Investigating effects of 3-D ray tracing methods in local earthquake tomography

Abstract

The evaluation of accuracy and precision of the employed forward solution method (ray tracer) and of its effects on the inverse solution is one of the key issues in quality and reliability assessment of tomographic images. In general, an analytical solution to the forward problem does not exist for arbitrary three-dimensional (3-D) velocity models. To analyze ray tracing performance and to evaluate the effects of numerical inaccuracies and approximations inherent to any such forward calculation method, we implement a 3-D ray shooting algorithm in the widely used SIMULPS software and compare it to its’ standard approximative pseudo-bending method (ART_PB). In a first step the effect of the different parametrizations of the velocity model required by the two ray tracers is assessed. This leads to the definition of specific ‘forward grids’ derived from and numerically representing the same seismic velocity model, thus ensuring that only insignificant differences in the ray tracing results originate from the different forward model representations. Hence, the observed differences in travel times and ray paths are then due to inaccuracies and lack of precision of the ray tracers. Precision of each ray tracer is assessed by exchanging source and receiver coordinate pairs and comparing the results from ray tracing in both directions, whereas accuracy is analyzed by comparing the results from the two ray tracers for the same source-receiver pair. Using realistic heterogeneous synthetic velocity models, our results indicate that both ray tracers are precise within ±10 ms in travel time for ray lengths less than about 60 km, and ray paths are identical with respect to appropriate Fresnel volumes. For longer rays, however, the ray shooting method yields significantly smaller errors than the ART_PB ray bending. Even with regard to optimal resolution in real tomographic images, differences between the two ray tracers are insignificant up to about 80 km raylength. Noteworthy differences, however, appear in the resolution matrix calculated for the same inverse problem with the two different ray tracers. In addition, differences in the take-off angle of the ray from the source are significant with respect to calculations of focal mechanisms.