MODELLING THE EARTH: COMPRESSIBLE VISCOELASTODYNAMICS, GRAVITATIONAL SEISMOLOGY AND TRUE POLAR WANDER

This thesis reviews and sheds new light on compressible Earth models and theories for the modelling of megathrust earthquakes and rotational instabilities caused by glacial isostatic adjustments and mantle convection. The basic theory is outlined in the first chapter, where we discuss the response of a self-gravitating Earth to external forces and loads seated at its surface or interior and we focus on elastic static perturbations and the transition between the elastic and fluid behaviours of the Earth that occurs on thousand and million years time scales. In the first part of this thesis, we derive the analytical solution of the momentum and Poisson equations for a spherically symmetric viscoelastic Earth model that accounts for compressibility both at the initial state of hydrostatic equilibrium and during the perturbations. This constitutes a step ahead with respect to all previous analytical solutions, which actually neglect compressibility in some aspects, and allows to gain deep insight into the relaxation spectrum of compressible viscoelastic Earth models. In the second part, we discuss long-wavelength gravity anomalies caused by the 2004 Sumatra earthquake and detected by the Gravity Recovery And Climate Experiment (GRACE) space mission. We extend the classic theory in order to interpret gravity anomalies in terms of volume changes within the solid Earth, advection of the initial density field and ocean water redistribution caused by perturbations of the ocean floor and surface topographies. This physics is then exploited in order to develop a novel procedure for the inversion of the principal seismic source parameters (hypocentre and moment tensor) of large earthquakes relying solely on space gravity data. This procedure, which complements traditional seismology and which we shall name Gravitational Centroid Moment Tensor (GCMT) analysis, is applied for the first time to the 2011 Tohoku earthquake. In the third part of the thesis, we discuss issues related to long time scale instabilities of the Earth's rotation. The slow motion of the rotation axis with respect to the mantle, called True Polar Wander (TPW), has continuously been debated after the pioneering works in the sixties by Munk, MacDonald and Gold. We thus discuss TPW due to variations of surface loading from ice ages on hundreds of thousand year time scales, its sensitivity to the elastic or viscoelastic rheologies of the lithosphere and the stabilizing role of mantle density heterogeneities. Also, we face the problem of TPW driven by mantle convection on the million years time scale. Most studies have assumed that on this long time scale the planet readjusts without delay and that the Earth's rotation axis and the maximum inertia direction of mantle convection coincide. We herein overcome this approximation and we provide a novel treatment of the Earth's rotation, which clearly explains the interaction between mantle convection and rotational bulge readjustments, and the physical laws for the characteristic times controlling the polar motion in the directions of the intermediate and minimum principal axes of the mantle convection inertia tensor. We thus clarify a fundamental issue related to mantle mass heterogeneities and TPW dynamics.