The complete ordered ray expansion‐I. Calculation of synthetic seismograms

SUMMARY As high‐quality broad‐band data become more widely available, efficient methods for modelling and inverting such data are increasingly required. In this paper we describe a novel method for calculating seismograms, referred to as the Complete Ordered Ray Expansion or CORE . This technique is based on a ray‐generation algorithm involving the symbolic manipulation of complete wavefield expressions from reflectivity theory, truncated to produce a finite ray series. CORE represents an extremely flexible tool for the generation of body wave synthetics, and for the interpretation of observed seismograms. It also provides a framework for waveform inversion that exploits the natural division between smooth structure and discontinuities. We describe the ray‐generation algorithm, and show examples of the effect of varying degrees of truncation on the ray series. Although CORE uses asymptotic ray theory to generate 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 as a comparison with observed data. Our method is particularly useful in modelling the complete broad‐band wave train at teleseismic distances, where the computing time for reflectivity becomes excessively large. The computational procedure is readily extended to a laterally heterogeneous model, where it forms the basis for a fully automated procedure for phase association and waveform inversion.