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Volumn 153, Issue 1, 2003, Pages 52-74

Symplectic structure of wave-equation imaging: A path-integral approach based on the double-square-root equation

Author keywords

Isochrones; Migration dip; Scattering angle azimuth; Wave equation imaging

Indexed keywords

ACOUSTIC WAVE; EQUATION; GREEN FUNCTION; HETEROGENEOUS MEDIUM; IMAGING METHOD; WAVE PROPAGATION;

EID: 0037394865     PISSN: 0956540X     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-246X.2003.01877.x     Document Type: Article
Times cited : (42)

References (67)
  • 2
    • 0030291317 scopus 로고    scopus 로고
    • 3-D prestack migration of commonazimuth data
    • Biondo, B. & Palacharla, G., 1996. 3-D prestack migration of commonazimuth data, Geophysics. 61, 1822-1832.
    • (1996) Geophysics , vol.61 , pp. 1822-1832
    • Biondo, B.1    Palacharla, G.2
  • 3
    • 0032848069 scopus 로고    scopus 로고
    • Migration of scattered teleseismic body waves
    • Bostock, M.G. & Rondenay, S., 1999. Migration of scattered teleseismic body waves. Geophys. J. Int., 137, 732-746.
    • (1999) Geophys. J. Int. , vol.137 , pp. 732-746
    • Bostock, M.G.1    Rondenay, S.2
  • 4
    • 0037219739 scopus 로고    scopus 로고
    • Focusing in dip and AVA compensation on scattering-angle/azimuth common image gathers
    • in print
    • Brandsberg-Dahl, S., De Hoop, M.V. & Ursin, B., 2003a. Focusing in dip and AVA compensation on scattering-angle/azimuth common image gathers, Geophysics, in print.
    • (2003) Geophysics
    • Brandsberg-Dahl, S.1    De Hoop, M.V.2    Ursin, B.3
  • 5
    • 0013096502 scopus 로고    scopus 로고
    • Seismic velocity analysis in the scattering-angle/azimuth domain
    • in print
    • Brandsberg-Dahl, S., Ursin, B. & De Hoop, M.V., 2003b. Seismic velocity analysis in the scattering-angle/azimuth domain. Geophys. Prospect., in print.
    • (2003) Geophys. Prospect.
    • Brandsberg-Dahl, S.1    Ursin, B.2    De Hoop, M.V.3
  • 7
    • 0030713495 scopus 로고    scopus 로고
    • Applications of an improved self-starter to geoacoustic inversion
    • Cederberg, R.J. & Collins, M.D., 1997. Applications of an improved self-starter to geoacoustic inversion, IEEE J. Ocean Eng., 22, 102-109.
    • (1997) IEEE J. Ocean Eng. , vol.22 , pp. 102-109
    • Cederberg, R.J.1    Collins, M.D.2
  • 9
    • 0001095190 scopus 로고
    • Coarse grid calculations of wave in inhomogeneous media with application to delineation of complicated seismic structure
    • Claerbout, J.F., 1970. Coarse grid calculations of wave in inhomogeneous media with application to delineation of complicated seismic structure, Geophysics, 35, 407-418.
    • (1970) Geophysics , vol.35 , pp. 407-418
    • Claerbout, J.F.1
  • 11
    • 0013146582 scopus 로고
    • Common midpoint migration
    • Stanford University
    • Clayton, R.W., 1978. Common midpoint migration, SEP- 14, (Stanford University) 21-36.
    • (1978) SEP , vol.14 , pp. 21-36
    • Clayton, R.W.1
  • 12
    • 0001418867 scopus 로고
    • Applications and time-domain solution of higher-order parabolic equations in underwater acoustics
    • Collins, M.D., 1989. Applications and time-domain solution of higher-order parabolic equations in underwater acoustics, J. acoust. Soc. Am., 86, 1097-1102.
    • (1989) J. Acoust. Soc. Am. , vol.86 , pp. 1097-1102
    • Collins, M.D.1
  • 13
    • 0030559551 scopus 로고    scopus 로고
    • Generalization of the Bremmer coupling series
    • De Hoop, M.V., 1996. Generalization of the Bremmer coupling series, J. Math. Phys., 37, 3246-3282.
