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Computation of uniform wave forms using complex rays.

Complex rays and polynomial phase functions are used to numerically solve the Helmholtz equation in a realistic two-dimensional smoothly varying heterogeneous velocity model with multiple adjacent cusp caustics. Together these two methods allow the determination of global uniformly asymptotic solutions in the presence of arbitrarily many caustics. Two algorithms are introduced to this end: a two-point ray tracing algorithm for complex rays and a perturbation method for constructing polynomial phase functions. Model representation in complex space is performed via discrete cosine transform analysis. Geometrical and uniformly asymptotic solutions are computed for a linear layer test model as well as a velocity model from Yucca Mountain.