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Browsing by Author "Symes, William W."

Now showing 1 - 6 of 6
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    An adaptive finite-difference method for traveltimes and amplitudes
    (2001-07) Qian, Jianliang; Symes, William W.
    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 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.
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    Computation of pseudo-differential operators
    (1992-11) Bao, Gang; Symes, William W.
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    Finite-difference quasi-P traveltimes for anisotropic media
    (2001-07) Qian, Jianliang; Symes, William W.
    The first-arrival quasi-P wave traveltime field in an anisotropic elastic solid solves a first-order nonlinear partial differential equation, the qP eikonal equation. The difficulty in solving this eikonal equation by a finite-difference method is that for anisotropic media the ray (group) velocity direction is not the same as the direction of traveltime gradient, so that the traveltime gradient can no longer serve as an indicator of the group velocity direction in extrapolating the traveltime field. However, establishing an explicit relation between the ray velocity vector and the phase velocity vector overcomes this difficulty. Furthermore, the solution of the paraxial qP eikonal equation, an evolution equation in depth, gives the first-arrival traveltime along downward propagating rays. A second-order upwind finite-difference scheme solves this paraxial eikonal equation in O(N) floating point operations, where N is the number of grid points. Numerical experiments using 2-D and 3-D transversely isotropic models demonstrate the accuracy of the scheme.
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    A note on consistency and adjointness for numerical schemes
    (1995-08) Sei, A.; Symes, William W.
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