    • (1996) J. Math. Phys. , vol.37 , pp. 3246-3282
    • De Hoop, M.V.1
  • 14
    • 0013099413 scopus 로고    scopus 로고
    • Direct, leading-order asymptotic, inverse scattering based on the generalized Bremmer series
    • ed. DeSanto, J.A., SIAM, Philadelphia
    • De Hoop, M.V., 1998. Direct, leading-order asymptotic, inverse scattering based on the generalized Bremmer series, in Mathematical and Numerical Aspects of Wave Propagation, pp. 249-253, ed. DeSanto, J.A., SIAM, Philadelphia.
    • (1998) Mathematical and Numerical Aspects of Wave Propagation , pp. 249-253
    • De Hoop, M.V.1
  • 15
    • 0001100735 scopus 로고    scopus 로고
    • Maslov asymptotic extension of generalized Radon transform inversion in anisotropic elastic media: A least-squares approach
    • De Hoop, M.V. & Brandsberg-Dahl, S., 2000. Maslov asymptotic extension of generalized Radon transform inversion in anisotropic elastic media: A least-squares approach, Inverse Problems, 16, 519-562.
    • (2000) Inverse Problems , vol.16 , pp. 519-562
    • De Hoop, M.V.1    Brandsberg-Dahl, S.2
  • 16
    • 0000370141 scopus 로고
    • Scalar space-time waves in their spectral-domain first- and second-order Thiele approximations
    • De Hoop, M.V. & De Hoop, A.T., 1992. Scalar space-time waves in their spectral-domain first- and second-order Thiele approximations, Wave Motion, 15, 229-265.
    • (1992) Wave Motion , vol.15 , pp. 229-265
    • De Hoop, M.V.1    De Hoop, A.T.2
  • 17
    • 0000432309 scopus 로고    scopus 로고
    • Wavefield reciprocity and local optimization in remote sensing
    • De Hoop, M.V. & De Hoop, A.T., 2000. Wavefield reciprocity and local optimization in remote sensing, Proc. R. Soc. Lond., A., 456, 641-682.
    • (2000) Proc. R. Soc. Lond., A , vol.456 , pp. 641-682
    • De Hoop, M.V.1    De Hoop, A.T.2
  • 18
    • 0033684767 scopus 로고    scopus 로고
    • Uniform asymptotic expansion of the generalized Bremmer series
    • De Hoop, M.V. & Gautesen, A.K., 2000. Uniform asymptotic expansion of the generalized Bremmer series, SIAM J. Appl. Math., 60, 1302-1329.
    • (2000) SIAM J. Appl. Math. , vol.60 , pp. 1302-1329
    • De Hoop, M.V.1    Gautesen, A.K.2
  • 19
    • 0033640518 scopus 로고    scopus 로고
    • Generalization of the phase-screen approximation for the scattering of acoustic waves
    • De Hoop, M.V., Le Rousseau, J.H. & Wu, R.-S., 2000. Generalization of the phase-screen approximation for the scattering of acoustic waves, Wave Motion, 31, 43-70.
    • (2000) Wave Motion , vol.31 , pp. 43-70
    • De Hoop, M.V.1    Le Rousseau, J.H.2    Wu, R.-S.3
  • 21
    • 0019701029 scopus 로고
    • Geometrical optics and wave theory of constant offset sections in layered media
    • Deregowski, S.M. & Rocca, F., 1981. Geometrical optics and wave theory of constant offset sections in layered media, Geophys. Prospect., 29, 374-406.
    • (1981) Geophys. Prospect. , vol.29 , pp. 374-406
    • Deregowski, S.M.1    Rocca, F.2
  • 22
    • 0000246164 scopus 로고
    • Path integration in non-relativistic quantum mechanics
    • De Witte-Morette, C., Maheshwari, A. & Nelson, B., 1979. Path integration in non-relativistic quantum mechanics, Phys. Rep., 50, 255-372.
