Reflection in a level set framework for geometric optics

CMES - Computer Modeling in Engineering and Sciences

Volumn 5, Issue 4, 2004, Pages 347-360

  Cheng, Li Tien ^a   Kang, Myungjoo ^b   Osher, Stanley ^b   Shim, Hyeseon ^b   Tsai, Yen Hsi ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Level Set Systems Inc   (United States)

^c PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIKONAL EQUATIONS; HAMILTON-JACOBI EQUATIONS; TRANSPORT EQUATIONS; TRAVELTIME;

ALGORITHMS; DATA PROCESSING; ELECTROMAGNETIC WAVE PROPAGATION; ELECTROMAGNETIC WAVE REFLECTION; SEISMOLOGY; TOMOGRAPHY; WAVEFRONTS;

RAY TRACING;

EID: 5144225979     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. Abgrall, R.; Benamou, J.-D. (1999): Big Ray Tracing and Eikonal Solver on Unstructured Grids: Application to the Computation of a Multivalued Travel-Time Field in the Marmousi Model. Geophysics, vol. 64, pp. 230-239.
2. Adalsteinsson, D.; Sethian, J. (1995): A Fast Level Set Method for Propagating Interfaces. J. Comput. Phys., vol. 118, pp. 269-277.
3. Arnol'd, V. (1992): Catastrophe Theory. Springer-Verlag.
4. Arnol'd, V.; Gusein-Zade, S.; Varchenko, A. (1986): Singularities of Differential Maps. Birkhauser.
5. Benamou, J.-B. (to appear): An Eulerian Numerical Method for Geometric Optics. To appear in COCV Proc., ??.
6. Benamou, J.-D. (1996): Big Ray Tracing: Multi-Valued Travel Time Field Computation Using Viscosity Solutions of the Eikonal Equation. J. Comput. Phys., vol. 128, pp. 463-474.
7. Benamou, J.-D. (1999): Direct Solution of Multi-Valued Phase-Space Solutions for Hamilton-Jacobi Equations. Comm. Pure Appl. Math., vol. 52.
8. Beylkin, G. (1985): Imaging of Discontinuities in the Inverse Scattering Problem by Inversion of a Causal Generalized Radon Transform. J. Math. Phys., vol. 26, pp. 99-108.
9. Beylkin, G.; Burridge, R. (1990): Linearized Inverse Scattering Problem of Acoustics and Elasticity. Wave Motion, vol. 12, pp. 15-22.
10. Bleszynski, E.; Bleszynski, M.; Jaroszewicz, T. (2004): Development of New Algorithms for High Frequency Electromagnetic Scattering. CMES: Computer Modeling in Engineering & Sciences, vol. 5, no. 4, pp. 295-318.
11. Brenier, Y.; Corrias, L. (1996): A Kinetic Formulation for Multi-Branch Entropy Solutions of Scalar Conservation Laws. Ann. IHP Analyse non-lineaire.
12. Bruno, O. (2002): New high-order, high-frequency integral methods in computational electromagnetism.
13. Burchard, P.; Cheng, L.-T.; Merriman, B.; Osher, S. (2001): Motion of Curves in Three Spatial Dimensions Using a Level Set Approach. J. Comput. Phys., vol. 170, no. 2, pp. 720-741.
14. Burridge, R.; de Hoop, M.; Miller, D.; Spencer, C. (1998): Multiparameter Inversion in Anisotropic Media. Geophys. J. Internat., vol. 134, pp. 757-777.
15. de Hoop, M.; Bleistein, N. (1997): Generalized Radon Transform Inversions for Reflectivity in Anisotropic Elastic Media. Inverse Problems, vol. 13, pp. 669-690.
16. Duistermaat, J. (1974): Oscillatory Integrals, Lagrange Immersions and Unfolding of Singularities. Comm. Pure Appl. Math., vol. 27, pp. 207-281.
17. Engquist, B.; Fatemi, E.; Osher, S. (1995): Numerical Resolution of the High Frequency Asymptotic Expansion of the Scalar Wave Equation. J. Comput. Phys., vol. 120, pp. 145-155.
