Microlocal analysis and seismic imaging
Séminaire Équations aux dérivées partielles (Polytechnique) (2003-2004), Talk no. 17, 20 p.

We study certain Fourier integral operators arising in the inversion of data from reflection seismology.

@article{SEDP_2003-2004____A17_0,
     author = {Stolk, Christiaan},
     title = {Microlocal analysis and seismic imaging},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2003-2004},
     note = {talk:17},
     mrnumber = {2117049},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_2003-2004____A17_0}
}
Stolk, Christiaan. Microlocal analysis and seismic imaging. Séminaire Équations aux dérivées partielles (Polytechnique) (2003-2004), Talk no. 17, 20 p. http://www.numdam.org/item/SEDP_2003-2004____A17_0/

[1] G. Beylkin. Imaging of discontinuities in the inverse scattering problem by inversion of a causal generalized Radon transform. J. Math. Phys., 26(1):99–108, 1985. | MR 776132

[2] J. F. Claerbout. Imaging the Earth’s Interior. Blackwell Scientific Publications, Oxford, 1985.

[3] J. J. Duistermaat. Fourier Integral Operators. Birkhäuser, Boston, 1996. | MR 1362544 | Zbl 0841.35137

[4] Victor Guillemin. On some results of Gelʼfand in integral geometry. In Pseudodifferential operators and applications (Notre Dame, Ind., 1984), pages 149–155. Amer. Math. Soc., Providence, RI, 1985. | MR 812288 | Zbl 0576.58028

[5] L. Hörmander. The Analysis of Linear Partial Differential Operators, volume 3,4. Springer-Verlag, Berlin, 1985. | Zbl 0601.35001

[6] V. P. Maslov and M. V. Fedoriuk. Semi-Classical Approximation in Quantum Mechanics. D. Reidel Publishing Company, 1981. | MR 634377 | Zbl 0458.58001

[7] C. J. Nolan and W. W. Symes. Global solution of a linearized inverse problem for the wave equation. Comm. Partial Differential Equations, 22(5-6):919–952, 1997. | MR 1452173 | Zbl 0889.35122

[8] Rakesh. A linearized inverse problem for the wave equation. Comm. Partial Differential Equations, 13(5):573–601, 1988. | MR 919443 | Zbl 0671.35078

[9] P. Shen, W. W. Symes, and C. C. Stolk. Differential semblance velocity analysis by wave-equation migration. In 73rd Ann. Internat. Mtg., pages 2132–2135. Soc. of Expl. Geophys., 2003. http://seg.org/publications.

[10] C. C. Stolk and M. V. De Hoop. Microlocal analysis of seismic inverse scattering in anisotropic elastic media. Comm. Pure Appl. Math., 55(3):261–301, 2002. | MR 1866365 | Zbl 1018.86002

[11] C. C. Stolk and M. V. De Hoop. Modeling of seismic data in the downward continuation approach. To appear in SIAM Journal on Applied Mathematics, 2004. http://www.math.polytechnique.fr/~stolk. | Zbl 1074.86003

[12] C. C. Stolk and M. V. De Hoop. Seismic inverse scattering in the downward continuation approach. Preprint, 2004. http://www.math.polytechnique.fr/~stolk.

[13] W. W. Symes. Extensions and nonlinear inverse scattering: Lecture at opening conference of IPRPI, April 2004. http://www.trip.caam.rice.edu/txt/tripinfo/other_list.html.

[14] W. W. Symes and J. Carazzone. Velocity inversion by differential semblance optimization. Geophysics, 56(5):654–663, 1991.

[15] A. P. E. Ten Kroode, D. J. Smit, and A. R. Verdel. A microlocal analysis of migration. Wave Motion, 28:149–172, 1998. | MR 1637771 | Zbl 1074.74582

[16] François Treves. Introduction to Pseudodifferential and Fourier Integral Operators, volume 2. Plenum Press, New York, 1980. | MR 597145 | Zbl 0453.47027