ARTICLE

Two factors affecting the speed of interpolation within ray cells

PETR BULANT
Show Less
Department of Geophysics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Praha 2, Czech Republic,
JSE 2021, 30(5), 447–453;
Submitted: 9 June 2025 | Revised: 9 June 2025 | Accepted: 9 June 2025 | Published: 9 June 2025
© 2025 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

Bulant, P., 2021. Two factors affecting the speed of interpolation within ray cells. Journal of Seismic Exploration, 30: 447-453. This short study is devoted to further investigation of the interpolation method by Bulant and KlimeS. 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 to which one of the two methods is preferable in general. Then the method by Bulant and Klimes 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.

Keywords
ray theory
traveltime
ray tracing
interpolation of the Green function
References
  1. Bucha, V. and Bulant, P. (Eds.), 2019. SW3D-CD-23 (DVD-ROM). Seismic Waves in
  2. Complex 3-D Structures, 29: 71-72, online at “http://sw3d.cz”.
  3. Bulant, P., 1999. Two-point ray-tracing and controlled initial-value ray-tracing in 3-D
  4. heterogeneous block structures. J. Seismic Explor., 8: 57-75.
  5. Bulant, P. and Klimes, L., 1998. Computations in the model composed during the 1998
  6. consortium meeting. Seismic Waves in Complex 3-D Structures, 7: 33-56, online
  7. at “http://sw3d.cz”.
  8. Bulant, P. and Klimes, L., 1999. Interpolation of ray theory traveltimes within ray cells.
  9. Geophys. J. Internat., 139: 273-282.
  10. Cerveny, V., Klime8, L. and PSen¢ik, I., 1988. Complete seismic—ray tracing in three—
  11. dimensional structures. In: Doornbos, D.J. (Ed.), Seismological Algorithms, 89-
  12. Academic Press, New York.
Share
Back to top
Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing