M. Abramowitz and I. Tstegun, Handbook of mathematical functions : with formulas, graphs, and mathematical tables, 1965.

I. Abubakirov and A. Etgusev, Estimation of scattering properties of lithosphere of Kamchatka based on Monte-Carlo simulation of record envelope of a near earthquake, Physics of the Earth and Planetary Interiors, vol.64, issue.1, pp.52-67, 1990.
DOI : 10.1016/0031-9201(90)90005-I

K. Aki, Analysis of the seismic coda of local earthquakes as scattered waves, Journal of Geophysical Research, vol.7, issue.1, pp.615-631, 1969.
DOI : 10.1029/JB074i002p00615

K. Aki and B. Etchouet, Origin of coda waves: Source, attenuation, and scattering effects, Journal of Geophysical Research, vol.73, issue.4, pp.803322-3342, 1975.
DOI : 10.1029/JB080i023p03322

K. Aki and V. Etferrazzini, Seismic monitoring and modeling of an active volcano for prediction, Journal of Geophysical Research: Solid Earth, vol.83, issue.3, pp.16617-16633, 2000.
DOI : 10.1029/2000JB900033

E. Akkermans and G. Tmontambaux, Physique mésoscopique des électrons et des photons, 2004.

M. Albada and A. Tlagendijk, Observation of weak localization of light in a random medium. Physical review letters, pp.552692-2695, 1985.

D. Anderson and R. Tseals, Pulse velocity as a predictor of 28-and 90-day strength, ACI Journal Proceedings, 1981.

J. Anderson and P. Tnerenst, Wave velocity in concrete, ACI Journal Proceedings, 1952.

P. Anderson, Absence of diffusion in certain random lattices, p.1492, 1958.

P. Anugonda, J. Wiehn, and J. Tturner, Diffusion of ultrasound in concrete, Ultrasonics, vol.39, issue.6, pp.429-435, 2001.
DOI : 10.1016/S0041-624X(01)00077-4

A. Aubry and A. Etderode, Random Matrix Theory Applied to Acoustic Backscattering and Imaging In Complex Media, Physical Review Letters, vol.102, issue.8, p.84301, 2009.
DOI : 10.1103/PhysRevLett.102.084301

J. Becker, L. Jacobs, and J. Tqu, Characterization of Cement-Based Materials Using Diffuse Ultrasound, Journal of Engineering Mechanics, vol.129, issue.12, pp.1478-1484, 2003.
DOI : 10.1061/(ASCE)0733-9399(2003)129:12(1478)

Y. Bibliographie-berthaud, Damage measurements in concrete via an ultrasonic technique. part i experiment. Cement and concrete research, pp.73-82, 1991.

F. Brenguier, M. Campillo, C. Hadziioannou, N. Shapiro, R. Nadeau et al., Postseismic Relaxation Along the San Andreas Fault at Parkfield from Continuous Seismological Observations, Science, vol.321, issue.5895, pp.3211478-1481, 2008.
DOI : 10.1126/science.1160943

URL : https://hal.archives-ouvertes.fr/hal-00353290

F. Brenguier, N. Shapiro, M. Campillo, V. Ferrazzini, Z. Duputel et al., Towards forecasting volcanic eruptions using seismic noise, Nature Geoscience, vol.33, issue.2, pp.126-130, 2008.
DOI : 10.1038/ngeo104

URL : https://hal.archives-ouvertes.fr/insu-00332590

C. Wunderlich and E. N. , Evaluation of Temperature Influence on Ultrasound Velocity in Concrete by Coda Wave Interferometry, International symposium on nondestructive testing of materials and structures, 2011.
DOI : 10.1007/978-94-007-0723-8_33

M. Campillo and A. Tpaul, Long-Range Correlations in the Diffuse Seismic Coda, Science, vol.299, issue.5606, pp.299547-549, 2003.
DOI : 10.1126/science.1078551

URL : https://hal.archives-ouvertes.fr/hal-00107924

S. Chandrasekhar, Radiative transfer, 1960.

R. Courant, K. Friedrichs, and H. Etlewy, On the Partial Difference Equations of Mathematical Physics, IBM Journal of Research and Development, vol.11, issue.2, pp.215-234, 1967.
DOI : 10.1147/rd.112.0215

