Normal Mode Relaxation Theory in Solid Earth and Planetary

  • Published: 2014-12-08
  • 2180

1 Normal mode theory in viscoelasticity.
Rheological models. Momentum an Poisson equation for a spherical, stratified and elastic
Earth’s model. Background density stratification for a self-compressed Earth.
Compressible and incompressible models, generalized Williamson-Adams equation.

2- Momentum and Poisson equations in spherical coordinates. Expansion in spherical harmonics. Spheroidal and toroidal parts.

3 -Development of the radial and tangential components of the differential equations in the radial variable describing the conservation of momentum, for the compressible and incompressible self-gravitating spherical stratified Earth.

4- Solution of the differential momentum and Poisson equations in closed analytical form for the incompressible self-gravitating Earth.

5 - Boundary conditions for the outer surface, for the inner CMB (Core Mantle Boundary), for internal and surface loads and for tidal loading.

5 Implementation of the fundamental matrix in closed analytical form for the incompressible stratified Earth. Propagator technique, from the CMB to the Earth’s surface. Correspondence Principle. Solution in the time domain for the linear viscoelastic Maxwell rheology.

6 Normal modes from Earth’s radial discontinuities in the elastic parameters and density.
Spectrum from compressible versus incompressible models and normal mode classification.

7- MacCullagh formula, perturbation of the moment of inertia from surface and internal loads, Liouville rotational equations.

8 Modelling of present-day J2 changes due to Post Glacial Rebound for a viscoelastic, incompressible Earth, based on analytical solutions and realistic loading history.

9 Polar Wandering on viscoelastic planets

10 Application of viscoelaticity for the modelling of present-day changes of radial and horizontal displacements and gravity perturbation from surface and internal mass redistribution, from earthquakes and comparison with GPS, DInSAR, GRACE and GOCE data.

Prof. Roberto Sabadini
Full Professor
of Solid Earth Geophysics
University of Milano