Transient VRM Response From a Large Circular Loop Over a Conductive and Magnetically Viscous Half-Space

To effectively characterize the impact of viscous remanent magnetization (VRM) on the transient electromagnetic response, we present a set of analytical expressions for the vertical and radial VRM responses generated by a large circular loop over a magnetically viscous half-space. For a step-off excitation, Néel relaxation theory is used to express the VRM within the half-space as the product of a static on-time magnetization and a time-dependent aftereffect function. Through heuristic and empirical approximations to the elliptic integral of the second kind, we are able to convert Hankel integral-based expressions for static fields into simplified analytical expressions. These were validated with a numerical 1-D forward modeling code. Analytical expressions show that VRM responses are largest near the transmitter wire, and that at the center of a large loop, the strength of the VRM response is inversely proportional to the loop's radius. We also present an estimate of the crossover time from which the VRM signal starts to dominate the transient response. We found that later crossover times were observed near the centers of large loops and that crossover times were much earlier near the transmitter wire. Also, the magnetic flux density has an earlier crossover time compared with its time derivative. To lower or remove the VRM response in an anticipated survey, our analytical expressions can be used straightforwardly to choose an appropriate loop size, identify the VRM response time window, and select an optimal set of time channels.