THE STATISTICS OF PINK NOISE ON A SPHERE: APPLICATIONS TO MANTLE DENSITY ANOMALIES

Abstract

This paper shows that the power spectrum of the Earth's gravity field is very well modelled by white noise signals originating at just four depths within the Earth. Being able to estimate both the lateral and the radial position of anomalous density gives a new and independent way of imaging mantle structure. The success of a four source-depth model undermines the evidence for the long-held picture that a surface observation of gravity reflects density anomalies distributed indistinguishably at all depths within the Earth, a picture largely based on an inappropriate definition of the power spectrum. All spherical harmonics of gravity observed at the Earth's surface with degree greater than about 60 originate within the lithosphere. Degrees less than 4 come from a poorly constrained source near the core-mantle boundary; all other wavelengths come from sources centred near white noise depths of 315 km and between 1100 and 1500 km. These depths are maxima: the same statistical model describes sources at a shallower depth but now representing a random process with a finite correlation length. The form of the spectrum requires mantle heterogeneity to increase by about two orders of magnitude between the asthenosphere and the core-mantle boundary. It is suggested that the variance of density inhomogeneities is related to mantle viscosity.