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Free oscillations of the Earth - NGEO104

Title:	Vlastní kmity Země
Guaranteed by:	Department of Geophysics (32-KG)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2022
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Ctirad Matyska, DrSc.

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KG (09.05.2013)

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.

Aim of the course -

Last update: T_KG (09.05.2013)

The aim of the lecture is to provide students with the theory of prestressed self-gravitating bodies and its application in seismology.

Course completion requirements -

Last update: prof. RNDr. František Gallovič, Ph.D. (10.06.2019)

Oral exam

Literature - Czech

Last update: T_KG (09.05.2013)

Dahlen, F. A., and J. Tromp (1998), Theoretical Global Seismology, Princeton University Press, Princeton.

Martinec, Z. (1984), Free Oscillations of the Earth, Travaux Geophysiques No 591.

Masters G., 2010. Mineos Package (http://geodynamics.org/cig/software/mineos)

Woodhouse, J.H. and A. Deuss, (2007), Theory and observations - Earth’s free oscillations, In: Romanowicz, B. and A. Dziewonski (Eds.), Treatise on Geophysics Vo. 1, pp. 31-65.

Zábranová, E., L. Hanyk and C. Matyska (2009), Matrix pseudospectral method for elastic tides modeling. In: Holota P. (Ed.), Mission and Passion: Science. Czech National Committee of Geodesy and Geophysics, Prague, pp. 243-260.

Teaching methods -

Last update: T_KG (09.05.2013)

Lecture

Syllabus -

Last update: T_KG (09.05.2013)

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.