Three-dimensional inversion of transient-electromagnetic data: A comparative study

Inversion of transient-electromagnetic (TEM) data arising from galvanic types of sources is approached by two different methods. Both methods reconstruct the subsurface three-dimensional (3D) electrical conductivity properties directly in the time-domain. A principal difference is given by the scale of the inversion problems to be solved. The first approach represents a small-scale 3D inversion and is based upon well-known tools. It uses a stabilized unconstrained least-squares inversion algorithm in combination with an existing 3D forward modeling solver and is customized to invert for 3D earth models with a limited model complexity. The limitation to only as many model unknowns as typical for classical least-squares problems involves arbitrary and rather unconventional types of model parameters. The inversion scheme has mainly been developed for the purpose of refining a priori known 3D underground structures by means of an inversion. Therefore, a priori information is an important requirement to design a model such that its limited degrees of freedom describe the structures of interest. The inversion is successfully applied to data from a long-offset TEM survey at the active volcano Merapi in Central Java (Indonesia). Despite the restriction of a low model complexity, the scheme offers some versatility as it can be adapted easily to various kinds of model structures. The interpretation of the resistivity images obtained by the inversion have substantially advanced the structural knowledge about the volcano. The second part of this work presents a theoretically more elaborate scheme. It employs imaging techniques originally developed for seismic wavefields. Large-scale 3D problems arising from the inversion for finely parameterized and arbitrarily complicated earth models are addressed by the method. The algorithm uses a conjugate-gradient search for the minimum of an error functional, where the gradient information is obtained via migration or backpropagation of the differences between the data observations and predictions back into the model in reverse time. Treatment for electric field and time derivative of the magnetic field data is given for the specification of the cost functional gradients. The inversion algorithm is successfully applied to a synthetic TEM data set over a conductive anomaly embedded in a half-space. The example involves a total number of more than 376000 model unknowns. The realization of migration techniques for diffusive EM fields involves the backpropagation of a residual field. The residual field excitation originates from the actual receiver positions and is continued during the simulated time range of the measurements. An explicit finite-difference time-stepping scheme is developed in advance of the imaging scheme in order to accomplish both the forward simulation and backpropagation of 3D EM fields. The solution uses a staggered grid and a modified version of the DuFort-Frankel stabilization method and is capable of simulating non-causal fields due to galvanic types of sources. Its parallel implementation allows for reasonable computation times, which are inherently high for explicit time-stepping schemes.