Computation of second-order traveltime perturbation by Hamiltonian ray theory

Abstract

Ray perturbation theory may be used to compute changes in ray paths and physical attributes (traveltime, polarization, amplitude) due to changes in the medium or in the boundary conditions of the rays. The theory developed in the Hamiltonian approach is valid for both isotropic and anisotropic media, including models with structural interfaces. First-order traveltime perturbation is given by the integral of the first-order term of the Hamiltonian perturbation. Computation of the second-order traveltime perturbation needs the computation of the first-order ray perturbation and the expression of the second-order term of the Hamiltonian. Endpoint boundary conditions are easy to introduce in this formulation using the paraxial propagator matrix. Examples computed in transverse isotropic media show that P-wave traveltimes may be well approximated by using the second-order expression even for strong anisotropy. A reference medium with elliptical anisotropy seems to be a better choice to develop the perturbation approach than an isotropic medium.