Mantle Electrical Conductivity and the Magnetic Field at the Core–Mantle Boundary

John V Shebalin

doi:10.3390/fluids6110403

Abstract

The Earth’s magnetic field is measured on and above the crust, while the turbulent dynamo in the outer core produces magnetic field values at the core–mantle boundary (CMB). The connection between the two sets of values is usually assumed to be independent of the electrical conductivity in the mantle. However, the turbulent magnetofluid in the Earth’s outer core produces a time-varying magnetic field that must induce currents in the lower mantle as it emerges, since the mantle is observed to be electrically conductive. Here, we develop a model to assess the possible effects of mantle electrical conductivity on the magnetic field values at the CMB. This model uses a new method for mapping the geomagnetic field from the Earth’s surface to the CMB. Since numerical and theoretical results suggest that the turbulent magnetic field in the outer core as it approaches the CMB is mostly parallel to this boundary, we assume that this property exists and set the normal component of the model magnetic field to zero at the CMB. This leads to a modification of the Mauersberger–Lowes spectrum at the CMB so that it is no longer flat, i.e., the modified spectrum depends on mantle conductance. We examined several cases in which mantle conductance ranges from low to high in order to gauge how CMB magnetic field strength and mantle ohmic heat generation may vary.

Highlights

The geomagnetic field is important as it protects the Earth from the effects of cosmic rays and solar wind
We want to be able to project the geomagnetic field observed on the surface down onto the core–mantle boundary (CMB) to provide a clearer picture of the magnetic field directly above the outer core
This leads to a new form for the geomagnetic power spectrum at the core–mantle boundary (CMB)

Summary

Introduction

The geomagnetic field is important as it protects the Earth (and humanity) from the effects of cosmic rays and solar wind. The Earth’s mantle has nonzero electrical conductivity [1,2,3], a property we take into account using the ansatz of [4] to represent the effects of an electrically conducting layer through the presence of a spherical surface current This leads to a new form for the geomagnetic power spectrum at the core–mantle boundary (CMB). Commensurate with these observations, the mantle, which lies (in a spherical polar coordinate system: r, θ, φ) between the Earth’s surface at r = re and the CMB at r = ro, is modeled as having an upper insulating part with no electrical current separated at r = rs from an electrically conducting lower part. We discuss how the magnetic spectrum at the CMB is modified for various levels of mantle electrical conductivity and estimate the associated rates of ohmic dissipation

Mantle Conductivity

Exterior Geomagnetic Field

Intermediate Magnetic Field

Power Spectrum of the Geomagnetic Field

Conclusions