Improvement of seismic tomographic results can be expected if we use not only the first P-arrival times but also incorporate later arrivals with more complicated ray paths. The later arrivals, which are generated by the complexity of the earth structure, provide more information on the media. However, traveltime tomography is a non-linear inverse problem and generally involves tens of thousands of arrival times. Sophisticated techniques for use in complex velocity structures are generally too time-consumming for our applications. An efficient technique for rapidly computing the traveltimes for ray paths through a realistic 2-D/3-D earth model is required.


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