Abstract
The eikonal equation in an attenuating medium has the form of acomplex-valued Hamilton-Jacobi equation and must be solved in terms of the complex-valued traveltime (complex-valued action function). A very suitable approximate method for calculating the complex-valued traveltime right in real space is represented by the perturbation from the reference traveltime calculated along real-valued reference rays to the complex-valued traveltime defined by the complex-valued Hamilton-Jacobi equation.
The real-valued reference rays are calculated using the reference Hamiltonian function. The perturbation Hamiltonian function is parametrized by one or more perturbation parameters, and smoothly connects the reference Hamiltonian function with the Hamiltonian function corresponding to a given complex-valued Hamilton-Jacobi equation.