Bending method revisited: a Hamiltonian approach

For anisotropic media with discontinuities, the bending method is introduced in a very simple way by using the Hamiltonian formulation. Rays propagating in the vicinity of a reference curve are obtained with the help of a propagator. Boundary conditions and interfaces are introduced easily in this formulation. In the second part of the paper, the efficient determination of the propagator is discussed for a 3-D isotropic heterogeneous medium. A finite element approach is proposed in which the medium is divided into a set of elements with a simple polynomial distribution. Analytical expressions of rays are obtained for such a medium. Examples of calculation of rays are presented.