Three-dimensional seismic ray tracing

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B.R. Julian
D. Gubbins


Two methods for tracing seismic rays between 2 given end points through three dimensional, continuously varying velocity structures are available. This paper describes and compares them for problems of practical interest and for analytical ray paths through an idealized velocity structure. One method involves "shooting" the ray from one point with a given starting direction and then modifying this starting direction until the ray emerges at the desired target, while the other method involves "bending" an initial path between the end points until it satisfies the principle of stationary time. For most of the models investigated, "bending" is computationally faster than "shooting" by a factor of 10 or more. The "bending" method can be modified to deal with discontinuities in the velocity model, and can also be adapted for use in conjunction with a table of distances as a function of ray parameter when the three dimensional anomaly influences only a small fraction of the total ray path. The geometrical spreading effect on the amplitude of the ray may be retrieved easily from the "bending" solution.

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Julian, B., & Gubbins, D. (1977). Three-dimensional seismic ray tracing. Journal of Geophysics, 43(1), 95-113. Retrieved from


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