메뉴 건너뛰기




Volumn 170, Issue 1, 2007, Pages 1-8

Automatic differentiation in geophysical inverse problems

Author keywords

Derivatives; Inverse problems; Sensitivity kernel

Indexed keywords

FINITE DIFFERENCE METHOD; GEOPHYSICAL METHOD; GIBBS FREE ENERGY; INVERSE PROBLEM; NUMERICAL MODEL; OPTIMIZATION; RAY TRACING; SENSITIVITY ANALYSIS;

EID: 34447267242     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2007.03400.x     Document Type: Article
Times cited : (38)

References (41)
  • 1
    • 0025596374 scopus 로고
    • On the nonuniqueness of receiver function inversions
    • Ammon, C.J., Randall, G.E. & Zandt, G., 1990. On the nonuniqueness of receiver function inversions, J. Geophys. Res., 95, 15303-15318.
    • (1990) J. Geophys. Res. , vol.95 , pp. 15303-15318
    • Ammon, C.J.1    Randall, G.E.2    Zandt, G.3
  • 3
    • 22544433836 scopus 로고
    • Programs for automatic differentiation for the machine BESM
    • Technical Report, Institute for Precise Mechanics and Computation Techniques, Academy of Science, Moscow, USSR (In Russian)
    • Beda, L.M., Korolev, L.N., Sukkikh, N.V. & Frolova, T.S., 1959. Programs for automatic differentiation for the machine BESM, Technical Report, Institute for Precise Mechanics and Computation Techniques, Academy of Science, Moscow, USSR (In Russian).
    • (1959)
    • Beda, L.M.1    Korolev, L.N.2    Sukkikh, N.V.3    Frolova, T.S.4
  • 4
    • 0037329874 scopus 로고    scopus 로고
    • Mantle circulation models with variational data assimilation: Inferring past mantle flow and structure from plate motion histories and seismic tomography
    • Bunge, H.-P., Hagelberg, C.R. & Travis, B.J., 2003. Mantle circulation models with variational data assimilation: Inferring past mantle flow and structure from plate motion histories and seismic tomography, Geophys. J. Int., 152, 280-301.
    • (2003) Geophys. J. Int. , vol.152 , pp. 280-301
    • Bunge, H.-P.1    Hagelberg, C.R.2    Travis, B.J.3
  • 5
    • 36749109879 scopus 로고
    • Sensitivity theory for nonlinear systems. I. Nonlinear functional analysis approach
    • Cacuci, D.G., 1981a. Sensitivity theory for nonlinear systems. I. Nonlinear functional analysis approach, J. Math. Phys., 22, 2794-2802.
    • (1981) J. Math. Phys. , vol.22 , pp. 2794-2802
    • Cacuci, D.G.1
  • 6
    • 36749113522 scopus 로고
    • Sensitivity theory for nonlinear systems. II. Extension to additional classes of responses
    • Cacuci, D.G., 1981b. Sensitivity theory for nonlinear systems. II. Extension to additional classes of responses, J. Math. Phys., 22, 2803-2812.
    • (1981) J. Math. Phys. , vol.22 , pp. 2803-2812
    • Cacuci, D.G.1
  • 9
    • 0023480375 scopus 로고
    • The computation of chemical equilibrium in complex systems containing non-ideal solutions
    • De Capitani, C. & Brown, T.H., 1987. The computation of chemical equilibrium in complex systems containing non-ideal solutions, Geochim. Cosmochim. Acta, 51, 2639-2652.
    • (1987) Geochim. Cosmochim. Acta , vol.51 , pp. 2639-2652
    • De Capitani, C.1    Brown, T.H.2
  • 10
    • 0032269567 scopus 로고    scopus 로고
    • Recipes for Adjoint code construction
    • Giering, R. & Kaminski, T., 1998. Recipes for Adjoint code construction, ACM Trans. Math Software, 24, 437-474.
    • (1998) ACM Trans. Math Software , vol.24 , pp. 437-474
    • Giering, R.1    Kaminski, T.2
  • 11
    • 0011521982 scopus 로고    scopus 로고
    • Recomputations in reverse mode AD
    • in Chap. 33, eds Corliss, G., Faure, C., Griewank, A., Hascoët, L. & Naumann, U., Springer, New York, NY
