Paraxial eikonal solvers for anisotropic quasi-P travel times

The first-arrival quasi-P wave travel-time field in an anisotropic elastic solid solves a first-order nonlinear partial differential equation, the qP eikonal equation, which is a stationary Hamilton-Jacobi equation. The solut ion of the paraxial quasi-P eikonal equation, an evolution Hamilton-Jacobi equation in depth. gives the first-arrival travel time along downward propa gating rays. We devise nonlinear numerical algorithms to compute the paraxi al Hamiltonian for quasi-P wave propagation ill general anisotropic media. A second-order essentially nonoscillatory (ENO) Runge-Kutta scheme solves t his paraxial eikonal equation with a point source as an initial condition i n O(N) floating point operations, where N is the number of grid points, Num erical experiments using 2-D transversely isotropic models with inclined sy mmetry axes demonstrate the accuracy of the algorithms. (C) 2001 Academic P ress.