Approximate calculation of low‐frequency three‐dimensional magnetotelluric responses using a multiple plate model

Abstract

The numerical methods now used to calculate the magnetotelluric (MT) response of three‐dimensional (3-D) conductive inhomogeneities are still expensive in terms of computing cost. This is a more severe problem in many actual field conditions where multiple conductors exist. There is then a clear need for the development of faster algorithms for data interpretation. We can rapidly compute the 3-D MT response of a multiple‐conductor structure embedded in a layered earth at low frequencies using an approximate algorithm where each conductor is simulated by a set of plates. There are two limitations to the technique. The first low‐frequency limitation is a requirement that the induction number of any plate in the model be small compared with unity. The second condition specifies that the range from an observation point on the surface of the earth to a typical plate must be small compared with the skin depth in the layered background medium. These conditions allow us to ignore local self‐induction within the plates and mutual induction between the plates and the host medium. The secondary anomalous fields generated by any plate are assumed to be due to a distribution of current dipoles in the plane of the plate. The strengths of the distributed dipoles are found by solving a Fredholm integral equation of the second kind with the layered earth MT electric field at depth as the driving function. MT responses obtained with our approximate algorithm for three prismatic models compare favorably with previously published data obtained with complete algorithms for the same models. The use of the technique to model multiple conductors is illustrated with controlled source MT data collected at the Cavendish Test Site.