Massively parallel computing of shortest raypath and traveltime in 2-D and 3-D models

Based on Huygens' principle, the authors present an accurate and computationally efficient method to compute the shortest raypath and traveltime in a two-and three-dimensional (2-D and 3-D) space of a discrete block model. The efficiency of the method is achieved through approximation, while the accuracy of the calculated traveltime solely depends on machine precession. The accuracy of the raypath is realized by the small increment in the orientation of the ray incidence. Whether the computational efficiency and accuracy can be justified depends on the model's complexity and requirements in its own application. In addition, the feasibility of implementing the algorithm on the Cray T3D Massively Parallel Processors (MPP) is proposed. The velocity distribution in a 2-D space is discretized into homogeneous polygonal cells. The search for the shortest traveltime and path between two given points can be reduced to a discrete graph searching. In the general 3D case, the velocity model is characterized by discrete convex blocks bounded by polyhedral surfaces. Although the 3-D algorithm is a straight-forward extension of the 2-D case, the computing operations in 3-D are much more CPU intensive. The method is demonstrated with examples showing raypaths and wavefronts in 2D and 3D block models. On the basis of these examples, the proposed algorithm is capable of solving the optimal raypaths from different source points in parallel on the MPP system.