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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)
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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)
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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)
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Last update: T_KG (07.04.2008)
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Lecture + exercises Last update: T_KG (11.04.2008)
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Zkouška je ústní, požadavky odpovídají sylabu v rozsahu prezentovaném na přednášce. Last update: Gallovič František, prof. RNDr., Ph.D. (06.10.2017)
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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
Last update: T_KG (03.05.2002)
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