    • (1979) Phys. Rep. , vol.50 , pp. 255-372
    • De Witte-Morette, C.1    Maheshwari, A.2    Nelson, B.3
  • 25
    • 0020970161 scopus 로고
    • Numerical methods for the migration of constant-offset sections in homogeneous and horizontally layered media
    • Dubrulle, A.A., 1983. Numerical methods for the migration of constant-offset sections in homogeneous and horizontally layered media, Geophysics, 48, 1195-1203.
    • (1983) Geophysics , vol.48 , pp. 1195-1203
    • Dubrulle, A.A.1
  • 27
    • 0033133604 scopus 로고    scopus 로고
    • True-amplitude frequency-wavenumber constant-offset migration
    • Ekren, B.O. & Ursin, B., 1999. True-amplitude frequency-wavenumber constant-offset migration, Geophysics, 64, 915-924.
    • (1999) Geophysics , vol.64 , pp. 915-924
    • Ekren, B.O.1    Ursin, B.2
  • 28
    • 33744583270 scopus 로고
    • Derivation and application of extended parabolic wave theories I. The factorized Helmholtz equation
    • Fishman, L. & McCoy, J.J., 1984a. Derivation and application of extended parabolic wave theories I. The factorized Helmholtz equation. J. Math. Phys., 25, 285-296.
    • (1984) J. Math. Phys. , vol.25 , pp. 285-296
    • Fishman, L.1    McCoy, J.J.2
  • 29
    • 36549094654 scopus 로고
    • Derivation and application of extended parabolic wave theories II. Path integral representations
    • Fishman, L. & McCoy, J.J., 1984b. Derivation and application of extended parabolic wave theories II. Path integral representations, J. Math. Phys., 25, 297-308.
    • (1984) J. Math. Phys. , vol.25 , pp. 297-308
    • Fishman, L.1    McCoy, J.J.2
  • 30
    • 0031237261 scopus 로고    scopus 로고
    • Uniform high-frequency approximations of the square root Helmholtz operator symbol
    • Fishman, L., Gautesen, A.K. & Sun, Z., 1997. Uniform high-frequency approximations of the square root Helmholtz operator symbol, Wave Motion, 26, 127-161.
    • (1997) Wave Motion , vol.26 , pp. 127-161
    • Fishman, L.1    Gautesen, A.K.2    Sun, Z.3
  • 31
    • 0034415797 scopus 로고    scopus 로고
    • Exact constructions of square-root Helmholtz operator symbols: The focusing quadratic profile
    • Fishman, L., De Hoop, M.V. & Van Stralen, M.J.N., 2000. Exact constructions of square-root Helmholtz operator symbols: the focusing quadratic profile, J. Math. Phys., 41, 4881-4938.
    • (2000) J. Math. Phys. , vol.41 , pp. 4881-4938
    • Fishman, L.1    De Hoop, M.V.2    Van Stralen, M.J.N.3
  • 33
    • 0021375550 scopus 로고
    • Migration of seismic data by phase shift plus interpolation
    • Gazdag, J. & Sguazzero, P., 1984. Migration of seismic data by phase shift plus interpolation, Geophysics, 49, 124-131.
    • (1984) Geophysics , vol.49 , pp. 124-131
    • Gazdag, J.1    Sguazzero, P.2
  • 34
    • 84975582150 scopus 로고
    • Wide-angle beam propagation using Padé approximant operator
    • Hadley, G.R., 1992. Wide-angle beam propagation using Padé approximant operator. Opt. Lett., 17, 1426-1428.
    • (1992) Opt. Lett. , vol.17 , pp. 1426-1428
    • Hadley, G.R.1
  • 35
    • 0026359208 scopus 로고
    • Migration via McClellan transformations
    • Hale, D., 1991. Migration via McClellan transformations, Geophysics, 43, 1778-1785.
    • (1991) Geophysics , vol.43 , pp. 1778-1785
    • Hale, D.1
  • 36
    • 0002820858 scopus 로고
    • Fourier integral operators 1
    • Hörmander, L., 1971. Fourier integral operators 1, Acta Math., 127, 79-183.