18. Engquist, B.; Runborg, O. (1995): Multi-Phase Computation in Geometrical Optics. Tech Report, Nada KTH, 1995.
19. Engquist, B.; Runborg, O.; Tornberg, A.-K. (2002): High Frequency Wave Propagation by the Segment Projection Method. J. Comput. Phys., vol. 178, no. 2, pp. 373-390.
20. Fomel, S.; Sethian, J. (2001): Fast Phase Space Computation of Multiple Arrivals. Technical Report LBNL-48976, LBL, 2001.
21. Izumiya, S. (1993): The Theory of Legendrian Unfoldings and First Order Differential Equations. Proc. Royal Soc. Edinburgh, vol. 123A, pp. 517-532.
22. Jiang, G.; Peng, D. (2000): Weighted ENO Schemes for Hamilton Jacobi Equations. SIAM J. Scient. Comput., vol. 21, no. 6, pp. 2126-2143.
23. Lax, P. D. (1957): Asymptotic solutions of oscillatory initial value problems. Duke Math. J., vol. 24, pp. 627-646.
24. Lorenson, W.; Cline, H. (1987): Marching cubes: A high resolution 3D surface reconstruction algorithm. Comp. Graphics, vol. 21, no. 4, pp. 163-169.
25. Osher, S.; Cheng, L.-T.; Kang, M.; Shim, H.; Tsai, Y.-H. (2002): Geometric Optics in a Phase Space Based Level Set and Eulerian Framework. J. Comput. Phys., vol. 179, no. 2, pp. 622-648.
26. Osher, S.; Sethian, J. (1988): Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations. J. Comput. Phys., vol. 169, no. 1, pp. 12-49.
27. Peng, D.; Merriman, B.; Osher, S.; Zhao, H.; Kang, M. (1999): A PDE-Based Fast Local Level Set Method. J. Comput. Phys., vol. 155, no. 2, pp. 410-438.
28. Qian, J.; Cheng, L.-T.; Osher, S. (2003): A Level Set Based Eulerian Approach for Anisotropic Wave Propagations. Wave Motion, vol. 37, no. 4, pp. 365-379.
29. Ruuth, S.; Merriman, B.; Osher, S. (2000): Fixed Grid Method for Capturing the Motion of Self-Intersecting Interfaces and Related PDEs. J. Comput. Phys., vol. 163, pp. 1-21.
30. Shu, C.-W.; Osher, S. (1988): Efficient Implementation of Essentially Nonoscillatory Shock-Capturing Schemes. J. Comput. Phys., vol. 77, no. 2, pp. 439-471.
31. Spiteri, R.; Ruuth, S. (2002): A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods. SIAM J. Numer. Anal., vol. 40, no. 2, pp. 469-491.
32. Steinhoff, J.; Fan, M.; Wang, L. (2000): A New Eulerian Method for the Computation of Propagating Short Acoustic and Electromagnetic Pulses. J. Comput. Phys., vol. 157, no. 2, pp. 683-706.
33. Symes, W. (1996): A Slowness Matching Finite Difference Method for Traveltimes Beyond Transmission Caustics. The Rice Inversion Project Annual Report, Rice University, 1996.
34. Symes, W.; Carazzone, J. (1991): Velocity Inversion by Differential Semblance Optimization. Geophysics, vol. 56, pp. 654-663.
35. Vinje, V.; Iversen, E.; Astebol, K.; ystdal, H. G. (1996): Estimation of Multivalued Arrivals in 3D Models using Wavefront Construction-Part I. Geophysical Prospecting, vol. 44, pp. 819-842.
36. Vinje, V.; Iversen, E.; Astebol, K.; ystdal, H. G. (1996): Part II: Tracing and Interpolation. Geophysical Prospecting, vol. 44, pp. 843-858.
37. Vinje, V.; Iversen, E.; ystdal, H. G. (1993): Traveltime and Amplitude Estimation using Wavefront Construction. Geophysics, vol. 58, no. 8, pp. 1157-1166.