M. V. De-hoop, J. L. Rousseau, and B. Biondi, Symplectic structure of wave-equation imaging: a path-integral approach based on the double-square-root equation, Geophysical Journal International, vol.153, issue.1, pp.52-74, 2003.
DOI : 10.1046/j.1365-246X.2003.01877.x

M. V. De-hoop, J. L. Rousseau, and R. Wu, Generalization of the phase-screen approximation for the scattering of acoustic waves, Wave Motion, vol.31, issue.1, pp.43-70, 2000.
DOI : 10.1016/S0165-2125(99)00026-8

J. J. Duistermaat, Fourier integral operators, Birkhäuser, 1996.

K. Engel and R. Nagel, One-parameter semigroups for linear evolution equations, Semigroup Forum, vol.63, issue.2, 1999.
DOI : 10.1007/s002330010042

L. Hörmander, The analysis of linear partial differential operators, volume III, 1985.

L. Hörmander, The analysis of linear partial differential operators, volume IV, 1985.

L. Hörmander, The analysis of linear partial differential operators, volume I, 1990.

T. Kato, Linear evolution equations of ``hyperbolic'' type, II, Journal of the Mathematical Society of Japan, vol.25, issue.4, pp.241-258, 1970.
DOI : 10.2969/jmsj/02540648

H. Kumano-go, and the fundamental solution for an operator of hyperbolic type, Communications in Partial Differential Equations, vol.51, issue.1, pp.1-44, 1976.
DOI : 10.1080/03605307608820002

J. and L. Rousseau, Fourier-Integral-Operator Approximation of Solutions to First-Order Hyperbolic Pseudodifferential Equations I: Convergence in Sobolev Spaces, Communications in Partial Differential Equations, vol.43, issue.6, pp.867-906, 2006.
DOI : 10.1002/cpa.3160280403

URL : https://hal.archives-ouvertes.fr/hal-00003815

J. , L. Rousseau, and M. V. De-hoop, Modeling and imaging with the scalar generalized-screen algorithms in isotropic media, Geophysics, vol.66, pp.1551-1568, 2001.

L. Rousseau and M. V. De-hoop, Generalized-Screen Approximation and Algorithm for the Scattering of Elastic Waves, The Quarterly Journal of Mechanics and Applied Mathematics, vol.56, issue.1, pp.1-33, 2003.
DOI : 10.1093/qjmam/56.1.1

J. , L. Rousseau, and G. Hörmann, Fourier-integral-operator approximation of solutions to pseudodifferential first-order hyperbolic equations II: microlocal analysis, J. Math. Pures Appl, vol.86, pp.403-426, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00005759

A. Pazy, Semigroups of linear operators and applications to partial differential equations, 1983.
DOI : 10.1007/978-1-4612-5561-1

H. Smith, A parametrix construction for wave equations with $C^{1,1}$ coefficients, Annales de l???institut Fourier, vol.48, issue.3, pp.797-835, 1998.
DOI : 10.5802/aif.1640

C. C. Stolk, A pseudodifferential equation with damping for one-way wave propagation in inhomogeneous acoustic media, Wave Motion, vol.40, issue.2, pp.111-121, 2004.
DOI : 10.1016/j.wavemoti.2003.12.016

URL : https://hal.archives-ouvertes.fr/hal-00121994

C. C. Stolk, Parametrix for a hyperbolic intial value problem with dissipation in some region, Asymptotic Analysis, vol.43, issue.12, pp.151-169, 2005.