Computing Uniformly Asymptotic Seismograms Using Complex Ray Tracing

Methods based on ray tracing are the tool of choice for modeling wave propagation through heterogeneous media at high frequencies. Reliable computation of amplitudes near caustics are still a problem though. We present a new method to compute these amplitudes accurately using complex rays and polynomial phase functions. This method allows the determination of global uniformly asymptotic solutions to the wave equation in the presence of arbitrarily many caustics. The model representation is done using the discrete cosine transform, rather than

cubic splines. This way the velocity model can be analytically continued without higher order discontinuities at the interfaces of the interpolation cells. The complex two-point ray tracing is done efficiently, thus avoiding a global search of complex space. With this method amplitudes are not only correctly computed near caustics but also in the shadow zones. Seismograms are computed for both geometrical and uniformly asymptotic solutions, using a velocity model from the Yucca Mountain test site that generates caustics.