much of the same information, but in a substantially reduced amount of time. (C) 1999 Elsevier Science B.V. All rights reserved.