Abstract
A new computational scheme for calculating the first-arrival travel times on a rectangular grid of points is proposed. The new proposed method is of second-order accuracy. This means that the error of the calculated travel time is proportional to the second power of the grid spacing. The method should be sufficiently accurate for all applications in smooth seismic models. On the other hand, the method is not, in its present form, proposed for models with structural interfaces which make the method unstable and generate travel-time errors of the first order. Equations are also presented for the appropriate evaluation of the errors of calculated travel times to check their accuracy, and the proposed method is compared with other numerical methods. The method is developed, described and demonstrated in 2-D, but may also be extended to 3-D models and to general models with structural interfaces.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Klimeš, L., andKvasnička, M. (1994),3-D Network Ray Tracing, Geophys. J. Int.116, 726–738.
Klimeš, L. (1996),Travel-time Calculation in Heterogeneous 3-D Structures, J. Seismol. Explor. (submitted).
Moser, T-J. (1989),Efficient Seismic Ray Tracing Using Graph Theory, Expanded Abstracts of 59th Annual Int. SEG Meeting (Dallas), pp. 1106–1108, Soc. Exploration Geophysicists, Tulsa.
Moser, T-J. (1991),Shortest Path Calculation of Seismic Rays, Geophysics56, 59–67.
Naganishi, I., andYamaguchi, K. (1986),A Numerical Experiment on Nonlinear Image Reconstruction from First-arrival Times for Two-dimensional Island Arc Structure, J. Phys. Earth34, 195–201.
Podvin, P., andLecomte, I. (1991),Finite Difference Computation of Traveltimes in Very Contrasted Velocity Models: A Massively Parallel Approach and its Associated Tools, Geophys. J. Int.105, 271–284.
Pusey, L. C., andVidale, J. E. (1991),Accurate Finite-difference Calculation of WKBJ Traveltimes and Amplitudes, Expanded Abstracts of 61st Annual Int. SEG Meeting (Houston), pp. 1513–1516, Soc. Exploration Geophysicists, Tulsa.
Qin, F., Luo, Y., Olsen, K. B., andSchuster, G. T. (1990),Solution of the Eikonal Equation by a Finite-difference Methoa, Expanded Abstracts of 60th Annual Int. SEG Meeting (San Francisco), pp. 1004–1007, Soc. Exploration Geophysicists, Tulsa.
Qin, F., Luo, Y., Olsen, K. B., Cai, W., andSchuster, G. T. (1992), Finite-difference Solution of the Eikonal Equation along Expanding Wavefront, Geophysics57, 478–487.
Saito, H. (1989),Traveltimes and Raypaths of First Arrival Seismic Waves: Computation Method Based on Huygens' Principle, Expanded Abstracts of 59th Annual Int. SEG Meeting (Dallas), pp. 244–247, Soc. Exploration Geophysicists, Tulsa.
Saito, H. (1990),3-D Ray-tracing Method Based on Huygens' Principle, Expanded Abstracts of 60th Annual Int. SEG Meeting (San Francisco), pp. 1024–1027, Soc. Exploration Geophysicists, Tulsa.
Van Trier, J., andSymes, W. W. (1990),Upwind Finite-difference Calculation of Seismic Traveltimes, Expanded Abstracts of 60th Annual Int. SEG Meeting (San Francisco), pp. 1000–1003, Soc. Exploration Geophysicists, Tulsa.
Van Trier, J., andSymes, W. W. (1991),Upwind Finite-difference Calculation of Traveltimes, Geophysics56, 812–821.
Vidale, J. E. (1988),Finite-difference Calculation of Travel Times, Bull. Seismol. Soc. Am.78, 2062–2076.
Vinje, V., Iversen, E., andGjøystdal, H. (1993),Traveltime and Amplitude Estimation Using Wavefront Construction, Geophysics58, 1157–1166.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Klimeš, L. Grid travel-time tracing: Second-order method for the first arrivals in smooth media. PAGEOPH 148, 539–563 (1996). https://doi.org/10.1007/BF00874578
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00874578