Resolution analysis in full waveform inversion

Geophysical Journal International

Volumn 187, Issue 3, 2011, Pages 1604-1624

  Fichtner, Andreas ^a   Trampert, Jeannot ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Computational seismology; Fourier analysis; Inverse theory; Seismic tomography; Theoretical seismology; Wave propagation

Indexed keywords

ADJOINT TECHNIQUES; COMPUTATIONAL REQUIREMENTS; CONJUGATE GRADIENT; EARTH MODELS; FOURIER; FULL-WAVEFORM INVERSION; FUNCTIONAL DESIGN; GAUSSIAN APPROXIMATIONS; GEORADARS; IMAGE DISTORTIONS; INVERSE THEORY; MICROWAVE DATA; NEWTON LIKE METHODS; OPTIMIZATION SCHEME; PARAMETRIZATIONS; QUADRATIC APPROXIMATION; RAY THEORY; RESOLUTION ANALYSIS; SEISMIC TOMOGRAPHY; SEISMIC WAVEFORM INVERSION; SUCCESSIVE DERIVATIVES; TOMOGRAPHIC METHODS;

EARTH (PLANET); FOURIER ANALYSIS; FOURIER TRANSFORMS; OPTIMIZATION; SEISMOGRAPHS; SEISMOLOGY; THREE DIMENSIONAL; WAVE PROPAGATION;

WAVEFORM ANALYSIS;

FOURIER TRANSFORM; INVERSE ANALYSIS; PARAMETERIZATION; QUANTITATIVE ANALYSIS; SEISMIC TOMOGRAPHY; SEISMIC WAVE; SEISMOLOGY; UPPER MANTLE; WAVE EQUATION; WAVE PROPAGATION; WAVEFORM ANALYSIS;

EUROPE;

EID: 81555219124     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2011.05218.x     Document Type: Article

References (104)