M. Cowan, I. Jones, J. Page, and D. Tweitz, Diffusing acoustic wave spectroscopy, Physical Review E, vol.65, issue.6, p.65066605, 2002.
DOI : 10.1103/PhysRevE.65.066605

M. Cowan, J. Page, and D. Etweitz, Velocity Fluctuations in Fluidized Suspensions Probed by Ultrasonic Correlation Spectroscopy, Physical Review Letters, vol.85, issue.2, pp.453-456, 2000.
DOI : 10.1103/PhysRevLett.85.453

J. Crank, The Mathematics of Diffusion, 1979.

J. De-rosny and P. Etroux, Multiple scattering in a reflecting cavity: Application to fish counting in a tank, The Journal of the Acoustical Society of America, vol.109, issue.6, pp.2587-2597, 2001.
DOI : 10.1121/1.1369101

A. Derode, V. Mamou, and A. Ttourin, Influence of correlations between scatterers on the attenuation of the coherent wave in a random medium, Physical Review E, vol.74, issue.3, p.36606, 2006.
DOI : 10.1103/PhysRevE.74.036606

A. Derode, P. Roux, and M. Tfink, Robust acoustic time reversal with highorder multiple scattering, Physical Review Letters, issue.23, pp.754206-4209, 1995.

A. Derode, A. Tourin, and M. Etfink, Random multiple scattering of ultrasound.???I.???Coherent and ballistic waves, Physical Review E, vol.64, issue.3, p.36605, 2001.
DOI : 10.1103/PhysRevE.64.036605

Z. Duputel, V. Ferrazzini, F. Brenguier, N. Shapiro, M. Campillo et al., Real time monitoring of relative velocity changes using ambient seismic noise at the Piton de la Fournaise volcano (La R??union) from January 2006 to June 2007, Journal of Volcanology and Geothermal Research, vol.184, issue.1-2, pp.164-173, 2006.
DOI : 10.1016/j.jvolgeores.2008.11.024

S. Feng and D. Tsornette, Acoustical nondestructive evaluation of heterogeneous materials in the multiple scattering regime, The Journal of the Acoustical Society of America, vol.90, issue.4, p.1742, 1991.
DOI : 10.1121/1.401654

L. Foldy, The Multiple Scattering of Waves. I. General Theory of Isotropic Scattering by Randomly Distributed Scatterers, Physical Review, vol.67, issue.3-4, pp.3-4107, 1945.
DOI : 10.1103/PhysRev.67.107

A. Frankel and R. Etclayton, Finite difference simulations of seismic scattering: Implications for the propagation of short-period seismic waves in the crust and models of crustal heterogeneity, Journal of Geophysical Research, vol.50, issue.B6, pp.6465-6489, 1986.
DOI : 10.1029/JB091iB06p06465

U. Frisch, Wave propagation in random media, Probabilistic methods in applied mathematics, p.75, 1968.

B. Froment, Utilisation du bruit sismique ambiant dans le suivi temporel de structures géologiques, Thèse de doctorat, 2011.

A. Grêt, R. Snieder, R. Aster, and P. Tkyle, Monitoring rapid temporal change in a volcano with coda wave interferometry, Geophysical Research Letters, vol.145, issue.10, pp.32-06304, 2005.
DOI : 10.1029/2004GL021143

C. Hadziioannou, E. Larose, O. Coutant, P. Roux, and M. Tcampillo, Stability of monitoring weak changes in multiply scattering media with ambient noise correlation: Laboratory experiments, The Journal of the Acoustical Society of America, vol.125, issue.6, pp.3688-3695, 2009.
DOI : 10.1121/1.3125345

URL : https://hal.archives-ouvertes.fr/hal-00377456

P. Hansen, Analysis of discrete ill-posed problems by means of the l-curve. SIAM review, pp.561-580, 1992.

R. Hennino, N. Tregoures, N. Shapiro, L. Margerin, M. Campillo et al., Observation of Equipartition of Seismic Waves, Physical Review Letters, vol.86, issue.15, pp.863447-3450, 2001.
DOI : 10.1103/PhysRevLett.86.3447