    • (1971) Acta Math. , vol.127 , pp. 79-183
    • Hörmander, L.1
  • 40
    • 0031513612 scopus 로고    scopus 로고
    • On the formulation of the Feynman path integral through broken line paths
    • Ichinose, W., 1997. On the formulation of the Feynman path integral through broken line paths, Comm. Math. Phys., 189, 17-33.
    • (1997) Comm. Math. Phys. , vol.189 , pp. 17-33
    • Ichinose, W.1
  • 41
    • 0033419886 scopus 로고    scopus 로고
    • On the convergence of the Feynman path integral formulated through broken line paths
    • Ichinose, W., 1999. On the convergence of the Feynman path integral formulated through broken line paths, Revs. Math. Phys., 11, 1001-1025.
    • (1999) Revs. Math. Phys. , vol.11 , pp. 1001-1025
    • Ichinose, W.1
  • 42
    • 0034310146 scopus 로고    scopus 로고
    • The phase space Feynman path integral with gauge covariance and its convergence
    • Ichinose, W., 2000. The phase space Feynman path integral with gauge covariance and its convergence, Revs. Math. Phys., 12, 1451-1463.
    • (2000) Revs. Math. Phys. , vol.12 , pp. 1451-1463
    • Ichinose, W.1
  • 43
    • 0027526788 scopus 로고
    • Maslov ray summation, pseudocaustics, Lagrangian equivalence and transient seismic waveforms
    • Kendall, J.-M. & Thomson, C.J., 1993. Maslov ray summation, pseudocaustics, Lagrangian equivalence and transient seismic waveforms, Geophys. J. Int., 113, 186-214.
    • (1993) Geophys. J. Int. , vol.113 , pp. 186-214
    • Kendall, J.-M.1    Thomson, C.J.2
  • 45
    • 0035454789 scopus 로고    scopus 로고
    • Modeling and imaging with the scalar generalized-screen algorithms in isotropic media
    • Le Rousseau, J.H. & De Hoop, M.V., 2001a. Modeling and imaging with the scalar generalized-screen algorithms in isotropic media, Geophysics, 66, 1551-1568.
    • (2001) Geophysics , vol.66 , pp. 1551-1568
    • Le Rousseau, J.H.1    De Hoop, M.V.2
  • 46
    • 0035455356 scopus 로고    scopus 로고
    • Scalar generalized-screen algorithms in transversely isotropic media with a vertical symmetry axis
    • Le Rousseau, J.H. & De Hoop, M.V., 2001b. Scalar generalized-screen algorithms in transversely isotropic media with a vertical symmetry axis, Geophysics, 66, 1538-1550.
    • (2001) Geophysics , vol.66 , pp. 1538-1550
    • Le Rousseau, J.H.1    De Hoop, M.V.2
  • 47
    • 0037295125 scopus 로고    scopus 로고
    • Generalized-screen approximation and algorithm for the scattering of elastic waves
    • in print
    • Le Rousseau, J.H. & De Hoop, M.V., 2003. Generalized-screen approximation and algorithm for the scattering of elastic waves, Q. J. Mech. Appl. Math., in print.
    • (2003) Q. J. Mech. Appl. Math.
    • Le Rousseau, J.H.1    De Hoop, M.V.2
  • 49
    • 0013148805 scopus 로고    scopus 로고
    • 3D depth imaging with generalized screens: A salt body case study
    • in print
    • Le Rousseau, J.H., Calandra, H. & De Hoop, M.V., 2003. 3D depth imaging with generalized screens: A salt body case study, Geophysics, in print.
    • (2003) Geophysics
    • Le Rousseau, J.H.1    Calandra, H.2    De Hoop, M.V.3
  • 52
    • 0031058871 scopus 로고    scopus 로고
    • Rational square-root approximations for parabolic equation algorithms
    • Milinazzo, F.A., Zala, C.A. & Brooke, G.H., 1997. Rational square-root approximations for parabolic equation algorithms, J. acoust. Soc. Am., 101, 760-766.
