V. A. Borovikov, Uniform Stationary Phase Method (IEE, 1994.

P. Y. Ufimtsev, Fundamentals of the Physical Theory of Diffraction, p.9, 2007.

V. A. Borovikov and B. Y. Kinber, Geometrical Theory of Diffraction (IEE, 1994.

J. B. Keller, Geometrical theory of diffraction, J. Opt. Soc. Am, vol.52, issue.2, pp.116-130, 1962.

J. D. Achenbach, A. K. Gautesen, and H. Mcmaken, Ray Methods for Waves in Elastic Solids, With Applications to Scattering by Cracks, pp.1-251, 1979.

G. Huet, M. Darmon, A. Lh-emery, and S. Mahaut, Modelling of corner echo ultrasonic inspection with bulk and creeping waves, Ultrasonic Wave Propagation in Non Homogeneous Media, vol.128, pp.217-226, 2009.

S. Mahaut, M. Darmon, S. Chatillon, F. Jenson, and P. Calmon, Recent advances and current trends of ultrasonic modelling in CIVA, Insight, vol.51, issue.2, pp.78-81, 2009.

M. Darmon and S. Chatillon, Main features of a complete ultrasonic measurement model, Open J. Acoust, vol.3, issue.3A, pp.43-53, 2013.

V. Zernov, L. Fradkin, and M. Darmon, A refinement of the Kirchhoff approximation to the scattered elastic fields, Ultrasonics, vol.52, issue.7, pp.830-835, 2011.

A. Mohorovi?icmohorovi?ic´, A translation appears in Geofizika, Jahrb. Meteorol. Obs. Zagreb F? ur, vol.4, pp.3-55, 1909.

V. Cerveny and R. Ravindra, Theory of Seismic Head Waves, pp.1-312, 1971.

W. S. Lihh, Frequency-and time-domain asymptotic fields near the critical cone in fluid-fluid configuration, J. Acoust. Soc. Am, vol.121, issue.5, pp.2655-2666, 2007.

A. Ciarkowski, Uniform asymptotic expansion of an integral with a saddle point, a pole and a branch point, Proc. R. Soc. London, Ser. A, vol.426, pp.273-286, 1989.

I. Thompson, An improved uniform approximation for diffraction, Proc. R. Soc. London, Ser. A, vol.462, pp.1341-1353, 2006.

D. Gridin, High-frequency asymptotic description of head waves and boundary layers surrounding the critical rays in an elastic half space, J. Acoust. Soc. Am, vol.104, issue.3, pp.1188-1197, 1998.

B. Caroli, C. Caroli, C. Misbah, and B. Roulet, On velocity selection for needle crystals in the fully nonlocal model of solidification, J. Phys, vol.48, pp.547-552, 1987.

R. Uitham and B. J. Hoenders, The electromagnetic Brillouin precursor in one-dimensional photonic crystals, Optics Comm, vol.281, pp.5910-5918, 2008.

M. V. Berry, Causal wave propagation for relativistic massive particles: Physical asymptotics in action, Eur. J. Phys, vol.33, issue.2, pp.279-294, 2012.

A. Kuznetsov, On the Riemann-Siegel formula, Proc. R. Soc. London, Ser. A, vol.463, pp.2557-2568, 2007.

J. D. Achenbach and A. K. Gautesen, Edge diffraction in acoustics and elastodynamics (low and high frequency asymptotics), Low and High Frequency Asymptotics-Acoustic, Electromagnetic and Elastic Wave Scattering, vol.2, pp.335-401, 1986.

A. K. Gautesen, A note on the diffraction coefficients for elastodynamic diffraction by sharp edges, Wave Motion, vol.47, issue.5, pp.327-332, 2010.

L. N. Trefethen and J. A. Weideman, The exponentially convergent trapezoidal rule, SIAM Rev, vol.56, issue.3, pp.385-458, 2014.

A. Iserles and S. P. Nørsett, Efficient quadrature of highly oscillatory integrals using derivatives, Proc. R. Soc. London, Ser. A, vol.461, pp.1383-1399, 2005.

L. Fradkin, M. Harmer, and M. Darmon, Edge diffraction coefficients around critical rays, Proceedings of the 12th Anglo-French Physical Acoustics Conference, vol.498, p.12010, 2014.
URL : https://hal.archives-ouvertes.fr/cea-01820753

L. Ju, A. P. Fradkin, and . Kiselev, The two-component representation of time-harmonic elastic body waves in the high-and intermediate-frequency regimes, J. Acoust. Soc. Am, vol.101, issue.1, pp.52-65, 1997.