previous up next print clean
Next: Incremental DELAUNAY TRIANGULATION and Up: Fomel: Fast marching Previous: Acknowledgments

REFERENCES

Abgrall, R., and Benamou, J.-D., 1996, Multivalued traveltime fields, ray tracing and ekonal solver on unstructured grids: 66th Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1208-1211.

Abgrall, R., 1996, Numerical discretization of the first-order Hamilton-Jacobi equation on triangular meshes: Comm. on Pure and Applied Math., XLIX, 1339-1373.

Albertin, U. K., and Wiggins, W., 1994, Embedding geologic horizon surfaces in tetrahedral meshes for geologic modeling: 64rd Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 502-505.

Alkhalifah, T., and Fomel, S., 1997, Implementing the fast marching eikonal solver: Spherical versus cartesian coordinates: SEP-95, 149-171.

Biondi, B., Fomel, S., and Alkhalifah, T., 1997, ``focusing'' eikonal equation and global tomography: SEP-95, 61-76.

Cao, S., and Greenhalgh, S. A., 1994, Finite-difference solution of the eikonal equation using an efficient, first-arrival wavefront tracking scheme: Geophysics, 59, no. 4, 632-643.

Chew, L. P., 1989, Constrained Delaunay triangulations: Algorithmica, 4, 97-108.

Cormen, T. H., Leiserson, C. E., and Rivest, R. L., 1990, Introduction to algorithms: McGraw-Hill.

Delaunay, B. N., 1934, Sur la sphère vide: Izv. Akad. Nauk SSSR, Otdel. Mat. Est. Nauk, 7, 793-800.

Dellinger, J., 1991, Anisotropic finite-difference traveltimes: 61st Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1530-1533.

Dijkstra, E. W., 1959, A note on two problems in connection with graphs: Numer. Math., 1, 269-271.

Edelsbrunner, H., and Tan, T. S., 1993, An upper bound for conforming Delaunay triangulation: Discrete Comput. Geom., 10, 197-213.

Fomel, S., 1995, Amplitude preserving offset continuation in theory, Part 1: The offset continuation equation: SEP-84, 179-198.

Fomel, S., 1996, Migration and velocity analysis by velocity continuation: SEP-92, 159-188.

Fortune, S., 1987, A sweepline algorithm for Voronoi diagram: Algorithmica, 2, 153-174.

Garland, M., and Heckbert, P. S., 1996, Fast and flexible polygonization of height fields: SIGGRAPH 96, Visual Proceedings, 143.

Guibas, L., and Stolfi, J., 1985, Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams: ACM Trans. Graphics, 4, 74-123.

Guibas, L. J., Knuth, D., and Sharir, M., 1992, Randomized incremental construction of Delaunay and Voronoi diagrams: Algorithmica, 7, 381-413.

Guiziou, J. L., Mallet, J. L., Nobili, P., Anandappane, R., and Thisse, P., 1991, 3-d ray-tracing through complex triangulated surfaces: 61st Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1497-1500.

Hale, D., and Cohen, J. K., 1991, Triangulated models of the Earth's subsurface: Center for Wave Phenomenon Report, CWP-107.

Hansen, A. J., and Levin, P. L., 1992, On conforming Delaunay mesh generation: Adv. in Eng. Soft., 14, 129-135.

Lanczos, C., 1966, The variational principles of mechanics: University of Toronto Press, Toronto.

Lee, D. T., and Lin, A. K., 1986, Generalized Delaunay triangulation for planar graphs: Discrete Comput. Geom., 1, 201-217.

Lions, P. L., 1982, Generalized solutions of Hamilton-Jacobi equations: Pitman.

Moser, T. J., 1991, Shortest path calculation of seismic rays: Geophysics, 56, no. 1, 59-67.

Osher, S., and Sethian, J. A., 1988, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulation: Jour. of Comp. Phys., 79, 12-49.

Podvin, P., and Lecomte, I., 1991, Finite difference computation of traveltimes in very contrasted velocity models: A massively parallel approach and its associated tools: Geophysical Journal International, 105, 271-284.

Qin, F., Luo, Y., Olsen, K. B., Cai, W., and Schuster, G. T., 1992, Finite-difference solution of the eikonal equation along expanding wavefronts: Geophysics, 57, no. 3, 478-487.

Rivara, M.-C., 1996, New mathematical tools and techniques for the refinement and/or improvement of unstructured triangulations: 5th International Meshing Roundtable, Proceedings, 77-86.

Ruppert, J., 1995, A Delaunay refinement algorithm for quality two-dimensional mesh generation: Journal of Algorithms, 18, 548-585.

Sethian, J. A., and Popovici, A. M., 1997, Three-dimensional traveltime computation using the fast marching method: submitted to Geophysics.

Sethian, J. A., 1996a, A fast marching level set method for monotonically advancing fronts: Proc. Nat. Acad. Sci., 93, no. 4, 1591-1595.

Sethian, J. A., 1996b, Level set methods: Evolving interfaces in geometry, fluid mechanics, computer vision, and materials science: Cambridge University Press.

Shamos, M., and Hoey, D., 1975, Closest point problems: 16th Annual IEEE Sympos. Found. Comput. Sci., Proceedings, 151-162.

Shewchuk, J. R., 1996, Robust adaptive floating-point geometric predicates: 12th Annual Symposium on Computational Geometry, 141-150.

Sibson, R., 1978, Locally equiangular triangulations: Comput. J., 21, 243-245.

Smirnov, V. I., 1964, A course on higher mathematics: Pergamon Press.

Stankovic, G. M., and Albertin, U. K., 1995, Raytracing in topological tetrahedral models: 65th Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1247-1250.

van Trier, J., and Symes, W. W., 1991, Upwind finite-difference calculation of traveltimes: Geophysics, 56, no. 6, 812-821.

Vidale, J. E., 1990, Finite-difference calculation of traveltimes in three dimensions: Geophysics, 55, no. 5, 521-526.

Wiggins, W., Albertin, U. K., and Stankovic, C., 1993, Building 3-D depth migration velocity models with topological objects: 63rd Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 170-173.

Woo, M., Neider, J., and Davis, T., 1997, OpenGL programming guide: Addison-Wesley.

A



Stanford Exploration Project
10/9/1997