    • Giering, R. & Kaminski, T., 2002. Recomputations in reverse mode AD, in Automatic Differentiation of Algorithms: From Simulation to Optimization, Chap. 33, pp. 283-291, eds Corliss, G., Faure, C., Griewank, A., Hascoët, L. & Naumann, U., Springer, New York, NY.
    • (2002) Automatic Differentiation of Algorithms: From Simulation to Optimization , pp. 283-291
    • Giering, R.1    Kaminski, T.2
  • 12
    • 33645479438 scopus 로고    scopus 로고
    • Applying TAF to generate efficient derivative code of Fortran 77-95 programs
    • Giering, R. & Kaminski, T., 2003. Applying TAF to generate efficient derivative code of Fortran 77-95 programs, Proc. Appl. Math. Mech.
    • (2003) Proc. Appl. Math. Mech.
    • Giering, R.1    Kaminski, T.2
  • 13
    • 0003086453 scopus 로고
    • On automatic differentiation
    • in eds Iri, M. & Tanabe, K., Kluwer Academic Publishers, Dordecht
    • Griewank, A., 1989. On automatic differentiation, in Mathematical Programming: Recent Developments and Applications, pp. 83-108, eds Iri, M. & Tanabe, K., Kluwer Academic Publishers, Dordecht.
    • (1989) Mathematical Programming: Recent Developments and Applications , pp. 83-108
    • Griewank, A.1
  • 14
    • 0037617007 scopus 로고
    • The chain rule revisited in scientific computing
    • Griewank, A., 1991. The chain rule revisited in scientific computing, SIAM News, 24 (No. 3), p. 20 & (No. 4) p. 8.
    • (1991) SIAM News , vol.20 , Issue.3-4 , pp. 20
    • Griewank, A.1
  • 15
    • 0003319841 scopus 로고    scopus 로고
    • Evaluating derivatives: Principles and techniques of algorithmic differentiation
    • in SIAM, Philadelphia, PA
    • Griewank, A., 2000. Evaluating derivatives: Principles and techniques of algorithmic differentiation, in Frontiers in Appl. Math., No. 19, SIAM, Philadelphia, PA.
    • (2000) Frontiers in Appl. Math. , Issue.19
    • Griewank, A.1
  • 16
    • 0023500627 scopus 로고
    • A chemical equilibrium algorithm for highly non-ideal multiphase systems: Free energy minimization
    • Harvie, C.E., Greenberg, J.P. & Weare, J.H., 1987. A chemical equilibrium algorithm for highly non-ideal multiphase systems: Free energy minimization, Geochim. Cosmochim. Acta, 51, 1045-1057.
    • (1987) Geochim. Cosmochim. Acta , vol.51 , pp. 1045-1057
    • Harvie, C.E.1    Greenberg, J.P.2    Weare, J.H.3
  • 17
    • 0002392976 scopus 로고
    • The dispersion of surface waves in multilayered media
    • Haskell, N.A., 1953. The dispersion of surface waves in multilayered media, Bull. Seism. Soc. Am., 43, 17-34.
    • (1953) Bull. Seism. Soc. Am. , vol.43 , pp. 17-34
    • Haskell, N.A.1
  • 18
    • 34447263743 scopus 로고    scopus 로고
    • Mountain belt growth inferred from past plate convergence: A new tectonic inverse problem
    • submitted
    • Iaffaldano, G., Bunge, H.-P. & Bücker, M., 2007. Mountain belt growth inferred from past plate convergence: A new tectonic inverse problem, Earth planet. Sci. Lett., submitted.
    • (2007) Earth Planet. Sci. Lett.
    • Iaffaldano, G.1    Bunge, H.-P.2    Bücker, M.3
  • 21
    • 0024485977 scopus 로고
    • Scattering of teleseismic body waves under Pasadena, California
    • Langston, C.A., 1989. Scattering of teleseismic body waves under Pasadena, California, J. Geophys. Res., 94, 1935-1951.
    • (1989) J. Geophys. Res. , vol.94 , pp. 1935-1951
    • Langston, C.A.1
  • 22
    • 0347107243 scopus 로고    scopus 로고
    • Plate tectonics and convection in the earth's mantle: Toward a numerical simulation
    • Moresi, L., Gurnis, M. & Zhong, S.J., 2000. Plate tectonics and convection in the earth's mantle: Toward a numerical simulation, Comput. Sci. Eng., 2, 22-33.