K. Holliger and A. Tlevander, A stochastic view of lower crustal fabric based on evidence from the Ivrea Zone, Geophysical Research Letters, vol.182, issue.44, pp.1153-1156, 1992.
DOI : 10.1029/92GL00919

H. Hulst, Multiple light scattering : tables, formulas, and applications, 1980.

D. Komatitsch and J. Tvilotte, The spectral element method : An efficient tool to simulate the seismic response of 2d and 3d geological structures, pp.368-392, 1998.
URL : https://hal.archives-ouvertes.fr/hal-00669068

A. Lagendijk and B. Tvan-tiggelen, Resonant multiple scattering of light, Physics Reports, vol.270, issue.3, pp.143-215, 1996.
DOI : 10.1016/0370-1573(95)00065-8

E. Larose, M. Campillo, A. Khan, and Y. Nakamura, Lunar subsurface investigated from correlation of seismic noise, Geophysical Research Letters, vol.87, issue.E6, p.32, 2005.
DOI : 10.1029/2005GL023518

URL : https://hal.archives-ouvertes.fr/hal-00109953

E. Larose, J. De-rosny, L. Margerin, D. Anache, P. Gouedard et al., Observation of multiple scattering of kHz vibrations in a concrete structure and application to monitoring weak changes, Physical Review E, vol.73, issue.1, p.16609, 2006.
DOI : 10.1103/PhysRevE.73.016609

URL : https://hal.archives-ouvertes.fr/insu-00267091

E. Larose and S. Hall, Monitoring stress related velocity variation in concrete with a 2??10???5 relative resolution using diffuse ultrasound, The Journal of the Acoustical Society of America, vol.125, issue.4, pp.1853-1856, 2009.
DOI : 10.1121/1.3079771

URL : https://hal.archives-ouvertes.fr/hal-00352370

E. Larose, L. Margerin, B. Van-tiggelen, and M. Tcampillo, Weak Localization of Seismic Waves, Physical Review Letters, vol.93, issue.4, p.48501, 2004.
DOI : 10.1103/PhysRevLett.93.048501

URL : https://hal.archives-ouvertes.fr/hal-00263629

V. Leroy and A. Etderode, Temperature???dependent diffusing acoustic wave spectroscopy with resonant scatterers, The Journal of the Acoustical Society of America, vol.123, issue.5, p.36602, 2008.
DOI : 10.1121/1.2935658

I. Lillamand, J. Chaix, M. Ploix, and V. Tgarnier, Acoustoelastic effect in concrete material under uni-axial compressive loading, NDT & E International, vol.43, issue.8, pp.43655-660, 2010.
DOI : 10.1016/j.ndteint.2010.07.001

URL : https://hal.archives-ouvertes.fr/hal-01300019

P. Lloyd and M. Tberry, Wave propagation through an assembly of spheres: IV. Relations between different multiple scattering theories, Proceedings of the Physical Society, pp.678-688, 1967.
DOI : 10.1088/0370-1328/91/3/321

O. Lobkis and R. Tweaver, On the emergence of the Green???s function in the correlations of a diffuse field, The Journal of the Acoustical Society of America, vol.110, issue.6, p.3011, 2001.
DOI : 10.1121/1.1417528

O. Lobkis and R. Etweaver, Conversion Rates in an Elastodynamic Billiard, Physical Review Letters, vol.90, issue.25, pp.90-254302, 2003.
DOI : 10.1103/PhysRevLett.90.254302

G. Mainsant, E. Larose, C. Brönnimann, D. Jongmans, C. Michoud et al., Ambient seismic noise monitoring of a clay landslide: Toward failure prediction, Journal of Geophysical Research: Earth Surface, vol.185, issue.1, p.1030, 2012.
DOI : 10.1111/j.1365-246X.2011.05015.x

