The Spatiotemporal Response of a Conducting Sphere in the Presence of a Zonal Magnetic Disturbance

The deployment of Earth-orbiting satellites carrying vector magnetometers has led to the hope that the measured spatiotemporal induction signal can be used to investigate the three-dimensional distribution of electrical conductivity in Earth's mantle. The folding-together of the time and space coordinates makes difficult however any intuitive interpretation of a satellite induction signal. This theoretical contribution examines the electromagnetic response that would be recorded by a vector magnetometer orbiting above a conducting sphere while a zonal external magnetic disturbance (storm) is in progress. The storm is modeled as a rapid intensification and slower recovery of an equatorial ring current. The magnetometer orbital period is considerably smaller than the decay time constant of the external disturbance. The radial and polar components of magnetic field evolve at different rates, so at some critical time after storm-onset the induction signal becomes independent of colatitude. This critical time is proportional to the conductivity of the sphere. The application of this concept using satellite-borne magnetometry will be discussed. Finally, modifications to the spatiotemporal induction signal caused by a buried target will be examined.