THE EVOLUTION OF PHASE FRONTS AND THE METHOD OF STRAINED COORDINATES

When waves propagate through a medium with smooth velocity perturbatio ns the propagation of wavefronts is determined by the eikonal equation . Here the propagation of wavefronts through a medium with small-scale velocity perturbations is analyzed using the method of strained coord inates. A partial differential equation for the first-order perturbati on of wavefronts is derived that includes frequency-dependent wave pro pagation effects. It is shown that for the special case of the scalar Helmholtz equation with a homogeneous reference medium this leads to t he same perturbation of wavefronts as obtained from the Rytov approxim ation. However, the method presented here can possibly be generalized to more complex wave propagation problems where the Rytov approximatio n cannot be used, such as the propagation of vector waves. (C) 1998 Ac oustical Society of America.