A comparison of the generalized ray and reflectivity methods of waveform synthesis

The generalized ray and reflectivity methods of waveform synthesis have been compared for realistic models of the upper mantle and of the oceanic crust. Both methods entail some approximations, but the one which requires the most careful testing is the truncation of the generalized ray sum. It has been shown in this study that for the types of time windows typically used in waveform modelling the generalized ray sum converges very rapidly to the reflectivity result. In most cases, it is only necessary to include the primary rays in the sum. Additional internal multiples are sometimes necessary if the model contains thin high gradient zones. The primary rays alone do not always correctly predict the amplitude decay of the supercritical reflection from the gradient. Multiples are also required to avoid long-period errors and truncation arrivals if very shallow travelling energy arrives within the time window of interest. It has also been shown that a number of fast approximate methods provide a very cost efficient alternative to the two more exact methods. The best approach to trial and error modelling studies appears to be to begin with a fast approximate method, to advance to generalized ray theory for the final iterations and to use reflectivity to test and to store the results.