Finite element dispersion analysis for the three-dimensional second-order scalar wave equation, International Journal for Numerical Methods in Engineering, vol.48, issue.6, pp.1183-1218, 1992. ,
DOI : 10.1002/nme.1620350604
Finite Element Heterogeneous Multiscale Method for the Wave Equation, Multiscale Modeling & Simulation, vol.9, issue.2, pp.766-792, 2011. ,
DOI : 10.1137/100800488
URL : https://hal.archives-ouvertes.fr/hal-01111169
-Version Finite Element Approximation at High Wave Number, SIAM Journal on Numerical Analysis, vol.42, issue.2, pp.553-575, 2004. ,
DOI : 10.1137/S0036142903423460
URL : https://hal.archives-ouvertes.fr/hal-00506914
Dispersive and Dissipative Properties of Discontinuous Galerkin Finite Element Methods for the Second-Order Wave Equation, Journal of Scientific Computing, vol.15, issue.2 ,
DOI : 10.1007/s10915-005-9044-x
Dispersive and Dissipative Behavior of the Spectral Element Method, SIAM Journal on Numerical Analysis, vol.47, issue.5, pp.3910-3937, 2009. ,
DOI : 10.1137/080724976
Velocity model building by 3D frequency-domain, full-waveform inversion of wide-aperture seismic data, GEOPHYSICS, vol.73, issue.5, p.101, 2008. ,
DOI : 10.1190/1.2957948
URL : https://hal.archives-ouvertes.fr/insu-00200039
An acoustic wave equation for anisotropic media, GEOPHYSICS, vol.65, issue.4, pp.1239-1250, 2000. ,
DOI : 10.1190/1.1444815
Homogenization and Two-Scale Convergence, SIAM Journal on Mathematical Analysis, vol.23, issue.6, pp.1482-1518, 1992. ,
DOI : 10.1137/0523084
URL : https://hal.archives-ouvertes.fr/hal-01111805
A Multiscale Finite Element Method for Numerical Homogenization, Multiscale Modeling & Simulation, vol.4, issue.3, pp.790-812, 2005. ,
DOI : 10.1137/040611239
Convergence Analysis of a Discontinuous Galerkin Method with Plane Waves and Lagrange Multipliers for the Solution of Helmholtz Problems, SIAM Journal on Numerical Analysis, vol.47, issue.2, pp.47-1038, 2009. ,
DOI : 10.1137/060673230
URL : https://hal.archives-ouvertes.fr/hal-00865802
Multifrontal parallel distributed symmetric and unsymmetric solvers, Computer Methods in Applied Mechanics and Engineering, vol.184, issue.2-4, pp.501-520, 2000. ,
DOI : 10.1016/S0045-7825(99)00242-X
URL : https://hal.archives-ouvertes.fr/hal-00856651
Three dimensional seg/eaeg models ? an update, The Leading Edge, pp.131-134, 1996. ,
Multiscale Hybrid-Mixed Method, SIAM Journal on Numerical Analysis, vol.51, issue.6, pp.3505-3531, 2013. ,
DOI : 10.1137/120888223
URL : https://hal.archives-ouvertes.fr/hal-01347517
An operator-based approach to upscaling the pressure equation, Computational Methods in Contamination and Remediation of Water Resources, pp.405-412, 1998. ,
Finite element analysis of a scattering problem, Mathematics of Computation, vol.37, issue.156, pp.261-272, 1981. ,
DOI : 10.1090/S0025-5718-1981-0628694-2
A two point boundary value problem with a rapidly oscillating solution, Numerische Mathematik, vol.28, issue.1-2, pp.107-121, 1988. ,
DOI : 10.1007/BF01395880
Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients, SIAM Journal on Numerical Analysis, vol.31, issue.4, pp.31-510, 1994. ,
DOI : 10.1137/0731051
Long-wave elastic anisotropy produced by horizontal layering, Journal of Geophysical Research, vol.27, issue.11, pp.4427-4440, 1962. ,
DOI : 10.1029/JZ067i011p04427
Upscaling for the Laplace problem using a discontinuous Galerkin method, Journal of Computational and Applied Mathematics, vol.240, pp.192-203, 2013. ,
DOI : 10.1016/j.cam.2012.05.025
URL : https://hal.archives-ouvertes.fr/hal-00757098
Stability analysis of heterogeous helmholtz problems and finite element solution based on propagation media approximation, 2015. ,
Stability of perfectly matched layers, group velocities and anisotropic waves, Journal of Computational Physics, vol.188, issue.2, pp.399-433, 2006. ,
DOI : 10.1016/S0021-9991(03)00184-0
A perfectly matched layer for the absorption of electromagnetic waves, Journal of Computational Physics, vol.114, issue.2, pp.185-200, 1994. ,
