Microlocal Analysis of Seismic Inverse Scattering in Anisotropic Elastic Media

Communications on Pure and Applied Mathematics

Volumn 55, Issue 3, 2002, Pages 261-301

  Stolk, Christiaan C ^a,c   De Hoop, Maarten V ^b  

^a UTRECHT UNIVERSITY   (Netherlands)

^b Department of Geology and Geological Engineering   (United States)

^c RICE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036110253     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpa.10019     Document Type: Article

References (33)

1. Aki, K.; Richards, P. G. Quantitative seismology: theory and methods. Vol. 1. W. H. Freeman, San Francisco, 1980.
2. Beylkin, G. The inversion problem and applications of the generalized Radon transform. Comm. Pure Appl. Math. 37 (1984), no. 5, 579-599.
3. Beylkin, G. Imaging of discontinuities in the inverse scattering problem by inversion of a causal generalized Radon transform. J. Math. Phys. 26 (1985), no. 1, 99-108.
4. Beylkin, G.; Burridge, R. Linearized inverse scattering problems in acoustics and elasticity. Wave Motion 12 (1990), no. 1, 15-52.
5. Bleistein, N. On the imaging of reflectors in the earth. Geophysics 52 (1987), no. 7, 931-942.
6. Braam, P. J.; Duistermaat, J. J. Normal forms of real symmetric systems with multiplicity. Indag. Mathem. (N.S.) 4 (1993), no. 4, 407-421.
7. Burridge, R.; Beylkin, G. On double integrals over spheres. Inverse Problems 4 (1988), no. 1, 1-10.
8. Chapman, C. H. Reflection/transmission coefficient reciprocities in anisotropic media. Geophys. J. Internat. 116 (1994), 498-501.
9. Dencker, N. On the propagation of polarization sets for systems of real principal type. J. Funct. Anal. 46 (1982), no. 3, 351-372.
10. Duistermaat, J. J. Fourier integral operators. Birkhäuser, Boston, 1996.
11. Frazer, N. L.; Sen, M. K. Kirchhoff-Helmholtz reflection seismograms in a laterally inhomogeneous multi-layered medium. I. Theory. Geophys. J. R. Astr. Soc. 80 (1985), 121-147.
12. Guillemin, V. On some results of Gel′fand in integral geometry. Pseudodifferential operators and applications (Notre Dame, Ind., 1984), 149-155. Proceedings of Symposia in Pure Mathematics, 43. American Mathematical Society, Providence, R.I., 1985.
13. Hansen, S. Solution of a hyperbolic inverse problem by linearization. Comm. Partial Differential Equations 16 (1991), no. 2-3, 291-309.
14. Hoop, M. V. de; Bleistein, N. Generalized Radon transform inversions for reflectivity in anisotropic elastic media. Inverse Problems 13 (1997), no. 3, 669-690.
15. Hoop, M. V. de; Brandsberg-Dahl, S. Maslov asymptotic extension of generalized Radon transform inversion in anisotropic elastic media: a least-squares approach. Inverse Problems 16 (2000), no. 3, 519-562.
16. Hörmander, L. The analysis of linear partial differential operators. Vol. 1. Grundlehren der mathematischen Wissenschaften, 256-257. Springer, Berlin, 1983.
17. Hörmander, L. The analysis of linear partial differential operators. Vol. 3. Grundlehren der mathematischen Wissenschaften, 274. Springer, Berlin, 1985.
18. Hörmander, L. The analysis of linear partial differential operators, Vol. 4. Grundlehren der mathematischen Wissenschaften, 275. Springer, Berlin, 1985.
19. Ivrii, V. Ja. Wave fronts of solutions of symmetric pseudodifferential systems. Sibirsk. Mat. Zh. 20 (1979), no. 3, 557-578, 692; translation in Siberian Math. J. 20 (1979), no. 3, 390-405.
20. Ivrii, V. Ja. Wave fronts of solutions of symmetric pseudodifferential systems. Sibirsk. Mat. Zh. 20 (1979), no. 3, 557-578, 692; translation in Siberian Math. J. 20 (1979), no. 3, 390-405.
21. Kennett, B. L. N. Seismic wave propagation in stratified media. Cambridge University Press, Cambridge, 1983.
22. Kroode, A. P. E. ten; Smit, D. J.; Verdel, A. R. A microlocal analysis of migration. Wave Motion 28 (1998), 149-172.
23. Lions, J. L.; Magenes, E. Non-homogeneous boundary value problems and applications. Vol. 1. Grundlehren der mathematischen Wissenschaften, 181. Springer, New York-Heidelberg, 1972.
24. Maslov, V. P.; Fedoriuk, M. V. Semiclassical approximation in quantum mechanics. Mathematical Physics and Applied Mathematics, 7. Contemporary Mathematics, 5. D. Reidel, Dordrecht-Boston, 1981.
25. Musgrave, M. J. P. Crystal acoustics. Holden-Day, San Francisco, 1970.
26. Nolan, C. J.; Symes, W. W. Global solution of a linearized inverse problem for the wave equation. Comm. Partial Differential Equations 22 (1997), no. 5-6, 919-952.
27. Rakesh. A linearised inverse problem for the wave equation. Comm. Partial Differential Equations 13 (1988), no. 5, 573-601.
28. Stolk, C. C. Microlocal analysis of a seismic linearized inverse problem. Wave Motion 32 (2000), 267-290.
29. Symes, W. W. A differential semblance algorithm for the inverse problem of reflection seismology. Comput. Math. Appl. 22 (1991), no. 4-5, 147-178.
30. Taylor, M. E. Reflection of singularities of solutions to systems of differential equations. Comm. Pure Appl. Math. 28 (1975), no. 4, 457-478.
31. Treves, F. Introduction to pseudodifferential and Fourier integral operators. Vol. 1. University Series in Mathematics. Plenum, New York, 1980.
32. Treves, F. Introduction to pseudodifferential and Fourier integral operators. Vol. 2. University Series in Mathematics. Plenum, New York, 1980.
33. Xu, S.; Chauris, H.; Lambaré, G.; Noble, M. Common angle migration: a strategy for imaging complex media. Preprint. École des Mines de Paris, 1999.