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
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.