DOI : 10.1006/jcph.1994.1159
Theory of propagation of elastic waves in a fluid-saturated porous solid. i. low-frequency range, The journal of the acoustical, pp.168-178, 1956. ,
URL : https://hal.archives-ouvertes.fr/hal-01368668
ContributionsàContributionsà la modélisation mathématique etàetà l'algorithmique par-alì ele pour l'optimisation d'un propagateur d'ondesélastiquesondesélastiques en milieu anisotrope, 2014. ,
Functional analysis, sobolev spaces and partial differential equations, 1983. ,
DOI : 10.1007/978-0-387-70914-7
1-d non-periodic homogenization for the seismisc wave equation, Geophys, J. Int, vol.181, pp.897-910, 2010. ,
Seismic modeling in viscoelastic media, GEOPHYSICS, vol.58, issue.1, pp.110-120, 1993. ,
DOI : 10.1190/1.1443340
Long???wave anisotropy in stratified media: A numerical test, GEOPHYSICS, vol.56, issue.2, pp.245-254, 1991. ,
DOI : 10.1190/1.1443037
Relationships between compressional???wave and shear???wave velocities in clastic silicate rocks, GEOPHYSICS, vol.50, issue.4, pp.571-581, 1985. ,
DOI : 10.1190/1.1441933
The Periodic Unfolding Method in Homogenization, SIAM Journal on Mathematical Analysis, vol.40, issue.4, pp.1585-1620, 2008. ,
DOI : 10.1137/080713148
URL : https://hal.archives-ouvertes.fr/hal-00693080
Absorbing boundary conditions for acoustic and elastic wave equations, Bulletin of the Seismological Society of America, vol.67, issue.6, pp.1529-1540, 1977. ,
A Born???WKBJ inversion method for acoustic reflection data, GEOPHYSICS, vol.46, issue.11, pp.1559-1567, 1981. ,
DOI : 10.1190/1.1441162
TOWARD A UNIFIED THEORY OF REFLECTOR MAPPING, GEOPHYSICS, vol.36, issue.3, pp.467-481, 1971. ,
DOI : 10.1190/1.1440185
SHARP REGULARITY COEFFICIENT ESTIMATES FOR COMPLEX-VALUED ACOUSTIC AND ELASTIC HELMHOLTZ EQUATIONS, Mathematical Models and Methods in Applied Sciences, vol.16, issue.01, pp.139-160, 2006. ,
DOI : 10.1142/S021820250600108X
Reflection and transmission coefficients for tranversly isotropic media, Bulletin of the Seismological Society of America, vol.67, issue.3, pp.661-675, 1977. ,
Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions, International Journal for Numerical Methods in Engineering, vol.142, issue.4, pp.471-499, 1999. ,
DOI : 10.1002/(SICI)1097-0207(19991010)46:4<471::AID-NME684>3.0.CO;2-6
Approches analytiques et numériques deprobì emes de transmision en propagation d'ondes en régime transitoire. application au couplage fluide-structure et aux méthodes de couches parfaitement adaptées, p.8708, 2005. ,
FREQUENCY DOMAIN TREATMENT OF ONE-DIMENSIONAL SCALAR WAVES, Mathematical Models and Methods in Applied Sciences, vol.03, issue.02, pp.171-194, 1993. ,
DOI : 10.1142/S0218202593000102
Absorbing boundary conditions for numerical simulation of waves, Proc. Natl. Acad. Sci. USA, pp.1765-1766, 1977. ,
Ray tracing in complex media, Journal of Applied Geophysics, vol.30, issue.1-2, pp.55-73, 1993. ,
DOI : 10.1016/0926-9851(93)90018-T
$hp$-Discontinuous Galerkin methods for the Helmholtz equation with large wave number, Mathematics of Computation, vol.80, issue.276, pp.1997-2024, 2011. ,
DOI : 10.1090/S0025-5718-2011-02475-0
Absolutely stable local discontinuous Galerkin methods for the Helmholtz equation with large wave number, Mathematics of Computation, vol.82, issue.283, pp.1269-1296, 2013. ,
DOI : 10.1090/S0025-5718-2012-02652-4
Mécanique des milieux continus, Ecole des mines de paris, available online: http://mms2.ensmp.fr, 2009. ,
High resolution velocity model estimation from refraction and reflection data, SEG Technical Program Expanded Abstracts 1998, pp.1211-1214, 1998. ,
DOI : 10.1190/1.1820111
On high order methods for the helmholtz equation in highly heterogeneous media, 2015. ,
Which parameterization is suitable for acoustic vertical transverse isotropic full waveform inversion? Part 1: Sensitivity and trade-off analysis, GEOPHYSICS, vol.78, issue.2, pp.81-105, 2013. ,
