The westward drift of the geomagnetic field caused by length-of-day variation, and the topography of the core-mantle boundary

Abstract

S U M M A R YWe propose that the westward drift of the geomagnetic field is caused by length-of-day (1.o.d.) variation through topographic coupling between the mantle and the core. Fluctuations of the rotation velocity of the mantle induce radial flow in the core through topographic coupling at the core-mantle boundary (CMB). The induced flow bends the toroidal field to generate a poloidal field which appears to drift westwards. A n analytical model is constructed to describe this situation on the basis of a quasi-geostrophic approximation. We compare our model with observations of the geomagnetic field over the last several hundred years. When the sectorial harmonic components of the Gauss coefficients, g z and h x , are plotted on a diagram with g as the abscissa and h as the ordinate, the observed trajectories follow a clockwise ellipse. The clockwise motion on the g-h plot signifies that the pattern of the magnetic field moves westwards. This behaviour is described well by our model if 1.o.d. variation is assumed to consist of one Fourier component. We find that the period of the Fourier component of 1.o.d. variation is about 700 yr. The relationship between the ellipticity of the trajectories and the eigenfrequencies of the slow magnetohydrodynamic oscillations enables us to infer the dispersion relation to the oscillations, which signifies that the strength of the toroidal field of the outer core is 50-100Gauss. We derive the topography of the CMB from the directions of the axes of the ellipses. The CMB topography is found to correlate well with the lower mantle structure.

Constraints on the core‐mantle boundary topography from P4KP‐PcP differential travel times

“…The locations of elevations and depressions have not been frequently discussed in studies on topographic coupling. Unusually, Yoshida and Hamano [1993] inferred the sectorial pattern of the CMB topography using a relationship between the westward drift of the geomagnetic field and the length of the day. They did not reveal the locations of elevation and depression but presented a black‐and‐white pattern indicating only the alternation of the topographic sign.…”

Slow magnetic Rossby waves in the Earth's core

“…We also note that stable layers beneath the Core-Mantle boundary could give rise to other wave modes not considered here, which might impact on the secular variation. Different mechanisms for westward drift lead to different dispersion relations: the flow advection with ∝ m, the magnetic Rossby mode with ∝ m 3 , and, for example, a topographic coupling with a constant drift rate, i.e., independent of m [Yoshida and Hamano, 1993]. Also, magnetic Rossby waves with a short length scale in the s direction (not evident in these simulations but possibly present in the core) will be affected by the s component ofB, which will give a different dispersion relation.…”

A generating process of geomagnetic drifting field

“…Magnetostrophic wave (often called magnetic Rossby wave) generated by combined effect of Coriolis, Lorentz and/or gravitational forces has been considered to be a cause of the westward drift of the magnetic field (see, e.g., Finlay et al 2010 for review). Yoshida and Hamano (1993), Hori et al (2018), for example, examined the magnetostrophic waves in the framework of quasi-geostrophic approximation. Yoshida and Hamano (1993) obtained the westward drifting field with phase velocity similar to the observed, which was excited by the oscillation of the mantle with respect to the core with heterogeneous topographic bottom boundary.…”

“…Yoshida and Hamano (1993), Hori et al (2018), for example, examined the magnetostrophic waves in the framework of quasi-geostrophic approximation. Yoshida and Hamano (1993) obtained the westward drifting field with phase velocity similar to the observed, which was excited by the oscillation of the mantle with respect to the core with heterogeneous topographic bottom boundary. To be noted is that they obtained the wave that was symmetric about the equator as expressed by sectorial harmonics.…”