Two factors affecting the speed of interpolation within ray cells

Petr Bulant


This short study is devoted to further investigation of the interpolation method by Bulant & Klimes (1999). The method was designed to cover the model volume by prismatic ray cells formed by six points on three rays forming the ray tube, but enabled also the interpolation within degenerate ray cells formed by five or four points on the rays. Some researchers including consortium members were curious about the numerical efficiency of the proposed algorithm based on prismatic ray cells. In the first part of this study we thus compare the CPU time requirements of the interpolation within prismatic cells and within tetrahedral ray cells, and we conclude that computational time is not a criterion, according which one of the two methods is preferable in general. Then the method by Bulant & Klimes (1999) offers bilinear interpolation scheme, and more precise bicubic interpolation scheme. In the second part of this short study we answer the question whether the bicubic interpolation is time consuming or not, and we conclude that this is not the case, and that it should be used whenever possible as it offers much higher accuracy compared to bilinear interpolation.


Ray theory, travel time, ray tracing, interpolation of the Green function

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Seismic Waves in Complex 3-D Structures, 30 (2020), 41-45 (ISSN 2336-3827, online at