DOI : 10.1190/geo2012-0204.1
URL : https://hal.archives-ouvertes.fr/hal-00830264
High-order local non-reflecting boundary conditions: a review, Wave Motion, vol.39, issue.4, pp.319-326, 2004. ,
DOI : 10.1016/j.wavemoti.2003.12.004
Elastic properties of marine sediments, Journal of Geophysical Research, vol.21, issue.SM2, 1971. ,
DOI : 10.1029/JB076i002p00579
Stability estimates for a class of Helmholtz problems, Communications in Mathematical Sciences, vol.5, issue.3, pp.665-678, 2007. ,
DOI : 10.4310/CMS.2007.v5.n3.a8
On constitutive inequalities for simple materials???I, Journal of the Mechanics and Physics of Solids, vol.16, issue.4, pp.229-242, 1968. ,
DOI : 10.1016/0022-5096(68)90031-8
A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media, Journal of Computational Physics, vol.134, issue.1, pp.169-189, 1997. ,
DOI : 10.1006/jcph.1997.5682
Finite element analysis of acoustic scattering, 1998. ,
DOI : 10.1007/b98828
Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM, Computers & Mathematics with Applications, vol.30, issue.9, pp.9-37, 1995. ,
DOI : 10.1016/0898-1221(95)00144-N
A generalized plane-wave numerical method for smooth nonconstant coefficients, IMA Journal of Numerical Analysis, vol.34, issue.3, pp.1072-1103, 2014. ,
DOI : 10.1093/imanum/drt030
Importance of anelasticity in the interpretation of seismic tomography, Geophysical Research Letters, vol.74, issue.15, pp.1623-1626, 1993. ,
DOI : 10.1029/93GL01767
A Matrix Analysis of Operator-Based Upscaling for the Wave Equation, SIAM Journal on Numerical Analysis, vol.44, issue.2, pp.586-612, 2006. ,
DOI : 10.1137/050625369
AVERAGING OF RANDOM OPERATORS, Mathematics of the USSR-Sbornik, vol.37, issue.2, pp.167-180, 1980. ,
DOI : 10.1070/SM1980v037n02ABEH001948
Transient shell response by numerical time integration, International Journal for Numerical Methods in Engineering, vol.40, issue.3, pp.273-286, 1973. ,
DOI : 10.1002/nme.1620070305
The bl2d mesh generator: Beginner's guide, user's and programmer's manual, p.69977, 2006. ,
Decay and scattering of solutions of a nonlinear Schr??dinger equation, Journal of Functional Analysis, vol.30, issue.2, pp.245-263, 1978. ,
DOI : 10.1016/0022-1236(78)90073-3
Continuous Mesh Framework Part I: Well-Posed Continuous Interpolation Error, SIAM Journal on Numerical Analysis, vol.49, issue.1, pp.38-60, 2011. ,
DOI : 10.1137/090754078
Analysis and finite element methods for a fluid-solid interaction problem in one dimesion, 1995. ,
Marmousi2: An elastic upgrade for marmousi , The Leading Edge, pp.156-166, 2006. ,
Prise en compte de vitesses de propation polynomiales dans un code de simulation galerkine discontinue, pp.1176854-1176855, 2015. ,
On generalized finite element methods, 1995. ,
General DG-Methods for Highly Indefinite Helmholtz Problems, Journal of Scientific Computing, vol.28, issue.4, pp.536-581, 2013. ,
DOI : 10.1007/s10915-013-9726-8
Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions, Mathematics of Computation, vol.79, issue.272, pp.1871-1914, 2010. ,
DOI : 10.1090/S0025-5718-10-02362-8
Time Decay for the Nonlinear Klein-Gordon Equation, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.306, issue.1486, pp.291-296, 1968. ,
DOI : 10.1098/rspa.1968.0151
Dispersion analysis of finite element semidiscretizations of the two-dimensional wave equation, International Journal for Numerical Methods in Engineering, vol.15, issue.1, pp.11-29, 1982. ,
DOI : 10.1002/nme.1620180103
3D finite-difference frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver: A feasibility study, GEOPHYSICS, vol.72, issue.5, pp.195-511, 2007. ,
DOI : 10.1190/1.2759835
URL : https://hal.archives-ouvertes.fr/insu-00355256
Finite-difference frequency-domain modeling of viscoacoustic wave propagation in 2D tilted transversely isotropic (TTI) media, GEOPHYSICS, vol.74, issue.5, pp.75-95, 2009. ,
DOI : 10.1190/1.3157243
URL : https://hal.archives-ouvertes.fr/hal-00413561
