3D ELECTROMAGNETIC INVERSION USING INTEGRAL EQUATIONS¹

Abstract

ABSTRACT Utilizing electromagnetic data in geophysical exploration work is difficult when measured responses are complicated by the effects of 3D structures. 1D and 2D models may not be capable of accurately simulating the physical processes that contribute to a measured response. 3D conductive‐host modelling is difficult, costly and time‐consuming. Using a 3D inverse procedure it is possible to automate the interpretation of controlled‐source electromagnetic data. This procedure uses an inverse formulation based on frequency‐domain, volume integral equations and a pulse‐basis representation for the internal electrical field and anomalous conductivity. Beginning with an initial model composed of a 3D inhomogeneous region residing in a laterally homogeneous (layered‐earth) geoelectrical section, iterative least‐squares algorithms are used to refine the geometry and the conductivity of the inhomogeneity. This novel approach for 3D electromagnetic interpretation yields a reliable and stable inverse solution provided constraints on how much the variable can change at each iteration are incorporated. Integral‐equation‐based inverse formulations that do not correctly address the non‐linearity of this inverse problem may have poor convergence properties, particularly when dealing with the high conductivity contrasts that are typical of many exploration problems. While problems associated with contamination of the data by random noise and non‐uniqueness of solutions do not usually influence the inverse solution in an adverse manner, problems associated with model inadequacy and errors in an assumed background conductivity structure can produce undesirable effects.