Rapid approximate 3D inversion of transient electromagnetic data

Three-dimensional geophysical inversion of EM data aims to give an idealised estimate of the 3D geoelectrical structure of the subsurface which can meaningfully describe a set of observations. Rigorous 3D inversion of time-domain electromagnetic data is an onerous computational challenge, often taking several hours or even days. Motivated by the demand for a rapid and reliable 3D inversion method for TEM data, a fast, approximate 3D inversion of transient electromagnetic data has been developed. The new scheme combines the TEM moments concept and geologically constrained 3D inversion methodology. The TEM moment inversion scheme builds on the pre-existing VPmg potential field modelling and inversion framework which has been extended and modified so as to accommodate approximate 3D TEM inversion. The method has potential for fast, constrained 3D inversion of large airborne TEM data sets. The moment transform of TEM data is a time-weighted integral of the impulse response which accentuates late-time features. Due to the time integration, a TEM decay is effectively reduced to a single value. Depth resolution is lost due to the time integration, which, in effect, converts the nonlinear 3D TEM inversion problem into a linear 3D magnetic inversion problem. Using TEM moments, EM interaction may tolerably be ignored, therefore justifying linear superposition of TEM responses. 3D TEM forward modelling is realised as a linear combmation of a discretised 3D target response and a continuous background response. Superposition of the TEM moment responses of magnetic dipoles, distributed on a cubic mesh, gives the target response whereas the TEM moment response of a half space serves as the background response. Computations are based on analytical formulae. For the approximate scheme, a reduction in accuracy is accepted as a trade-off for much improved speed of calculation. For the 3D inversion, a starting model (or a set of weights) generated from conductivity-depth imaging ( cor) is used to inject depth resolution. The CDis are based on total magnetic field data which facilitates derivation of unambiguous apparent conductivities for fixed-loop TEM. Depth resolution is also recovered by means of geological constraints and depth weighting. The underlying model is both geological and petrophysical, so that the inversion can be focused on selected units. A fast steepest descent method is employed, so that computationally slow matrix inversion is not required Typically, for ground-TEM, the fast approximate 3D inversion completes in minutes, thus facilitating exploration of non-uniqueness. The inversion scheme was successfully tested on synthetic fixed-loop TEM examples and on fixed-loop TEM field data from South Africa.