URL : https://hal.archives-ouvertes.fr/hal-00706907

L. Margerin, Mean-field t-matrix approach to elastic wave scattering by small and point-like objects, Waves in Random and Complex Media, pp.628-644, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00677313

D. Masera, P. Bocca, and A. Tgrazzini, Coda Wave Interferometry Method Applied in Structural Monitoring to Assess Damage Evolution in Masonry and Concrete Structures, Journal of Physics : Conference Series, p.12108, 2011.
DOI : 10.1088/1742-6596/305/1/012108

D. Mccann and M. Etforde, Review of NDT methods in the assessment of concrete and masonry structures, NDT & E International, vol.34, issue.2, pp.71-84, 2001.
DOI : 10.1016/S0963-8695(00)00032-3

J. Meunier, F. Huguet, and P. Tmeynier, Reservoir monitoring using permanent sources and vertical receiver antennae the céré-la-ronde case study. The Leading Edge, pp.622-629, 2001.

J. Michaels and T. Tmichaels, Detection of structural damage from the local temporal coherence of diffuse ultrasonic signals. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, issue.10, pp.521769-1782, 2005.

S. Naffa, M. Goueygou, B. Piwakowski, and F. Buyle-bodin, Detection of chemical damage in concrete using ultrasound, Ultrasonics, vol.40, issue.1-8, pp.247-251, 2002.
DOI : 10.1016/S0041-624X(02)00146-4

URL : https://hal.archives-ouvertes.fr/hal-00250183

N. Nakata and R. Tsnieder, Near-surface weakening in Japan after the 2011 Tohoku-Oki earthquake, Geophysical Research Letters, vol.115, issue.3, pp.38-17302, 2011.
DOI : 10.1029/2011GL048800

T. Nieuwenhuizen and M. Etv-anrossum, R??le of a single scatterer in a multiple scattering medium, Physics Letters A, vol.177, issue.1, pp.102-106, 1993.
DOI : 10.1016/0375-9601(93)90382-A

F. Niu, P. Silver, T. Daley, X. Cheng, and E. Tmajer, Preseismic velocity changes observed from active source monitoring at the Parkfield SAFOD drill site, Nature, vol.12, issue.7201, pp.454204-208, 2008.
DOI : 10.1038/nature07111

J. Nocedal and S. Twright, Numerical optimization, 1999.
DOI : 10.1007/b98874

A. Obermann, T. Planès, E. Larose, and M. Etcampillo, Imaging structural changes on a volcano using ambient seismic noise (subm.), J. Geophys. Res, 2013.

A. Obermann, T. Planès, E. Larose, C. Sens-schönfelder, and M. Tcampillo, Depth sensitivity of seismic coda waves to velocity perturbations in an elastic heterogeneous medium, Geophysical Journal International, vol.194, issue.1, pp.372-382, 2013.
DOI : 10.1093/gji/ggt043

J. Paasschens, Solution of the time-dependent Boltzmann equation, Physical Review E, vol.56, issue.1, p.1135, 1997.
DOI : 10.1103/PhysRevE.56.1135

C. Pacheco and R. Etsnieder, Time-lapse travel time change of multiply scattered acoustic waves, The Journal of the Acoustical Society of America, vol.118, issue.3, p.1300, 2005.
DOI : 10.1121/1.2000827

C. Payan, V. Garnier, J. Moysan, and P. Tjohnson, Determination of third order elastic constants in a complex solid applying coda wave interferometry, Applied Physics Letters, vol.94, issue.1, pp.11904-011904, 2009.
DOI : 10.1063/1.3064129

D. Pine, D. Weitz, P. Chaikin, and E. Therbolzheimer, Diffusing wave spectroscopy, Physical Review Letters, vol.60, issue.12, pp.1134-1137, 1988.
DOI : 10.1103/PhysRevLett.60.1134

URL : https://hal.archives-ouvertes.fr/jpa-00212514

J. Popovics and J. Etrose, A survey of developments in ultrasonic nde of concrete. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, vol.41, issue.1, pp.140-143, 1994.

