An Adaptive Finite-Di erence Method for Traveltimes and Amplitudes
نویسندگان
چکیده
The point source traveltime eld has an upwind singularity at the source point. Consequently, all formally high-order nite-diierence eikonal solvers exhibit rst-order convergence and relatively large errors. Adaptive upwind nite-diierence methods based on high-order Weighted Essentially NonOscillatory (WENO) Runge-Kutta diierence schemes for the paraxial eikonal equation overcome this diiculty. The method controls error by automatic grid reenement and coarsening based on an a posteriori error estimation. It achieves prescribed accuracy at far lower cost than does the xed-grid method. Moreover, the achieved high accuracy of traveltimes yields reliable estimates of auxiliary quantities such as takeoo angles and geometrical spreading factors.
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