    • (1997) J. Acoust. Soc. Am. , vol.101 , pp. 760-766
    • Milinazzo, F.A.1    Zala, C.A.2    Brooke, G.H.3
  • 54
    • 0030235836 scopus 로고    scopus 로고
    • Prestack migration by split-step DSR
    • Popovici, A.M., 1996. Prestack migration by split-step DSR. Geophysics, 61, 1412-1416.
    • (1996) Geophysics , vol.61 , pp. 1412-1416
    • Popovici, A.M.1
  • 55
    • 0032986791 scopus 로고    scopus 로고
    • A path integral formulation of acoustic wave propagation
    • Schlottmann, R.B., 1999. A path integral formulation of acoustic wave propagation. Geophys. J. Int., 137, 353-363.
    • (1999) Geophys. J. Int. , vol.137 , pp. 353-363
    • Schlottmann, R.B.1
  • 59
    • 0141799935 scopus 로고    scopus 로고
    • Seismic inverse scattering in the 'wave-equation' approach
    • preprint
    • Stolk, C.C. & De Hoop, M.V., 2001. Seismic inverse scattering in the 'wave-equation' approach. MSRI, 2001-2047 preprint.
    • (2001) MSRI , pp. 2001-2047
    • Stolk, C.C.1    De Hoop, M.V.2
  • 60
    • 0036110253 scopus 로고    scopus 로고
    • Microlocal analysis of seismic inverse scattering in anistropic elastic media
    • Stolk, C.C. & De Hoop, M.V., 2002. Microlocal analysis of seismic inverse scattering in anistropic elastic media. Comm. Pure Appl. Math., 55, 261-301.
    • (2002) Comm. Pure Appl. Math. , vol.55 , pp. 261-301
    • Stolk, C.C.1    De Hoop, M.V.2
  • 61
    • 0000420257 scopus 로고
    • A differential semblance algorithm for the inverse problem of reflection seismology
    • Symes, W.W., 1991. A differential semblance algorithm for the inverse problem of reflection seismology. Comp. Math. Appl., 22, 147-178.
    • (1991) Comp. Math. Appl. , vol.22 , pp. 147-178
    • Symes, W.W.1
  • 62
    • 0000978807 scopus 로고
    • The parabolic approximation method
    • eds Keller, J.B. & Papadakis, J.S., Lecture Notes in Physics, Springer-Verlag, New York
    • Tappert, F.D., 1977. The parabolic approximation method, in Wave Propagation and Underwater Acoustics, pp. 224-287, eds Keller, J.B. & Papadakis, J.S., Lecture Notes in Physics, vol. 70, Springer-Verlag, New York.
    • (1977) Wave Propagation and Underwater Acoustics , vol.70 , pp. 224-287
    • Tappert, F.D.1
  • 63
    • 0032986907 scopus 로고    scopus 로고
    • The 'gap' between seismic ray theory and 'full' wavefield extrapolation
    • Thomson, C.J., 1999. The 'gap' between seismic ray theory and 'full' wavefield extrapolation. Geophys. J. Int., 137, 364-380.
    • (1999) Geophys. J. Int. , vol.137 , pp. 364-380
    • Thomson, C.J.1
  • 64
    • 0003961310 scopus 로고
    • Distributions and Kernels. Academic, New York
    • Treves, F., 1967. Topological Vector Spaces. Distributions and Kernels. Academic, New York.
    • (1967) Topological Vector Spaces
    • Treves, F.1
  • 66
    • 0032190238 scopus 로고    scopus 로고
    • Generalized Bremmer series with rational approximation for the scattering of waves in inhomogeneous media
    • Van Stralen, M.J.N., De Hoop, M.V. & Blok, H., 1998. Generalized Bremmer series with rational approximation for the scattering of waves in inhomogeneous media, J. Acoust. Soc. Am., 104, 1943-1963.
    • (1998) J. Acoust. Soc. Am. , vol.104 , pp. 1943-1963
    • Van Stralen, M.J.N.1    De Hoop, M.V.2    Blok, H.3
  • 67
    • 0004201980 scopus 로고
    • Princeton University Press, Princeton
    • Widder, D.V., 1946. The Laplace Transform. Princeton University Press, Princeton.
    • (1946) The Laplace Transform
    • Widder, D.V.1


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