Preprint 2000-039

An Adaptive Finite-difference Method for Traveltimes and Amplitudes

Jianliang Qian and William W. Symes

Abstract: The point source traveltime field has an upwind singularity at the source point. Consequently, all formally high-order finite-difference eikonal solvers exhibit first-order convergence and relatively large errors. Adaptive upwind finite-difference methods based on high-order Weighted Essentially NonOscillatory (WENO) Runge-Kutta difference schemes for the paraxial eikonal equation overcome this difficulty. The method controls error by automatic grid refinement and coarsening based on an {\em a posteriori} error estimation. It achieves prescribed accuracy at far lower cost than does the fixed-grid method. Moreover, the achieved high accuracy of traveltimes yields reliable estimates of auxiliary quantities such as takeoff angles and geometrical spreading factors.

Available as PostScript (1.2 Mbytes) or gzipped PostScript (220 Kbytes; uncompress using gunzip).
Jianliang Qian, <>
William W. Symes
Publishing information:
Submitted by:
<> September 18 2000.

[ 1996 | 1997 | 1998 | 1999 | 2000 | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <>
Last modified: Tue Sep 19 09:44:20 MET DST 2000