메뉴 건너뛰기




Volumn 14, Issue 3, 1998, Pages 387-404

The role of nonlinearity in inverse problems

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0000702501     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/14/3/003     Document Type: Article
Times cited : (86)

References (48)
  • 1
    • 84981758808 scopus 로고
    • Numerical applications of a formalism for geophysical inverse problems
    • Backus G E and Gilbert J F 1967 Numerical applications of a formalism for geophysical inverse problems Geophys. J. R. Astron. Soc. 13 247-76
    • (1967) Geophys. J. R. Astron. Soc. , vol.13 , pp. 247-276
    • Backus, G.E.1    Gilbert, J.F.2
  • 2
    • 84977245393 scopus 로고
    • The resolving power of gross Earth data
    • _ 1968 The resolving power of gross Earth data Geophys. J. R. Astron. Soc. 16 169-205
    • (1968) Geophys. J. R. Astron. Soc. , vol.16 , pp. 169-205
  • 3
    • 33646975016 scopus 로고
    • Eine Umkehrung der Sturm-Liouvillischen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
    • Borg G 1946 Eine Umkehrung der Sturm-Liouvillischen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte Acta Math. 78 1-96
    • (1946) Acta Math. , vol.78 , pp. 1-96
    • Borg, G.1
  • 4
    • 84963264467 scopus 로고
    • The Gel'fand-Levitan, the Marchenko, and the Gopinath-Sondi integral equations of inverse scattering theory, regarded in the context of the inverse impulse response problems
    • Burridge R 1980 The Gel'fand-Levitan, the Marchenko, and the Gopinath-Sondi integral equations of inverse scattering theory, regarded in the context of the inverse impulse response problems Wave Motion 2 305-23
    • (1980) Wave Motion , vol.2 , pp. 305-323
    • Burridge, R.1
  • 5
    • 0023525470 scopus 로고
    • Occam's inversion: A practical algorithm for generating smooth models from electromagnetic sounding data
    • Constable S C, Parker R L and Constable C G 1987 Occam's inversion: a practical algorithm for generating smooth models from electromagnetic sounding data Geophys. 52 289-300
    • (1987) Geophys. , vol.52 , pp. 289-300
    • Constable, S.C.1    Parker, R.L.2    Constable, C.G.3
  • 8
    • 0030858282 scopus 로고    scopus 로고
    • Error propagation in nonlinear delay time tomography
    • Dorren H J S and Snieder R K 1997 Error propagation in nonlinear delay time tomography Geophys. J. Int. 128 632-8
    • (1997) Geophys. J. Int. , vol.128 , pp. 632-638
    • Dorren, H.J.S.1    Snieder, R.K.2
  • 9
    • 0030436514 scopus 로고    scopus 로고
    • Ensemble inference in terms of emperical orthogonal functions
    • Douma H, Snieder R and Lomax A 1996 Ensemble inference in terms of emperical orthogonal functions Geophys. J. Int. 127 363-78
    • (1996) Geophys. J. Int. , vol.127 , pp. 363-378
    • Douma, H.1    Snieder, R.2    Lomax, A.3
  • 10
    • 49849114033 scopus 로고
    • Well-posed stochastic extensions of ill-posed linear problems
    • Franklin J N 1970 Well-posed stochastic extensions of ill-posed linear problems J. Math. Anal. Appl. 31 682-716
    • (1970) J. Math. Anal. Appl. , vol.31 , pp. 682-716
    • Franklin, J.N.1
  • 11
    • 84981750910 scopus 로고
    • Determination of a seismic velocity from a travel time curve
    • Gerver and Markushevitch 1966 Determination of a seismic velocity from a travel time curve Geophys. J. R. Astron. Soc. 11 165-73
    • (1966) Geophys. J. R. Astron. Soc. , vol.11 , pp. 165-173
    • Gerver1    Markushevitch2
  • 12
    • 0000515915 scopus 로고    scopus 로고
    • Resolution of seismic waveform inversion: Bayes versus Occam
    • Gouveia W P and Scales J A 1997 Resolution of seismic waveform inversion: Bayes versus Occam Inverse Problems 13 323-49
    • (1997) Inverse Problems , vol.13 , pp. 323-349
    • Gouveia, W.P.1    Scales, J.A.2
  • 13
    • 0031872455 scopus 로고    scopus 로고
    • Bayesian seismic waveform inversion: Parameter estimation and uncertainty analysis
    • _ 1998 Bayesian seismic waveform inversion: parameter estimation and uncertainty analysis J. Geophys. Res. 103 2759-77
    • (1998) J. Geophys. Res. , vol.103 , pp. 2759-2777
  • 14
    • 0010860394 scopus 로고
    • Über das Benndorfsche Problem für Fortplanzungsgeschwindigkeit der Eardbebensstralen
    • Herglotz G 1907 Über das Benndorfsche Problem für Fortplanzungsgeschwindigkeit der Eardbebensstralen Z. Geophys. 8 145-7
    • (1907) Z. Geophys. , vol.8 , pp. 145-147