    • (2000) Comput. Sci. Eng. , vol.2 , pp. 22-33
    • Moresi, L.1    Gurnis, M.2    Zhong, S.J.3
  • 23
    • 0037455633 scopus 로고    scopus 로고
    • Lagrangian integration point finite element method for large deformation modeling of viscoelastic geomaterials
    • Moresi, L., Dufor, F. & Mulhlaus, H.B., 2003. Lagrangian integration point finite element method for large deformation modeling of viscoelastic geomaterials, J. Comp. Phys., 184, 476-497.
    • (2003) J. Comp. Phys. , vol.184 , pp. 476-497
    • Moresi, L.1    Dufor, F.2    Mulhlaus, H.B.3
  • 25
    • 0002249579 scopus 로고    scopus 로고
    • An introduction to automatic differentiation
    • in eds Berz, M., Bischof, C.H., Corliss, G.F. & Griewank, A., SIAM, Philadelphia, PA
    • Rall, L.B. & Corliss, G.F., 1996. An introduction to automatic differentiation, in Computational Differentiation: Techniques, Applications, and Tools, pp. 1-17, eds Berz, M., Bischof, C.H., Corliss, G.F. & Griewank, A., SIAM, Philadelphia, PA.
    • (1996) Computational Differentiation: Techniques, Applications, and Tools , pp. 1-17
    • Rall, L.B.1    Corliss, G.F.2
  • 26
    • 33749340080 scopus 로고    scopus 로고
    • Joint three-dimensional inversion of coupled groundwater flow and heat transfer based on automatic differentiation: Sensitivity calculation, verification, and synthetic examples
    • doi:. 10.1111/j.1365-246X.2006.03074.x
    • Rath, V., Wolf, A. & Bücker, H., 2006. Joint three-dimensional inversion of coupled groundwater flow and heat transfer based on automatic differentiation: Sensitivity calculation, verification, and synthetic examples, Geophys. J. Int., 167, 453-466, doi:. 10.1111/ j.1365-246X.2006.03074.x
    • (2006) Geophys. J. Int. , vol.167 , pp. 453-466
    • Rath, V.1    Wolf, A.2    Bücker, H.3
  • 27
    • 33645472496 scopus 로고    scopus 로고
    • Seismic traveltime tomography of the crust and lithosphere
    • Rawlinson, N. & Sambridge, M., 2003. Seismic traveltime tomography of the crust and lithosphere, Geophys. J. Int., 46, 81-197.
    • (2003) Geophys. J. Int. , vol.46 , pp. 81-197
    • Rawlinson, N.1    Sambridge, M.2
  • 28
    • 0036765114 scopus 로고    scopus 로고
    • Monte Carlo methods in geophysical inverse problems
    • doi 10.1029/2000RG000089
    • Sambridge, M. & Mosegaard, K., 2002. Monte Carlo methods in geophysical inverse problems, Rev. of Geophys., 40, 3.1-3.29, doi 10.1029/2000RG000089
    • (2002) Rev. of Geophys. , vol.40
    • Sambridge, M.1    Mosegaard, K.2
  • 29
    • 0030186104 scopus 로고    scopus 로고
    • Genetic algorithm inversion for receiver functions with application to crust and uppermost mantle structure beneath eastern australia
    • Shibutani, T., Sambridge, M. & Kennett, B.L.N., 1996. Genetic algorithm inversion for receiver functions with application to crust and uppermost mantle structure beneath eastern australia, Geophys. Res. Lett., 23, 1829-1832.
    • (1996) Geophys. Res. Lett. , vol.23 , pp. 1829-1832
    • Shibutani, T.1    Sambridge, M.2    Kennett, B.L.N.3
  • 30
    • 33847791348 scopus 로고    scopus 로고
    • Finite-frequency sensitivity of surface waves to anisotropy based on adjoint methods
    • Sieminski, A., Liu, Q., Trampert, J. & Tromp, J., 2007. Finite-frequency sensitivity of surface waves to anisotropy based on adjoint methods, Geophys. J. Int., 16 (3), 1153-1174.
    • (2007) Geophys. J. Int. , vol.16 , Issue.3 , pp. 1153-1174
    • Sieminski, A.1    Liu, Q.2    Trampert, J.3    Tromp, J.4
  • 31
    • 34447250993 scopus 로고    scopus 로고
