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Matrix Methods in Seismology - NGEO018

Title:	Maticové metody v seismologii
Guaranteed by:	Department of Geophysics (32-KG)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2013 to 2021
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
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Oldřich Novotný, CSc.
Classification:	Physics > Geophysics

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Annotation -

Last update: T_KG (20.05.2002)

The matrix relation between the displacements and stresses at the boundary of one layer and of a stack of layers. Thomson-Haskell matrices and their modifications. Applications in the theory of body and surface waves.

Aim of the course -

Last update: T_KG (11.04.2008)

Students will be acquainted with the theory of elastic wave propagation in layered media and with various possibilities of matrix formulation of particular problems.

Literature - Czech

Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)

T.A. Proskurjakova, O. Novotny, E.V. Voronina: Izučenie stroenija Zemli metodom poverchnostnych voln (Central'naja Evropa). Nauka, Moskva 1981. (Studies of the Earth's Structure by the Surface-Wave Method (Central Europe), rusky).

B.L.N. Kennett: Seismic Wave Propagation in Stratified Media. Cambridge University Press, New York 1983.

X. Chen: A systematic and efficient method of computing normal modes for multilayered half-space. Geophys. J. Int. 115 (1993), 391-409.

O. Novotný: Seismic Surface Waves. Lecture notes. UFBA, Salvador, Bahia 1999.

Teaching methods -

Last update: T_KG (11.04.2008)

Lecture

Syllabus -

Last update: T_KG (19.01.2003)

1. Introduction

Simple types of dispersion relations; expressions in terms of determinants; Knopoff's method.

2. Matrix method for Love waves

Model of a layered medium. Expressions for the displacement and stress for plane shear waves. Matrix for one layer; matrix for a stack of layers. Dispersion relation for Love waves in a layered medium. Various modifications of the dispersion relation: Thomson-Haskell matrices, Knopoff's matrices. Some problems of programming: matrices with real elements, elimination of overflow. Various representations of the dispersion curves. Computation of eigenfunctions; accuracy of the results.

3. Application of matrix methods to other types of problems

SH body waves in a layered medium: motion of the free surface due to the incidence of a plane wave from below; reflection and transmission at a transition zone. Temperature and electromagnetic waves in a layered medium.

4. Matrix method for Rayleigh waves

Expression for the displacement and stress in terms of potentials. Matrices of the fourth order (4x4) for one layer and for a stack of layers. Dispersion relation for Rayleigh waves. Loss-of-precision problems in the methods of the Thomson-Haskell type, their causes. Matrix formulations eliminating the loss of precision: associated matrices 6x6 (delta-matrices, Thrower, Dunkin), reduced associated matrices 5x5 (Watson). Acquaintance with computer programs.

5. Computing the group velocity and some derivatives

Computing the group velocity and the partial derivatives of the phase and group velocities with respect to the parameters of the medium: numerical differentiation, analytical computation using variational methods and the implicit-function method.