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We present a cut-&-paste strategy for the 3D inversion of helicopter-borne frequency-domain electromagnetic data. Standard interpretation procedures often involve laterally constrained stitched 1D inversion techniques to create pseudo-3D models that are largely representative for smoothly varying conductivity distributions in the subsurface. Pronounced lateral conductivity changes may, however, produce significant artefacts that can lead to serious misinterpretation. Still, 3D inversions are numerically very expensive. Our approach therefore restricts the full 3D inversion to those parts of the survey where the 1D inversion actually fails. Using a cut-&-paste technique, those regions are extracted, separately inverted in 3D, and finally re-introduced into the original model. We apply a Gauss-Newton inversion scheme using a staggered-grid finite-difference forward operator that takes into account the dielectric response. An explicit representation of the Jacobian matrix serves for optimum computational performance. We introduce a three-way tensor quantity which facilitates the matrix assembly of the forward operator as well as the efficient calculation of the Jacobian. Finally, we deliver the proof of concept for the inversion using a synthetic and a field data set from the Cuxhaven tunnel valley in Germany.

When simulating controlled-source electromagnetic data at frequencies significantly lower than 1 Hz, standard formulations based, e.g., on the vector Helmholtz equation for the electric field, may fail to produce faithful results, because the term in the Helmholtz equation involving conductivity decays linearly with frequency. To stabilize low-frequency simulations, we introduce an auxiliary potential, constrained to be zero by boundary conditions, and explicitly enforce a divergence condition. We present an implementation of our stabilization technique within a finite-difference frequency-domain algorithm. The utility of the stabilized approach is demonstrated by showing synthetic data for frequencies as low as 0.001 Hz for a 3D model roughly mimicking the geometry of the CO2 sequestration pilot site in Ketzin, Germany. In these synthetic data, we observe that instability occurring primarily in the air for non-stabilized simulations disappears for stabilized computations. As expected, the auxiliary potential assumes near-zero values, but its amplitude increases with decreasing frequency due to numerical limitations. The amplitude characteristics of the auxiliary potential, and good accuracy of our synthetic data in comparison with 1D simulation results, suggest that the stabilization is usable down to frequencies at which electromagnetic fields can effectively be considered static.