A Paraxial Formulation for the Viscosity Solution of Quasi-P Eikonal Equations

Stationary quasi-P eikonal equations, stationary Hamilton-Jacobi equations, arise from the asymptotic approximation of anisotropic wave propagation. A paraxial formulation of the quasi-P eikonal equation results in a paraxial quasi-P eikonal equation, an evolution Hamilton-Jacobi equation in a preferred direction, which provides a fast and efficient way for computing viscosity solutions of quasi-P eikonal equations. Under the assumption that the initial condition is continuous (and possibly unbounded), the (unbounded) viscosity solution exists and is unique for the paraxial quasi-P eikonal equations. c © 2003 Elsevier Science Ltd. All rights reserved. Keywords—Paraxial eikonal equations, Hamilton-Jacobi equations, Viscosity solutions, Firstarrival traveltimes.