    • Computational petrology: Subsolidus equilibria in the upper mantle
    • PhD thesis, The Australian National University
    • Sommacal, S., 2004. Computational petrology: Subsolidus equilibria in the upper mantle, PhD thesis, The Australian National University.
    • (2004)
    • Sommacal, S.1
  • 32
    • 0345530488 scopus 로고
    • Computation of chemical equilibrium compositions
    • Storey, S.H. & van Zeggeren, F., 1964. Computation of chemical equilibrium compositions, Can. J. Chem. Eng., 42, 54-55.
    • (1964) Can. J. Chem. Eng. , vol.42 , pp. 54-55
    • Storey, S.H.1    van Zeggeren, F.2
  • 33
    • 0001634765 scopus 로고
    • The use of adjoint equations in numerical modelling of the atmospheric circulation
    • in eds Griewank, A. & Corlis, G.F., SIAM, Philadelphia, PA
    • Talagrand, O., 1991. The use of adjoint equations in numerical modelling of the atmospheric circulation, in Automatic Differentiation of Algorithms: Theory, Implementation, and Application, pp. 169-180, eds Griewank, A. & Corlis, G.F., SIAM, Philadelphia, PA.
    • (1991) Automatic Differentiation of Algorithms: Theory, Implementation, and Application , pp. 169-180
    • Talagrand, O.1
  • 34
    • 0023128058 scopus 로고
    • Variational assimilation of meteorological observarions with the adjoint vorticity equation. I: Theory
    • Talagrand, O. & Courtier, P., 1987. Variational assimilation of meteorological observarions with the adjoint vorticity equation. I: theory, Q. J. R. Meteorol. Soc., 113, 1311-1328.
    • (1987) Q. J. R. Meteorol. Soc. , vol.113 , pp. 1311-1328
    • Talagrand, O.1    Courtier, P.2
  • 35
    • 0021474580 scopus 로고
    • Inversion of seismic reflection data in the acoustic approximation
    • Tarantola, A., 1984. Inversion of seismic reflection data in the acoustic approximation, Geophysics, 49, 1259-1266.
    • (1984) Geophysics , vol.49 , pp. 1259-1266
    • Tarantola, A.1
  • 36
    • 0024257273 scopus 로고
    • Theoretical background for the inversion of seismic waveforms, including elasticity and attenuation
    • Tarantola, A., 1988. Theoretical background for the inversion of seismic waveforms, including elasticity and attenuation, Pure Appl. Geophys., 128, 365-399.
    • (1988) Pure Appl. Geophys. , vol.128 , pp. 365-399
    • Tarantola, A.1
  • 38
    • 0001252941 scopus 로고
    • Fitting dynamics to data
    • Thacker, W. & Long, R.B., 1988. Fitting dynamics to data, J. Geophys. Res., 93, 1227-1240.
    • (1988) J. Geophys. Res. , vol.93 , pp. 1227-1240
    • Thacker, W.1    Long, R.B.2
  • 39
    • 36849122738 scopus 로고
    • Transmission of elastic waves through a stratified solid
    • Thomson, W.T., 1950. Transmission of elastic waves through a stratified solid, J. Appl. Phys., 21, 89-93.
    • (1950) J. Appl. Phys. , vol.21 , pp. 89-93
    • Thomson, W.T.1
  • 40
    • 13344261374 scopus 로고    scopus 로고
    • Seismic tomography, adjoint methods, time reversal, and banana-donut kernels
    • doi 10.1111/j.1365-246X.2004.02456.x
    • Tromp, J., Tape, C. & Liu, Q., 2005. Seismic tomography, adjoint methods, time reversal, and banana-donut kernels, Geophys. J. Int., 160, 195-216, doi 10.1111/j.1365-246X.2004.02456.x
    • (2005) Geophys. J. Int. , vol.160 , pp. 195-216
    • Tromp, J.1    Tape, C.2    Liu, Q.3
  • 41
    • 0000547784 scopus 로고
    • A simple automatic derivative evaluation program
    • Wengert, R., 1964. A simple automatic derivative evaluation program, Commun. ACM, 7 (8), 463-464.
    • (1964) Commun. ACM , vol.7 , Issue.8 , pp. 463-464
    • Wengert, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.