Fast kinematic ray tracing of first‐ and later‐arriving global seismic phases

Summary We have developed a ray tracing algorithm that traces first- and later-arriving global seismic phases precisely (traveltime errors of the order of 0.1 s), and with great computational efficiency (15 rays s− 1). To achieve this, we have extended and adapted two existing ray tracing techniques: a graph method and a perturbation method. The two resulting algorithms are able to trace (critically) refracted, (multiply) reflected, some diffracted (Pdiff), and (multiply) converted seismic phases in a 3-D spherical geometry, thus including the largest part of seismic phases that are commonly observed on seismograms. We have tested and compared the two methods in 2-D and 3-D Cartesian and spherical models, for which both algorithms have yielded precise paths and traveltimes. These tests indicate that only the perturbation method is computationally efficient enough to perform 3-D ray tracing on global data sets of several million phases. To demonstrate its potential for non-linear tomography, we have applied the ray perturbation algorithm to a data set of 7.6 million P and pP phases used by Bijwaard et al. (1998) for linearized tomography. This showed that the expected heterogeneity within the Earth’s mantle leads to significant non-linear effects on traveltimes for 10 per cent of the applied phases.