Ray-tracing and eikonal solutions for low-frequency wavefields

Chad M. Hogan, Gary F. Margrave

High-frequency approximations to the wavefield, such as the eikonal equation and raytracing, are only valid when the scale of variation in the medium is significantly larger than the wavelengths considered. Geology, however, commonly varies on spatial scales that are comparable to or even smaller than the typical wavelengths used in seismic imaging. We investigate the possible consequences of this effect, and test one simple method for extending the range of validity of eikonal and ray-tracers: a frequency-dependent Gaussian smoothing of the underlying velocity model. We show that this smoothing not only leads to eikonal and ray-tracing solutions which better match the kinematics of the full wavefield, but also leads to a convergence of eikonal and ray-tracing solutions. Although there are other methods for treating band-limited raypaths, the primary advantage of this method is its simplicity.