The Spatio-Temporal Behavior of the Sensitivity of Geophysical Time-Domain Electromagnetics

Summary

In this paper, we derive and compare two approaches for computing the three-dimensional sensitivity of time-domain electromagnetic (TEM) data with respect to subsurface electrical conductivity: the convolutional adjoint state method and the sensitivity equation approach. Both methods are examined within the diffusive regime, neglecting displacement currents and, without loss of generality, considering measurements of the time derivative of the magnetic flux density ∂B/∂t following the abrupt shutoff of a source signal. As our source, we consider an electric current flowing through a small, finite-length wire loop. To illustrate the complex spatio-temporal behavior of the sensitivity, the source-receiver configuration is based on a TEM field survey conducted at Iceland’s Strokkur geyser. With a separate-loop configuration, we observed a significant decrease in ∂Bz/∂>t field values at early times and an increase at later times, which is attributed to an increase in electrical conductivity near the surface during an eruption. This effect is explained by the sensitivity analyses presented here, including a sign change of the sensitivity at early times. Owing to its numerical efficiency and high accuracy yielded by second order Nédélec finite elements on unstructured grids, the sensitivity equation approach has been implemented in FEMALY, a MATLAB library developed at TU Bergakademie Freiberg and TU Chemnitz, making it well suited for practical applications and three-dimensional inversions.