Morrey???Campanato Estimates for Helmholtz Equations, Journal of Functional Analysis, vol.164, issue.2, pp.340-355, 1999. ,
DOI : 10.1006/jfan.1999.3391
Three-dimensional frequency-domain full-waveform inversion with an iterative solver, GEOPHYSICS, vol.74, issue.6, pp.149-157, 2009. ,
DOI : 10.1190/1.3211198
A comparison between one-way and two-way waveequation migration, Geophysics, vol.69, pp.1491-1504, 2004. ,
Gauss-newton and full newton methods in frequency-space seismic waveform inversion, Geophysics. J. Int, pp.341-362, 1998. ,
Real and complex analysis, 1987. ,
Non-homogeneous media and vibration theory, 1980. ,
Boundary element methods, 2011. ,
An observation concerning Ritz-Galerkin methods with indefinite bilinear forms, Mathematics of Computation, vol.28, issue.128, pp.959-962, 1974. ,
DOI : 10.1090/S0025-5718-1974-0373326-0
Tetgen ? a quality tetrahedral mesh generator and three-dimensional delaunay triangulator, Web Intelligence and Agent Systems, An International Journal -WIAS, vol.75, 2007. ,
Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies, GEOPHYSICS, vol.69, issue.1, pp.231-248, 2003. ,
DOI : 10.1190/1.1649391
Scalar reverse???time depth migration of prestack elastic seismic data, GEOPHYSICS, vol.66, issue.5, pp.1519-1527, 2001. ,
DOI : 10.1190/1.1487098
Reverse time migration with optimal checkpointing, GEOPHYSICS, vol.72, issue.5, pp.213-221, 2007. ,
DOI : 10.1190/1.2742686
First-arrival traveltime tomography based on the adjoint-state method, GEOPHYSICS, vol.74, issue.6, pp.57-66, 2009. ,
DOI : 10.1190/1.3250266
Inversion of seismic reflection data in the acoustic approximation, GEOPHYSICS, vol.49, issue.8, pp.1259-1266, 1984. ,
DOI : 10.1190/1.1441754
The discontinuous enrichment method for medium-frequency Helmholtz problems with a spatially variable wavenumber, Computer Methods in Applied Mechanics and Engineering, vol.268, pp.126-140, 2013. ,
DOI : 10.1016/j.cma.2013.08.017
Complex wavenumber Fourier analysis of the p-version finite element method, Computational Mechanics, vol.2, issue.4, pp.255-275, 1994. ,
DOI : 10.1007/BF00350228
Weak elastic anisotropy, Geophysics, vol.51, issue.10, pp.1954-1966, 1986. ,
Conditions transparentes pour la diffraction d'ondes en milieú elastique anisotrope, 2015. ,
Lattice preferred orientation and seismic anisotropy in sedimenary rocks, Geophys. J. Int, pp.166-652, 2006. ,
An a priori error analysis of operator upcaling for the acoustic wave equation, International journal of numerical analysis and modeling, vol.5, issue.4, pp.543-569, 2008. ,
Operator Upscaling for the Acoustic Wave Equation, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1305-1338, 2005. ,
DOI : 10.1137/050622146
P-sv wave propagation in heterogeneous media: Velocity-stress finitedifference method, Geophysics, vol.51, issue.4, 1986. ,
An overview of full-waveform inversion in exploration geophysics, GEOPHYSICS, vol.74, issue.6, pp.127-152, 2009. ,
DOI : 10.1190/1.3238367
URL : https://hal.archives-ouvertes.fr/hal-00457989
The static condensation algorithm, International Journal for Numerical Methods in Engineering, vol.3, issue.1, pp.198-203, 1974. ,
DOI : 10.1002/nme.1620080115
Pre-asymptotic error analysis of CIP-FEM and FEM for the Helmholtz equation with high wave number. Part I: linear version, IMA Journal of Numerical Analysis, vol.34, issue.3, pp.1266-1288, 2013. ,
DOI : 10.1093/imanum/drt033
A stable TTI reverse time migration and its implementation, GEOPHYSICS, vol.76, issue.3, pp.3-11, 2011. ,
DOI : 10.1190/1.3554411
An anisotropic acoustic wave equation for modeling and migration in 2d tti media, An anisotropic acoustic wave equation for modeling and migration, 2D TTI media: 76th Annual International Meeting, SEG, Expanded Astracts, 2006. ,
Preasymptotic Error Analysis of CIP-FEM and FEM for Helmholtz Equation with High Wave Number. Part II: $hp$ Version, SIAM Journal on Numerical Analysis, vol.51, issue.3, pp.1828-1852, 2013. ,
DOI : 10.1137/120874643