G. Poupinet, W. Ellsworth, and J. Etfrechet, Monitoring velocity variations in the crust using earthquake doublets: An application to the Calaveras Fault, California, Journal of Geophysical Research: Solid Earth, vol.42, issue.4, 1984.
DOI : 10.1029/JB089iB07p05719

G. Poupinet, A. Ratdomopurbo, and O. Etcoutant, On the use of earthquake multiplets to study fractures and the temporal evolution of an active volcano, Annals of Geophysics, vol.39, issue.2, 1996.

W. Press, S. Teukolsky, W. Vetterling, and B. Tflannery, Numerical recipes 3rd edition : The art of scientific computing, 2007.

D. Rivet, M. Campillo, N. Shapiro, V. Cruz-atienza, M. Radiguet et al., Seismic evidence of nonlinear crustal deformation during a large slow slip event in Mexico, Geophysical Research Letters, vol.108, issue.B6, pp.38-08308, 2011.
DOI : 10.1029/2011GL047151

URL : https://hal.archives-ouvertes.fr/insu-00681437

V. Rossetto, L. Margerin, T. Planès, and E. Tlarose, Locating a weak change using diffuse waves: Theoretical approach and inversion procedure, Journal of Applied Physics, vol.109, issue.3, pp.34903-034903, 2011.
DOI : 10.1063/1.3544503

URL : https://hal.archives-ouvertes.fr/hal-00563872

H. Sato, Energy Transportation In One- and Two-Dimensional Scattering Media: Analytic Solutions of the Multiple Isotropic Scattering Model, Geophysical Journal International, vol.112, issue.1, pp.141-146, 1993.
DOI : 10.1111/j.1365-246X.1993.tb01443.x

H. Sato and M. Tfehler, Seismic Wave Propagation and Scattering in the Heterogeneous Earth, 1998.

K. Sawazaki, H. Sato, H. Nakahara, and T. Etnishimura, Time-Lapse Changes of Seismic Velocity in the Shallow Ground Caused by Strong Ground Motion Shock of the 2000 Western-Tottori Earthquake, Japan, as Revealed from Coda Deconvolution Analysis, Bulletin of the Seismological Society of America, vol.99, issue.1, pp.352-366, 2009.
DOI : 10.1785/0120080058

D. Schurr, MONITORING DAMAGE IN CONCRETE USING DIFFUSE ULTRASONIC CODA WAVE INTERFEROMETRY, 2010.
DOI : 10.1063/1.3592081

D. Schurr, J. Kim, K. Sabra, and L. Tjacobs, Damage detection in concrete using coda wave interferometry, NDT & E International, vol.44, issue.8, pp.44728-735, 2011.
DOI : 10.1016/j.ndteint.2011.07.009

C. Sens-schönfelder and E. Etlarose, Temporal changes in the lunar soil from correlation of diffuse vibrations, Physical Review E, vol.78, issue.4, p.45601, 2008.
DOI : 10.1103/PhysRevE.78.045601

C. Sens-schönfelder and E. Tlarose, Lunar noise correlation, imaging and monitoring, Earthquake Science, vol.168, issue.13, pp.519-530, 2010.
DOI : 10.1007/s11589-010-0750-6

C. Sens-schönfelder and U. Twegler, Passive image interferometry and seasonal variations of seismic velocities at Merapi Volcano, Indonesia, Geophysical Research Letters, vol.33, issue.3, pp.33-21302, 2006.
DOI : 10.1029/2006GL027797

C. Sens-schönfelder and U. Twegler, Passive image interferometry for monitoring crustal changes with ambient seismic noise, Comptes Rendus Geoscience, vol.343, issue.8-9, pp.639-651, 2011.
DOI : 10.1016/j.crte.2011.02.005

T. Shang and L. Tgao, Transportation theory of multiple scattering and its application to seismic coda waves of impulsive source, Sci. Sinica, vol.31, pp.1503-1514, 1988.

P. Sheng, Introduction to wave scattering, localization and mesoscopic phenomena, 2006.

P. Shokouhi, A. Zoëga, and H. Etwiggenhauser, Nondestructive investigation of stress-induced damage in concrete Advances in Civil Engineering, 2010.

