THE COMPLETE ORDERED RAY EXPANSION .1. CALCULATION OF SYNTHETIC SEISMOGRAMS

As high-quality broad-band data become more widely available, efficien t methods for modelling and inverting such data are increasingly requi red. In this paper we describe a novel method for calculating seismogr ams, referred to as the Complete Ordered Ray Expansion or CORE. This t echnique is based on a ray-generation algorithm involving the symbolic manipulation of complete wavefield expressions from reflectivity theo ry, truncated to produce a finite ray series. CORE represents an extre mely flexible tool for the generation of body wave synthetics, and for the interpretation of observed seismograms. It also provides a framew ork for waveform inversion that exploits the natural division between smooth structure and discontinuities. We describe the ray-generation a lgorithm, and show examples of the effect of varying degrees of trunca tion on the ray series. Although CORE uses asymptotic ray theory to ge nerate the seismograms from the ray series, the resulting traces show surprisingly good agreement with full reflectivity synthetics. We show comparisons of broad-band CORE and reflectivity synthetics, as well a s a comparison with observed data. Our method is particularly useful i n modelling the complete broad-band wave train at teleseismic distance s, where the computing time for reflectivity becomes excessively large . The computational procedure is readily extended to a laterally heter ogeneous model, where it forms the basis for a fully automated procedu re for phase association and waveform inversion.