Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Spectral Methods in Geophysics - NGEO095

Title:	Spektrální metody řešení parciálních diferenciálních rovnic v geofyzice
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:	taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. RNDr. Ondřej Čadek, CSc.

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

Last update: T_KG (14.04.2008)

Spherical harmonic functions, vectors and tensors. Spectral approximation of data given on a sphere in terms of generalized spherical harmonics. Application to solving PDF. Spectral solution of the following problems: Laplace-Poisson equation for gravitational potential, deformation of a spherical elastic shall, thermal convection in a mantle, viscoelastic relaxation of a spherical body, and the problem of electromagnetic induction.

Aim of the course -

Last update: T_KG (14.04.2008)

Getting practice in application of spectral methods to solving basic geophysical problems in spherical geometry.

Course completion requirements - Czech

Last update: prof. RNDr. Ondřej Čadek, CSc. (06.10.2017)

Zkouška probíhá formou testu, v rámci kterého studenti vyřeší zadanou rovnici spektrální metodou. V případě nejasností následuje ústní zkouška.

Literature - Czech

Last update: T_KG (14.04.2008)

Jones M. N.: Spherical Harmonics and Tensors for Classical Field Theory, Research Studies Press Ltd., 1985

Syllabus -

Last update: T_KG (14.04.2008)

Basic principle of spectral methods. Basis functions. Fourier series. Spherical harmonic functions. Various definitions of vector and tensor spherical harmonics (SH). Approximation of geophysical quantities in terms of spherical harmonics. Products of SH series. Application of differential operators. Exercises.

Laplace-Poisson equation. Solution for gravitational potential and acceleration. Expression of centrifugal and tidal forces.

Deformation of an elastic shall with radially dependent material paremeters. Methods of including lateral variations of parameters. Elastic membrane.

Momentum and heat transport equations. Nonlinear terms. Degree 0 and 1.

Viscoelastic deformation of a spherical body, evaluation of the memory term. Compressibility and selfgravitation.

Maxwell equations. Problem of electromagnetic induction. Generation of magnetic field in the core.