Introduction.

Ray theory for the scalar wave equation and scalar Helmholtz equation

• The ray theory ansatz, amplitude and phase, slowness and travel time
• The eikonal equation
• The transport equation(s)
• The ray-tube-area method to obtain the amplitudes
• Caustics

Dynamic ray theory

• The second derivatives of the phase function
• The first variation of the ray equations
• The transverse components of the Hessian of the phase
• The dynamic ray equation and the simultaneous solution of the ray and dynamic ray equations
• The solution of the transport equation using the results of dynamic ray theory

The elastic wave equation

• Isotropy
• Isotropy: P and S waves
• The transport of the S polarization
• Anisotropic ray theory

Ray theory for a symmetric hyperbolic system

• Group velocity: various properties

The aim for the course is to be self contained at the expense of being formal. For instance, methods of calculating coefficients in an asymptotic series will be treated without proving that the series is indeed asymptotic.