    • Herglotz, G.1
  • 15
    • 0022269167 scopus 로고
    • A Bayesian approach to nonlinear inversion
    • Jackson J J and Matsu'ura M 1985 A Bayesian approach to nonlinear inversion J. Geophys. Res. 90 581-91
    • (1985) J. Geophys. Res. , vol.90 , pp. 581-591
    • Jackson, J.J.1    MatsU'Ura, M.2
  • 16
    • 0037806519 scopus 로고
    • Determination of the potential from scattering data
    • Keller J B, Kay I and Shmoys J 1956 Determination of the potential from scattering data Phys Rev. 102 557-9
    • (1956) Phys Rev. , vol.102 , pp. 557-559
    • Keller, J.B.1    Kay, I.2    Shmoys, J.3
  • 18
    • 84984402335 scopus 로고
    • Identifying sets of acceptable models to nonlinear geophysical inverse problems
    • Lomax A and Snieder R 1995a Identifying sets of acceptable models to nonlinear geophysical inverse problems Nonlinear Processes Geophys. 2 222-7
    • (1995) Nonlinear Processes Geophys. , vol.2 , pp. 222-227
    • Lomax, A.1    Snieder, R.2
  • 19
    • 0029518652 scopus 로고
    • The contrast in upper mantle shear-velocity between the East European Platform and tectonic Europe obtained with a genetic algorithm of Rayleigh wave group dispersion
    • _ 1995b The contrast in upper mantle shear-velocity between the East European Platform and tectonic Europe obtained with a genetic algorithm of Rayleigh wave group dispersion Geophys. J. Int. 123 169-82
    • (1995) Geophys. J. Int. , vol.123 , pp. 169-182
  • 20
    • 0000861291 scopus 로고
    • The construction of the potential energy from the phases of scattered waves
    • Marchenko V A 1955 The construction of the potential energy from the phases of scattered waves Dokl. Akad. Nauk 104 695-8
    • (1955) Dokl. Akad. Nauk , vol.104 , pp. 695-698
    • Marchenko, V.A.1
  • 21
    • 0000462567 scopus 로고    scopus 로고
    • Resolution analysis of general inverse problems through inverse Monte Carlo sampling
    • Mosegaard K 1998 Resolution analysis of general inverse problems through inverse Monte Carlo sampling Inverse Problems 14 405-26
    • (1998) Inverse Problems , vol.14 , pp. 405-426
    • Mosegaard, K.1
  • 22
    • 0029481451 scopus 로고
    • Monte Carlo sampling of solutions to inverse problems
    • Mosegaard K and Tarantola A 1995 Monte Carlo sampling of solutions to inverse problems J. Geophys. Res. 100 12431-47
    • (1995) J. Geophys. Res. , vol.100 , pp. 12431-12447
    • Mosegaard, K.1    Tarantola, A.2
  • 23
    • 0019377876 scopus 로고
    • Inversion of reflection data for layered media: A review of exact methods
    • Newton R G 1981 Inversion of reflection data for layered media: A review of exact methods Geophys. J. R. Astron. Soc. 65 191-215
    • (1981) Geophys. J. R. Astron. Soc. , vol.65 , pp. 191-215
    • Newton, R.G.1
  • 25
    • 0025593555 scopus 로고
    • Partitioned waveform inversion and two-dimensional structure under the network of autonomously recording seismographs
    • Nolet G 1990 Partitioned waveform inversion and two-dimensional structure under the network of autonomously recording seismographs J. Geophys. Res. 95 8499-512
    • (1990) J. Geophys. Res. , vol.95 , pp. 8499-8512
    • Nolet, G.1
  • 28
    • 0029503091 scopus 로고
    • Using differential waveform data to retrieve local S-velocity structure of path-averaged S-velocity gradients
    • Passier M L and Snieder R K 1995 Using differential waveform data to retrieve local S-velocity structure of path-averaged S-velocity gradients J. Geophys. Res. 100 24061-78
    • (1995) J. Geophys. Res. , vol.100 , pp. 24061-24078
    • Passier, M.L.1    Snieder, R.K.2
  • 29
    • 0031156305 scopus 로고    scopus 로고
    • Surface waveform inversions for local shear-velocity under eastern Australia
    • Passier M L, van der Hilst R D and Snieder R K 1997 Surface waveform inversions for local shear-velocity under eastern Australia Geophys. Res. Lett. 24 1291-4
    • (1997) Geophys. Res. Lett. , vol.24 , pp. 1291-1294
    • Passier, M.L.1    Van Der Hilst, R.D.2    Snieder, R.K.3
  • 30
    • 0012101378 scopus 로고
    • Formal solutions of inverse scattering problems
    • Prosser R T 1968 Formal solutions of inverse scattering problems J. Math. Phys. 10 1819-22
    • (1968) J. Math. Phys. , vol.10 , pp. 1819-1822
    • Prosser, R.T.1
  • 31
    • 0022220802 scopus 로고
    • Nonlinear inversion, statistical mechanics and residual statics estimation
