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Ray Methods in Seismology - NGEO032
Title: Paprskové metody v seismice
Guaranteed by: Department of Geophysics (32-KG)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/1, C+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
Guarantor: doc. RNDr. Johana Prokop Brokešová, CSc.
Teacher(s): doc. RNDr. Johana Prokop Brokešová, CSc.
Classification: Physics > Geophysics
Annotation -
Ray solution of elastodynamic equations in 3D and 2D media. Asymptotic ray series. Eikonal equation. Transport equation. Seismic rays - ray tracing systems. Ray coordinates, ray-centered coordinates. Polarization vectors of ray amplitudes.Ray tubes, ray Jacobian, geometrical spreading. Dynamic ray tracing system. Paraxial approximation. Ray synthetic seismograms.
Last update: T_KG (16.05.2001)
Aim of the course -

Basic theory for the ray asymptotic calculation of seismic wavefield in 3D isotropic and anisotropic inhomogeneous continuum (including R/T problem at a structural interface).

Last update: T_KG (09.04.2008)
Course completion requirements - Czech

Podmínkou udělení zápočtu je aktivní účast na cvičeních a seznámení se s programem ZRAYAMP.

Povaha kontroly studia předmětu vylučuje opravné termíny zápočtu.

Získání zápočtu je podmínkou pro konání zkoušky.

Last update: Gallovič František, prof. RNDr., Ph.D. (06.10.2017)
Literature - Czech
  • Červený, V.: Paprskové metody v seismice, MFF UK, 1978.
  • Červený, V.: Ray synthetic seismograms for complex two-dimensional and three-dimensional structures, J. Geophys, Vol. 58, 1985, 2 - 26
  • Červený, V., Molotkov, I.A., Pšenčík, I.: Ray method in seismology, MFF UK, Praha
  • Brokešová, J.: Asymptotic ray method in seismology: A tutorial, Matfyzpress, 2006.
Last update: T_KG (07.04.2008)
Teaching methods -

Lecture + exercises

Last update: T_KG (11.04.2008)
Requirements to the exam - Czech

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

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

1. Introduction, advantages and disadvantages of asymptotic methods in comparison with 'exact' methods (FD, FE).

2. Equations of motion in acoustic, elastic isotropic and elastic anisotropic medium. Asymptotic solution for inhomogeneous complex medium. Ray series.

3. Zero-order ray theory approximation. Eikonal equation and transport equations in anisotropic, isotropic and elastic media.

4. Solution of the eikonal equation by the method of characteristics. Seismic rays. Ray tracing system in 3D, 2D and 1D media.

5. Rays and wavefronts. Rays and energy flux trajectories. Fermat's principle. Analytic ray solutions in simple structures.

6. Rays in layered structures. Problem of reflection and transmission of rays on an interface. General form of Snell's law. Slowness vectors of waves generated at an interface.

7. Ray fields. Ray coordinates. Ray tubes. Geometrical spreading.

8. Ray centered coordinates. Polarization vectors. Calculation of polarization vectors along rays.

9. Computation of geometrical spreading. Dynamic ray tracing system in Cartesian and ray centered coordinates. Introduction to paraxial seismics.

10. Solution of the transport equation. Continuation formula. Initial amplitude - radiation patterns. R/T coefficients.

11. Ray synthetic seismograms.

Bibliography

  • Červený V., Molotkov I.A., Pšencík I.: Ray method in seismology, MFF UK, Prague 1977
  • Červený V.: Ray synthetic seismograms for complex two-dimensional and three-dimensional structures, J. Geophys., Vol. 58, 1985, 2 - 26
  • Červený V.: Seismic ray theory, Cambridge University Press, 2001

Last update: T_KG (03.05.2002)
 
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