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Last update: T_KG (10.05.2002)
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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. |
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Last update: prof. RNDr. František Gallovič, Ph.D. (10.06.2019)
Oral exam |
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Last update: T_KG (14.04.2008)
Červený, V.: Seismic Ray Theory. Cambridge Univ. Press, Cambridge, 2001. |
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Last update: T_KG (11.04.2008)
Lecture |
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Last update: prof. RNDr. František Gallovič, Ph.D. (06.10.2017)
Zkouška je ústní, požadavky odpovídají sylabu v rozsahu prezentovaném na přednášce. |
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Last update: T_KG (11.04.2008)
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. |