Quantifying 3D Modeling Errors in Time-Domain Electromagnetics: Implications for Deterministic and Probabilistic Inversions

Frederik Alexander Falk, Anders Vest Christiansen, Thomas Mejer Hansen

Subsurface resistivity in geophysics is commonly estimated indirectly from dependent measurements. This relationship can be approximated in a forward operator using physical models, such as Maxwell’s equations for time-domain electromagnetics (TDEM), where measured voltages in receiver coils arise from decaying magnetic fields. In TDEM, the inverse operator usually does not exist, so inversion methods estimate resistivity by incorporating measurements, prior information, error assumptions, and the forward operator. A common assumption in forward models is that the subsurface is one-dimensional (1D), with resistivity varying only vertically. When lateral variations are present, this assumption introduces a 3D modeling error. Understanding these errors and their resulting artifacts is crucial, as the 1D assumption is widely used but often inaccurate. The effect of 3D modeling errors in TDEM inversion is examined using three distinct three-layer geological model types: a buried valley, a lens at the surface, and variation in topography. Realistic 3D data are computed for each of the three scenarios, and the impact of using deterministic and probabilistic 1D inversion is investigated. In all three cases, features appear in the solution to the inverse problem that are not consistent with the reference model. The erroneous features can be directly linked to using a 1D forward model to describe 3D data. Goodness-of-fit metrics such as the normalized data residual are analyzed and found to be unreliable indicators of whether the inversion model structure is real or a 3D artifact. Lastly, a case is presented where inversion models of SkyTEM data from Ribe in southern Denmark show structures similar to those found in the analysis, highlighting the applicability of this analysis to interpretations of real TDEM datasets.