The correlation between gravitational and geomagnetic fields caused by interaction of the core fluid motion with a bumpy core-mantle interface

The correlation discovered by Hide and Malin between the variable parts of the Earth's gravitational field and magnetic field (suitably displaced in longitude) was tentatively and qualitatively explained by them in terms of the influence on both fields of irregularities (or “surface bumps”) at the core-mantle interface. In this paper, a quantitative analysis of this phenomenon is developed, through study of an idealised problem in which conducting fluid occupying the region z < η(x) flows over the surface z = η(x) in the presence of a magnetic field (B₀,0,0), the whole system rotating with angular velocity (0,0,Ω). It is assumed that $\text{|η′(x)| « 1}$ so that perturbation methods are applicable. Determination of the magnetic potential in the “mantle” region z < η(x) requires solution of the full hydromagnetic problem in the fluid. It is shown that three wave modes are excited, two of which (for values of the parameters of the problem of geophysical interest) have a boundary layer character. Phase interactions between these modes lead to a shift and a distortion of the magnetic pattern relative to the gravitational pattern. The correlation between the gravitational potential and the magnetic potential (shifted by a distance x₀) is determined on the plane $\text{z = d (d}\text{a}\text{?}\text{|η|)}$ as a function of x₀/d and the curves obtained are qualitatively similar to that based on the observed data; the maximum correlation obtained varies between 0.67 and 1, depending on values of the parameters of the problem, and is about 0.72 for reasonable estimates of these parameters in the geophysical context.