New advances in three dimensional transient electromagnetic inversion

Inversion of transient electromagnetic (TEM) data sets to image the subsurface three-dimensional (3-D) electrical conductivity and magnetic permeability properties can be done directly in the time domain. The technique, first introduced by Wang et al. (1994) for causal and diffusive electromagnetic fields and subsequently implemented by Zhdanov and Portniaguine (1997) in the framework of iterative migration, is based upon imaging methods originally developed for seismic wavefields (Claerbout, 1971; Tarantola, 1984). In this paper we advance the original derivations of Wang et al. (1994) and Zhdanov and Portniaguine (1997) to treat non-causal TEM fields, as well as correct a flaw in the theory for treatment of magnetic field data. Our 3D imaging scheme is based on a conjugate-gradient search for the minimum of an error functional involving EM measurements governed by Maxwell's equations without displacement currents. Treatment for magnetic field, voltage (time derivative of the magnetic field) and electric field data are given. The functional can be computed by propagating the data errors back into the model in reverse time along with a DC field, sourced by the integrated data errors over the measurement time range. By correlating these fields, including the time-integrated back-propagated fields, with the corresponding incident field and its initial value at each image point, efficient computational forms for the gradients are developed. The forms of the gradients allow for additional efficiencies when voltage and electric field data are inverted. In such instances the combined data errors can be back-propagated jointly, significantly reducing the computation time required to solve the inverse problem. The inversion algorithm is applied to the long offset transient electromagnetic measurement (LOTEM) configuration thereby demonstrating its capability in inverting non-causal field measurements of electric field and voltage, sourced by a grounded wire, over complex structures. Findings also show that migration, without iteration or preconditioning, is not an effective imaging strategy; reconstructions at the first inversion iteration bear little resemblance to simple or complex test models.