    • Rothman D H 1985 Nonlinear inversion, statistical mechanics and residual statics estimation Geophys. 50 2784-96
    • (1985) Geophys. , vol.50 , pp. 2784-2796
    • Rothman, D.H.1
  • 33
    • 3342935300 scopus 로고
    • Discrete ambiguities and equivalent potentials
    • Sabatier P C 1973 Discrete ambiguities and equivalent potentials Phys. Rev. A 8 589-601
    • (1973) Phys. Rev. A , vol.8 , pp. 589-601
    • Sabatier, P.C.1
  • 34
    • 0025627945 scopus 로고
    • Non-linear arrival time inversion: Constraining velocity anomalies by seeking smooth models in 3-D
    • Sambridge M S 1990 Non-linear arrival time inversion: constraining velocity anomalies by seeking smooth models in 3-D Geophys. J. Int. 102 653-77
    • (1990) Geophys. J. Int. , vol.102 , pp. 653-677
    • Sambridge, M.S.1
  • 35
    • 0002455337 scopus 로고    scopus 로고
    • Exploring multidimensional landscapes without a map
    • Sambridge M 1998 Exploring multidimensional landscapes without a map Inverse Problems 14 427-40
    • (1998) Inverse Problems , vol.14 , pp. 427-440
    • Sambridge, M.1
  • 36
    • 0026470087 scopus 로고
    • Genetic algorithms in seismic waveform inversion
    • Sambridge M and Drijkoningen G 1992 Genetic algorithms in seismic waveform inversion Geophys. J. Int. 109 323-42
    • (1992) Geophys. J. Int. , vol.109 , pp. 323-342
    • Sambridge, M.1    Drijkoningen, G.2
  • 37
    • 0000910078 scopus 로고    scopus 로고
    • To Bayes or not to Bayes?
    • Scales J A and Snieder R 1997 To Bayes or not to Bayes? Geophys. 62 1045-6
    • (1997) Geophys. , vol.62 , pp. 1045-1046
    • Scales, J.A.1    Snieder, R.2
  • 38
    • 0026471182 scopus 로고
    • Rapid sampling of model space using genetic algorithms: Examples of seismic waveform inversion
    • Sen M K and P L Stoffa 1992 Rapid sampling of model space using genetic algorithms: examples of seismic waveform inversion Geophys. J. Int. 108 281-92
    • (1992) Geophys. J. Int. , vol.108 , pp. 281-292
    • Sen, M.K.1    Stoffa, P.L.2
  • 39
    • 0025205565 scopus 로고
    • A perturbative analysis of non-linear inversion
    • Snieder R 1990a A perturbative analysis of non-linear inversion Geophys. J. Int. 101 545-56
    • (1990) Geophys. J. Int. , vol.101 , pp. 545-556
    • Snieder, R.1
  • 40
    • 3342886574 scopus 로고
    • The role of the Born approximation in nonlinear inversion
    • _ 1990b The role of the Born approximation in nonlinear inversion Inverse Problems 247-66
    • (1990) Inverse Problems , pp. 247-266
  • 41
    • 0026172482 scopus 로고
    • An extension of Backus-Gilbert theory to nonlinear inverse problems
    • _ 1991 An extension of Backus-Gilbert theory to nonlinear inverse problems Inverse Problems 409-33
    • (1991) Inverse Problems , pp. 409-433
  • 42
    • 3342947189 scopus 로고
    • Perturbation theory for travel times
    • Snieder R and Aldridge D F 1995 Perturbation theory for travel times J. Acoust. Soc. Am. 125 796-812
    • (1995) J. Acoust. Soc. Am. , vol.125 , pp. 796-812
    • Snieder, R.1    Aldridge, D.F.2
  • 43
    • 0027834938 scopus 로고
    • The ambiguity in ray perturbation theory
    • Snieder R and Sambridge M 1993 The ambiguity in ray perturbation theory J. Geophys. Res. 98 22021-34
    • (1993) J. Geophys. Res. , vol.98 , pp. 22021-22034
    • Snieder, R.1    Sambridge, M.2
  • 44
    • 0001190098 scopus 로고
    • Lateral heterogeneity and azimuthal anisotropy of the upper mantle: Love and Rayleigh waves 100-250
    • Tanimoto T and Anderson D L 1985 Lateral heterogeneity and azimuthal anisotropy of the upper mantle: Love and Rayleigh waves 100-250 J. Geophys. Res. 90 1842-58
    • (1985) J. Geophys. Res. , vol.90 , pp. 1842-1858
    • Tanimoto, T.1    Anderson, D.L.2
  • 46
    • 0029730021 scopus 로고    scopus 로고
    • Model estimation biased by truncated expansions: Possible artifacts in seismic tomography
    • Trampert J and Snieder R 1996 Model estimation biased by truncated expansions: possible artifacts in seismic tomography Science 271 1257-60
    • (1996) Science , vol.271 , pp. 1257-1260
    • Trampert, J.1    Snieder, R.2
  • 48
    • 0000842512 scopus 로고
    • The inverse problem of geomagnetic induction
    • Weidelt P 1972 The inverse problem of geomagnetic induction Z. Geophys. 38 257-89
    • (1972) Z. Geophys. , vol.38 , pp. 257-289
    • Weidelt, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.