1991 年 44 巻 3 号 p. 165-176
We present a new ‘bending’ formulation of three-dimensional ray tracing in a spherical Earth. This is suitable for computer programming, and we have already corrected some errors in previously published formulations. By using this formulation we calculate a seismic ray traveling in a velocity model for the subduction zone around the Japan islands. The result is compared with those by appoximate ray-tracing methods, such as Ray Initializer, Circular Ray Tracer and Pseudo-Bending. The model includes the Conrad and Moho discontinuities, and the upper boundary of the subducting Pacific plate. To evaluate the effect of the discontinuities we also calculate exact rays for continuous models derived from the Lagrange or spline interpolation of the discontinuous model. The comparison shows that appoximate ray-tracing methods and smoothed continuous models may lead detailed seismic tomography of the subduction zone to a wrong result. In particular, the discontinuities should be taken into calculations to obtain precise trajectories of rays traveling through a subducting slab.