Subjects

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

Modelling Seismic Wave Fields - NDGF003

Title:	Modelování seismických vlnových polí
Guaranteed by:	Department of Geophysics (32-KG)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	both
E-Credits:	3
Hours per week, examination:	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
Note:	you can enroll for the course in winter and in summer semester

Guarantor:	RNDr. Luděk Klimeš, DrSc.
Class:	DS, geofyzika
Classification:	Physics > Geophysics

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KG (10.05.2002)

Viscoelastodynamic equations. seismic model of the medium. Green tensor. Travel times. Initial value ray-tracing. Calculation of ray-theory travel times. Calculation of first-arrival travel times. Ray-theory synthetic seismograms. Accuracy and validity conditions of asymptotic ray methods. Full-wave finite differences in 3-D. Ray method for surface waves in Cartesian and curvilinear coordinates.

Aim of the course -

Last update: T_KG (14.04.2008)

Acquiring knowledge of methods for calculating seismic waves or their properties, and knowledge of applicability and accuracy of these methods.

Course completion requirements -

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

Oral exam

Literature - Czech

Last update: T_KG (14.04.2008)

Červený, V.: Seismic Ray Theory. Cambridge Univ. Press, Cambridge, 2001.

Teaching methods -

Last update: T_KG (11.04.2008)

Lecture

Requirements to the exam - Czech

Last update: prof. RNDr. František Gallovič, Ph.D. (06.10.2017)

Zkouška je ústní, požadavky odpovídají sylabu v rozsahu prezentovaném na přednášce.

Syllabus -

Last update: T_KG (11.04.2008)

Viscoelastodynamic equations:

Linear constitutive equations for viscoelastic medium, relaxation functions. Anisotropic and isotropic viscoelastodynamic equations. Dispersion and attenuation.

Seismic model of the medium (macro model):

Coordinate systems and metric tensors. Computer representation of the model.

Green tensor.

Travel times:

Kinds of travel times. Isotropic and anisotropic eikonal equations. First-arrival travel times. Ray-theory travel times, elementary waves.

Initial-value ray tracing:

Hamiltonian ray tracing, rays as geodesics, wave-propagation metric tensor. Kinematic and dynamic ray tracing. Second and higher partial travel-time derivatives.

Calculation of ray-theory travel times:

Two-point ray tracing, shooting methods, bending methods. Computation of travel times on regular rectangular grids. Ray cells, weighting of paraxial ray approximations. Wavefront tracing.

Calculation of first-arrival travel times:

Network shortest-path ray tracing, grid travel-time tracing.

Ray-theory synthetic seismograms:

Isotropic and anisotropic ray theories. Weak anisotropy. Complex-valued rays and travel times. Space-time ray theory. Gaussian beams and packets, Chapman-Maslov asymptotic theory.

Accuracy and validity conditions of asymptotic ray methods:

Kirchhoff integrals, Fresnel zones, representation theorems, Fresnel volumes.

Full-wave finite differences in 3-D:

Accuracy of various finite-difference schemes, grid dispersion. Waves as structural interfaces. Fast calculation of the first-arrival waveforms.

Ray method for surface waves in Cartesian and curvilinear coordinates.