Counteracting sensitivity accumulation near source and receiver locations in 3D inversion of controlled-source electromagnetic data

We present a synthetic inversion study illustrating two approaches which help to deal with heterogeneous sensitivities in 3D frequency-domain controlled-source electromagnetic inverse problems.

Using edge-based vector finite-element approximations on tetrahedral meshes and a preconditioned non-linear conjugate gradient algorithm, we invert for impedance tensor elements generated by a set of two coincident perpendicularly oriented horizontal electric or horizontal magnetic dipole sources. Depending on the number and locations of sources and the choice of impedance tensor components used for inversion, the sensitivity patterns can differ significantly. Measurement setups with a small number of sources, but many receiver stations at the surface covering near-field, transition zone and far-field, are often deployed for land-based controlled-source electromagnetic measurements. Such a setup can result in accumulated sensitivities close to the sources and receivers, which implies strongest model updates in these regions and can mislead the inverse algorithm to a search direction, where no physically meaningful model can be produced nor the data are fitted.
 
In order to mitigate the influence of strong sensitivities near sources and receivers on the inversion process, we apply an efficient preconditioner and customisable weights in the model regularisation matrix. The preconditioner is updated with the Broyden-Fletcher-Goldfarb-Shanno algorithm using the diagonal of the approximate Hessian matrix as start preconditioner. The latter is computationally expensive to obtain, but aims at finding a favourable search direction for the inverse algorithm already in early iterations and distributing the model update more evenly in the domain. To account for the sensitivity loss with depth, we implemented a depth weighting functional in the model regularisation term. The approach is based on counteracting the exponential and geometrical decay of the electromagnetic fields with depth and distance from the sources. In practical, we increase the smoothing in the shallow part of the model close to the source locations, where no structure is expected. We present synthetic examples indicating that this approach is an efficient way of helping the inversion to converge, obtaining a reliable model and resolving structure at depth.