Fluctuating gravity of Earth's core

For centuries, we have known that Earth's magnetic field varies with time. Edmond Halley (better known for his eponymous recurring comet) first recognized this time variation of magnetic compass needle direction and even offered a remarkable theory that required an intervening fluid between Earth's solid outer shell and a hypothesized innermost solid core (1). For decades, consensus has emerged for an explanation of this time variation that depends on the dynamics of Earth's liquid metallic outer core. In this dynamo theory (2), the fluid motions responsible for field regeneration arise because of density differences within the fluid, much as density and pressure differences in Earth's atmosphere or ocean can drive circulation and vertical motions in those regions of Earth. Density differences necessarily imply changes in Earth's gravity field, so it is only a small step in logic to imagine that there could be changes in the gravity field that correlate with changes in the magnetic field, with both changes arising from fluid flow in the core. In PNAS, Mandea et al. (3) claim to have found possible evidence for such a correlation on a time scale of a few years to a decade.