R. Snieder, The Theory of Coda Wave Interferometry, Pure and Applied Geophysics, vol.163, issue.2-3, pp.455-473, 2006.
DOI : 10.1007/s00024-005-0026-6

R. Snieder, A. Grêt, H. Douma, and J. Tscales, Coda Wave Interferometry for Estimating Nonlinear Behavior in Seismic Velocity, Science, vol.295, issue.5563, pp.2952253-2255, 2002.
DOI : 10.1126/science.1070015

R. Snieder and M. Ethagerty, Monitoring change in volcanic interiors using coda wave interferometry: Application to Arenal Volcano, Costa Rica, Geophysical Research Letters, vol.42, issue.7, pp.31-09608, 2004.
DOI : 10.1029/2004GL019670

S. Stähler, C. Sens-schönfelder, and E. Tniederleithinger, Monitoring stress changes in a concrete bridge with coda wave interferometry, The Journal of the Acoustical Society of America, vol.129, issue.4, 1945.
DOI : 10.1121/1.3553226

A. Tarantola, Inverse problem theory and methods for model parameter estimation, Society for Industrial Mathematics, 2005.
DOI : 10.1137/1.9780898717921

A. Tarantola and B. Tvalette, Generalized nonlinear inverse problems solved using the least squares criterion, Reviews of Geophysics, vol.10, issue.1, pp.219-232, 1982.
DOI : 10.1029/RG020i002p00219

A. Tikhonov, Solution of incorrectly formulated problems and the regularization method, Soviet Math. Dokl, vol.5, p.1035, 1963.

A. Tourin, Diffusion multiple et renversement du temps des ondes ultrasonores, Thèse de doctorat, p.7, 1999.

J. Tromp, D. Komattisch, and Q. Tliu, Spectral-element and adjoint methods in seismology, Communications in Computational Physics, vol.3, issue.1, pp.1-32, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00721213

J. Turner, Scattering and diffusion of seismic waves, pp.276-283, 1998.

M. Van-rossum and T. Etnieuwenhuizen, Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion, Reviews of Modern Physics, vol.71, issue.1, p.313, 1999.
DOI : 10.1103/RevModPhys.71.313

C. Vanneste, S. Feng, and D. Tsornette, Nondestructive evaluations in multiple scattering media, The Journal of the Acoustical Society of America, vol.93, issue.4, pp.2311-2312, 1993.
DOI : 10.1121/1.406421

P. Waterman and R. , Multiple Scattering of Waves, Journal of Mathematical Physics, vol.2, issue.4, p.512, 1961.
DOI : 10.1063/1.1703737

R. Weaver, On diffuse waves in solid media, The Journal of the Acoustical Society of America, vol.71, issue.6, p.1608, 1982.
DOI : 10.1121/1.387816

R. Weaver, Diffuse elastic waves at a free surface, The Journal of the Acoustical Society of America, vol.78, issue.1, p.131, 1985.
DOI : 10.1121/1.392576

Y. Zhang, O. Abraham, F. Grondin, A. Loukili, V. Tournat et al., Study of stress-induced velocity variation in concrete under direct tensile force and monitoring of the damage level by using thermally-compensated Coda Wave Interferometry, Ultrasonics, vol.52, issue.8, pp.1038-1045, 2012.
DOI : 10.1016/j.ultras.2012.08.011

URL : https://hal.archives-ouvertes.fr/hal-01007343

Y. Zhang, O. Abraham, F. Grondin, A. Loukili, V. Tournat et al., Validation of a thermal bias control technique for coda wave interferometry (cwi) (in press) Ultrasonics, 2012.

Y. Zhang, O. Abraham, E. Larose, T. Planes, L. Duff et al., FOLLOWING STRESS LEVEL MODIFICATION OF REAL SIZE CONCRETE STRUCTURES WITH CODA WAVE INTERFEROMETRY (CWI), AIP Conf. Proc, vol.1335, pp.1291-1298, 2011.
DOI : 10.1063/1.3592082

URL : https://hal.archives-ouvertes.fr/hal-00903851