A Slowness Matching Nite Diierence Method for Traveltimes beyond Transmission Caustics
نویسنده
چکیده
Conventional nite diierence eikonal solvers produce only the rst arrival time. However suitable solvers (of suuciently high order of accuracy) may be extended via Fermat's principle to yield a simple algorithm which computes all traveltimes to each subsurface point, with cost on the same order as that of a rst arrival solver.
منابع مشابه
An Adaptive Finite-Di erence Method for Traveltimes and Amplitudes
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. ...
متن کاملWavefronts of Linear Elastic Waves: Local Convexity and Modeling
Seismic techniques incorporating high frequency asymptotic representation of the 3D elastic Green's function require eecient solution methods for the computation of traveltimes. For nite diierence eikonal solvers, upwind diierences are requisite to sharply resolve discontinuities in the traveltime derivatives. In anisotropic media the direction of energy propagation is not in general tangent to...
متن کاملA Slowness Matching Eulerian Method for Multivalued Solutions of Eikonal Equations
Traveltime, or geodesic distance, is locally the solution of the eikonal equation of geometric optics. However traveltime between sufficiently distant points is generically multivalued. Finite difference eikonal solvers approximate only the viscosity solution, which is the smallest value of the (multivalued) traveltime (‘‘first arrival time’’). The slowness matching method stitches together loc...
متن کاملUpwind Nite Diierence Traveltime for Anisotropic Media
The rst arrival quasi-P wave traveltime eld in an anisotropic elastic solid solves a rst order nonlinear partial diierential equation, the qP eikonal equation. Since the qP slowness surface is convex, the rst arrival traveltime along downward propagating rays solves the paraxial qP eikonal equation, an evolution equation in depth. A second order upwind nite diierence scheme solves this paraxial...
متن کاملKirchhoo Simulation, Migration, and Inversion Using Finite Diierence Traveltimes and Amplitudes
High frequency asymptotic approximation of the acoustic Green's function leads to eecient modeling and migration methods for primaries only reeection seismograms. A volume (as opposed to interface) oriented description of reeectivity allows symmetry between modeling and migration. With proper selection of amplitudes and dis-cretization, the migration and modeling operations are mathematically a...
متن کامل