S U M M A R YWe present a new 3-D vector finite element code and demonstrate its strength by modelling a realistic marine CSEM scenario. Unstructured tetrahedral meshes easily allow for the inclusion of arbitrary seafloor bathymetry so that natural environments are mapped into the model in a close-to-reality way. A primary/secondary field approach, an adaptive mesh refinement strategy as well as a higher order polynomial finite element approximation improve the solution accuracy. A convergence study strongly indicates that the use of higher order finite elements is beneficial even if the solution is not globally smooth. The marine CSEM scenario also shows that seafloor topography gives an important response which needs to be reproduced by numerical modelling to avoid the misinterpretation of measurements.

Airborne time-domain electromagnetic surveys are effective tools for mineral exploration and geologic mapping. 3D inversion of airborne electromagnetic data is a challenging computational problem. The size of the surveys and the spatial resolution required to adequately discretize the transmitters and receivers results in very large meshes. Solving the forward problem repeatedly on such a mesh can quickly become impractical. Fortunately, using a single mesh for both the forward and inverse problem for all of the transmitters is not necessary. The forward problem for a single source or a small group of sources can be solved on different meshes, each of which only needs to be locally refined close to the selected transmitters and receivers. Away from the selected transmitters and receivers, the mesh can be coarsened. The forward problem can then be broken into a number of highly parallel problems. Each forward modelling mesh is optimized specifically to the selected transmitters and receivers and has far fewer cells than the fine inversion mesh. Further efficiency can be gained by using stochastic Gauss–Newton methods where a stochastic approximation to the gradient, Hessian or both are used. In this paper, we present new algorithms for airborne data inversion and their implementation using a finite volume discretization on OcTree meshes. We demonstrate our approach on a large-scale synthetic versatile time-domain electromagnetic surveying data set.

S U M M A R YWe introduce the concept of multi-objective optimization to cast the regularized inverse direct current resistivity problem into a general formulation. This formulation is suitable for the efficient application of a genetic algorithm, which is known as a global and non-linear optimization tool. The genetic inverse algorithm generates a set of solutions reflecting the trade-off between data misfit and some measure of model features. Examination of such an ensemble is highly preferable to classical approaches where just one 'optimal' solution is examined since a better overview over the range of possible inverse models is gained. However, the computational cost to obtain this ensemble is enormous. We demonstrate that at the current state of computer performance inversion of 2-D direct current resistivity data using genetic algorithms is possible if state-of-the-art computational techniques such as parallelization and efficient 2-D forward operators are applied.

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We have developed a method to invert time-domain airborne electromagnetic (AEM) data using a parametric level-set approach combined with a conventional voxel-based technique to form a parametric hybrid inversion. The approach was designed for situations in which a voxel-based inversion alone may struggle. Such an example is where a distinct anomaly is present with sharp boundaries, and there is a large contrast between a low-resistivity target and a high-resistivity background. The first step of the proposed hybrid method used our novel parametric inversion to recover a best-fitting skewed Gaussian ellipsoid that represented the target of interest. Subsequently, the parametric result was set as an initial and reference model for the second stage, where smooth features with smaller resistivity contrasts were introduced into the model through a conventional voxel-based approach. The approach was tested with synthetic and field data. In the synthetic case, we recovered the size and dip of a conductive, thin, dipping plate with better accuracy compared with a voxel-based inversion. In the field example, we inverted AEM data over the Caber volcanogenic massive sulfide deposit. Based on information from past drilling, our results improve upon previous parametric plate inversions of the deposit itself, while additionally imaging the conductive cover over the deposit. These findings showcased how our parametric hybrid method can improve the accuracy of time-domain AEM inversions for thin dipping targets with large resistivity contrasts compared with the background. Preliminary results presented at SEG 2014 in a talk entitled: "Recovering a thin dipping conductor with 3D electromagnetic inversion over the Caber deposit." Manuscript