It is well known, that even in quite simple seismic models we need some kind of the two-point ray tracer to find all existing two-point rays for all the receivers. One solution is a sophisticated shooting program, based on an accurate searching for the subdomains of ray take-off parameters, where the two-point rays may occur. The subdomains may be found by a special triangularization of the 2-D domain of ray take-off parameters. The two-point rays may be then identified inside the triangles whose all the three vertices are formed by rays arriving into a receiver area.
Once the domain of ray take-off parameters is triangularized, we can use the triangles mentioned above to construct the ray cells through the model volume, and to interpolate travel times and other quantities inside the cells, like in the wavefront tracing method. The described controlled initial-value ray tracing method is a useful extension of two-point ray tracing programs based on triangularization, providing interpolated values of ray-theory travel times and other quantities at dense grids located in the seismic model.
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