Can a 1D mantle electrical conductivity model generate geomagnetic jerk differential time delays?

Abstract

Geomagnetic jerks are abrupt temporal variations of the magnetic field believed to be due to motions in the fluid core. The most well known jerks, in 1969 and 1978, are worldwide and show an intriguing spacetime pattern: a first arrival in the Northern hemisphere followed by a delayed arrival in the Southern hemisphere of about 3 years. There are two possible hypotheses to explain this temporal pattern: the first is to consider these differential time delays as being generated by dynamical processes in the core which do not occur simultaneously; the second is to consider jerks generated instantaneously in the core and the time delays as being caused by a conducting mantle. In this paper we analyze the second hypothesis so that the geomagnetic field observed at the surface will correspond to a filtered version of the original field generated in the core. We developed the forward approach to this problem using a radial mantle conductivity model acting as linear, causal and time-invariant filter. The jerk is simulated as an impulse in time at the core-mantle boundary (CMB) and its morphology in the core obtained from a global spherical harmonic model. The key point is that the mantle filter is different for each harmonic degree. Therefore, because the mixing of harmonics varies with location at the CMB, distinct time delays will exist in different locations at the Earth's surface. By using Backus' (1983) mantle filter theory we demonstrate that a simple 1D mantle electrical conductivity model is able to generate differential jerk time delays similar to those observed at the surface.