Syllabus
* Fundamental equations for prestressed self-gravitating continuum
Basic axioms in continuum mechanics, the Cauchy and Piola-Kirchhoff stress tensors and momentum equations, boundary conditions; linearized theory - relation between the Cauchy and Piola-Kirchhoff stress tensors in a prestressed body and the momentum equation for a general model of the Earth.
* Eigenfrequencies and eigenfunctions of the SNREI model
Decomposition to toroidal and spheroidal oscillations using spherical harmonics; first- and second-order ordinary-differential-equation eigenproblems and numerical methods of their solution, the MINEOS code and the program based on direct numerical discretization.
* Influence of ellipticity, rotation and the Coriolis force, calculation of the quality factors of normal modes
Multiplet splittings - first and second order effects, relation between frequency-dependence of elastic moduli and the quality factors of normal modes.
* Synthetic-seismograms and co-seismic-response calculations
Seismic-moment tensor, calculations of synthetic seismograms and co-seismic response for spherical models with non-splitted multiplets, synthetic seismograms for splitted multiplets.
* Inverse problem for seismic-source parameters
Data from broadband seismographs, superconducting gravimeters and GNSS stations, sensitivity of normal modes to seismic-moment-tensor parameters.
* Theory of splitting for aspherical structural models
Perturbation theory for isolated multiplets.
Annotation
Fundamental equations for prestressed self-gravitating bodies and their application to elastic models of the Earth, modal summation for synthetic-seismograms and co-seismic-response calculations, relation between seismic- source parameters and oscillation amplitudes.