Syllabus
1. Equations of motion. Initial and boundary conditions.
2. Plane waves. Time harmonic and transient waves in acoustic, elastic isotropic and anisotropic media. Analytic signal. Inhomogeneous plane waves.
3. Lame's potentials. Christoffel matrix.
4. Energy of elastic plane waves. Energy flux.
5. Spherical waves. Cylindric waves.
6. Weyl's and Sommerfeld's integral.
7. Reflection and transmission of seismic waves at interfaces. Boundary conditions at an interface. Slowness vectors of generated waves. Coefficients of reflection and transmission. R/T problem in acoustic, elastic isotropic and anisotropic media.
8. Rayleigh waves. Love waves.
9. Head waves.
10. Asymptotic integral expansions. Method of stationary phase. Method of steepest descent.
11. Reflection and transmission of spherical waves at an interface.
12. Green's tensor. Analytic solution in acoustic and elastodynamic case. Reciprocity.
13. Representation theorem. Kirchoff representation. Born approxiamtion.
14. Waves in dissipative media. * Bibliography - Aki K., Richards P.G.: Quantitative seismology. Theory and methods. W.H. Freeman, San Francisco 1980 - Červený V.: Seismic ray theory, Cambridge University Press, 2001
Annotation
Equations of motion in inhomogeneous acoustic, elastic isotropic and anisotropic media.
Lame potentials. Christoffel matrix. Plane waves, spherical waves, Weyl integral.
Reflection/transmission of plane waves at plane interfaces. Reflection/transmission of spherical waves at plane interfaces - method of stationary phase and steepest descent.
Head waves. Elastodynamic and acoustic Green function. Elastodynamic and acoustic representation theorems.