The determination of fluid flow at the core surface from geomagnetic observations

Abstract

We examine the problem of using observations of the Earth’s magnetic field to study the kinematics of fluid flow at the surface of the core. In particular, we study two nonlinear inverse problems: the problem of inferring maps of the magnetic field at the core-mantle boundary from observations of the field made at the earth’s surface; and the problem of using maps of the field at the core-mantle boundary to infer the fluid flow in the core immediately beneath the boundary. Both inverse problems are continuous and unstable: adequate regularization conditions must be employed if meaningful solutions are to be obtained. We highlight the inadequacy of the traditional approach to these problems, that of arbitrarily truncating the resulting expansions in terms of spherical harmonic basis functions, in the framework of stochastic inversion, to regularize the solutions based on the requirement that the solutions should be spatially smoothly-varying. We present models of the field at the core-mantle boundary for 1842, 1905, 1969 and 1980. In order to invert these models of the magnetic field for fluid motions the field must satisfy certain necessary conditions. We find some weak evidence that the field violates these conditions, resulting from the effects of electrical diffusion in the core, over the period 1969–1980. We find very simple, but necessarily nonunique, fluid flow solutions for the periods 1842–1905, 1905–1980 and 1966–1980: the effects of diffusion are clearly apparent in the 1905–1980 solution. We investigate a simple explanation for the rapid diffusion observed during the period 1905–1980, and discuss how diffusive effects may be incorporated into the solutions.