A Stochastic Model of the Earth's Interior.

Abstract:

Spectral analysis of observational data by Pelletier (2002) indicates that the geomagnetic field has a variance spectrum which follows a 1/f power law and that a return period of geomagnetic reversals similar to that observed is a direct consequence of such a power law spectrum. A stochastic model of the earth's interior is proposed in which the number of assumptions is kept to a minimum, i.e. specific heat, thermal conductivity, radiogenic heating and density are constant. Despite this simplicity, complex behaviour occurs as a consequence of further assumptions: that Rayleigh-Bernard convection cells form spontanously and at random in the outer liquid core as heat builds up from radioactive sources, that each of these cells spontaneously generates its own magnetic field by a MHD dynamo effect, that each cell melts the solid mantle immediately above it because of the extra heat being convected outward from the hot core and that in this way each convection cell propagates upwards through the otherwise solid mantle at a speed determined by the solution of the Stefan problem for a liquid-solid boundary. The upward-moving, liquid-in-solid convection cells formed in this way are proposed as the primary mechanism by which the core is cooled. The totality of convection cell MHD dynamo fields is proposed as the origin of the geomagnetic field which will have a 1/f spectrum and experience reversals similar to those observed. Because cooling is a stochastic process, there will be times when the earth is heating faster than it is cooling and vice versa. Hence there will be times when the volume and surface of the earth are expanding and new crust is formed and there will be other times when the surface is contracting and the crust, being too large for the smaller surface, is forced to ramp up, wrinkle and subduct in order to be accomodated by the smaller area. Ref: Pelletier, J.D. (2002) PNAS, 99, supp. 1, pp2546-2553.