Syllabus
* 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.
Annotation
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.