Abstract During the last century, electrical geophysics has been transformed from a simple resistivity method to a modern technology that uses complex data-acquisition systems and high-performance computers for enhanced data modeling and interpretation. Not only the methods and equipment have changed but also our ideas about the geoelectrical models used for interpretation have been modified tremendously. This paper describes the evolution of the conceptual and technical foundations of EM methods. It outlines a framework for further development, which should focus on multitransmitter and multireceiver surveys, analogous to seismic data-acquisition systems. Important potential topics of future research efforts are in the areas of multidimensional modeling and inversion, including a new approach to the formulation and understanding of EM fields based on flux and voltage representation, which corresponds well to geophysical experiments involving the measurement of voltage and flux of electric and magnetic fields.

Summary Parameter estimation in geoelectromagnetics aims to obtain the most important parameters of a well-defined conductivity model of the Earth. These parameters are features of typical geological structures, such as depth and size of conductive or resistive targets, angle of dike inclination and its length, and conductivity of anomalous bodies. We develop this approach through regularized nonlinear optimization. We use finite differences of forward computations and Broyden’s updating formula to compute sensitivities (Frechet or partial derivatives) for each parameter. To estimate the optimal step length, we apply line search, with a simple and fast parabolic correction. Our inversion also includes Tikhonov’s regularization procedure. We use our method to study measurements of the magnetic fields from a conductive body excited by a loop source at the surface. Keeping the depth of the body constant, we estimate the horizontal coordinates of the body from three components of the magnetic field measured in a borehole. These measurements accurately determine the direction to the conductive target.