1. Aoki, N. & Schuster, G.T., 2009. Fast least-squares migration with a deblurring filter, Geophysics, 74, WCA83-WCA93.
2. Backus, G.E. & Gilbert, F., 1967. Numerical application of a formalism for geophysical inverse problems, Geophys. J. R. astr. Soc., 13, 247-276.
3. Bamberger, A., Chavent, G. & Lailly, P., 1977. Une application de la théorie du contrôle à un problème inverse sismique, Ann. Geophys., 33, 183-200.
4. Bamberger, A., Chavent, G., Hemons, C. & Lailly, P., 1982. Inversion of normal incidence seismograms, Geophysics, 47, 757-770.
5. Bassin, C., Laske, G. & Masters, G., 2000. The current limits of resolution for surface wave tomography in North America, EOS, Trans. Am. geophys. Un., 81, F897.
6. Bendinelli, O., Parmeggiani, G. & Zavatti, F., 1987. An analytical approximation of the Hubble space telescope monochromatic point spread function, J. Astrophys. Astron., 8, 343-350.
7. Bernauer, M., Fichtner, A. & Igel, H., 2009. Inferring earth structure from combined measurements of rotational and translational ground motions, Geophysics, 74, WCD41-WCD47.
8. Bijwaard, H., Spakman, W. & Engdahl, E.R., 1998. Closing the gap between regional and global traveltime tomography, J. geophys. Res., 103, 30055-30078.
9. Bleibinhaus, F., Hole, J.A. & Ryberg, T., 2007. Structure of the California Coast Ranges and San Andreas Fault at SAFOD from seismic waveform inversion and reflection imaging, J. geophys. Res., 112, doi:.
10. Bleibinhaus, F., Lester, R.W. & Hole, J.A., 2009. Applying waveform inversion to wide angle seismic surveys, Tectonophysics, 472, 238-248.
11. Bodin, T. & Sambridge, M., 2009. Seismic tomography with the reversible jump algorithm, Geophys. J. Int., 178, 1411-1436.
12. Boschi, L., 2003. Measures of resolution in global body wave tomography, Geophys. Res. Lett., 30, doi:.
13. Boschi, L., Ekström, G. & Kustowski, B., 2004. Multiple resolution surface wave tomography: the Mediterranean basin, Geophys. J. Int., 157, 293-304.
14. Bozdaǧ, E., Trampert, J. & Tromp, J., 2011. Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements, Geophys. J. Int., 185, 845-870.
15. Brossier, R., Operto, S. & Virieux, J., 2009. Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion, Geophysics, 74, WCC105-WCC118.
16. Brossier, R., Operto, S. & Virieux, J., 2010. Which data residual norm for robust elastic frequency-domain full waveform inversion? Geophysics, 75, R37-R46.
17. Bunks, C., Saleck, F.M., Zaleski, S. & Chavent, G., 1995. Multiscale seismic waveform inversion, Geophysics, 60, 1457-1473.
18. Cara, M., Lévèque, J.J. & Maupin, V., 1984. Density-versus-depth models from multimode surface waves, Geophys. Res. Lett., 11, 633-636.
19. Charlier, C.V.L., 1905. Über die Darstellung willkürlicher Funktionen, Arkiv för Matematik, Astronomi och Fysik, 20(2), 1-35.
20. Chavent, G. & Plessix, R.-E., 1999. An optimal true-amplitude least-squares prestack depth-migration operator, Geophysics, 64, 508-515.
21. Chen, P., 2011. Full-wave seismic data assimilation: theoretical background and recent advances, Pure Appl. Geophys. 168, 1527-1552, doi:.
22. Chen, P., Zhao, L. & Jordan, T.H., 2007. Full 3D tomography for the crustal structure of the los angeles region, Bull. seism. Soc. Am., 97, 1094-1120.
23. Chew, W.C. & Lin, J.H., 1995. A frequency-hopping approach for microwave imaging of large inhomogeneous bodies, IEEE Microw. Guid. Wave Lett., 5, 439-441.
24. Cramér, H., 1957. Mathematical Methods of Statistics, Princeton University Press, Princeton, NJ.
25. Crase, E., Pica, A., Noble, M., McDonald, J. & Tarantola, A., 1990. Robust elastic nonlinear waveform inversion: application to real data, Geophysics, 55, 527-538.
26. Debayle, E. & Sambridge, M., 2004. Inversion of massive surface wave data sets: model construction and resolution assessment, J. geophys. Res., 109, B02316, doi:.
27. Del Brio, E.B., Niguez, T.M. & Perote, J., 2009. Gram-Charlier densities: a multivariate approach, Quant. Finance, 9, 855-868.
28. Devaney, A.J., 1984. Geophysical diffraction tomography, IEEE Trans. Geos. Remote Sens., 22, 3-13.
29. Devilee, R.J.R., Curtis, A. & Roy-Chowdhury, K., 1999. An efficient, probabilistic neural network approach to solving inverse problems: inverting surface wave velocities for Eurasian crustal thickness, J. geophys. Res., 104, 28841-28857.
30. Dondi, F., Betti, A., Blo, G. & Bighi, C., 1981. Statistical analysis of gas-chromatographic peaks by the Gram-Charlier series of type A and the Edgeworth-Cramer series, Anal. Chem., 53, 496-504.
31. Dziewonski, A.M. & Anderson, D.L., 1981. Preliminary reference Earth model, Phys. Earth planet. Inter., 25, 297-356.
32. Epanomeritakis, I., Akcelik, V., Ghattas, O. & Bielak, J., 2008. A Newton-CG method for large-scale three-dimensional elastic full waveform seismic inversion, Inverse Probl., 24, doi:.
33. Ernst, J.R., Green, A.G., Maurer, H. & Holliger, K., 2007. Application of a new 2D time-domain full-waveform inversion scheme to crosshole radar data, Geophysics, 72, J53-J64.
34. Fang, Y., Cheney, M. & Roecker, S., 2010. Imaging from sparse measurements, Geophys. J. Int., 180, 1289-1302.
35. Ferreira, A.M.G. & Igel, H., 2009. Rotational motions of seismic surface waves in a laterally heterogeneous Earth, Bull. seism. Soc. Am., 99, 1429-1436.
36. Fichtner, A., 2010. Full Seismic Waveform Modelling and Inversion, Springer, Heidelberg.
37. Fichtner, A. & Igel, H., 2008. Efficient numerical surface wave propagation through the optimization of discrete crustal models: a technique based on non-linear dispersion curve matching (DCM), Geophys. J. Int., 173, 519-533.
38. Fichtner, A. & Trampert, J., 2011. Hessian kernels of seismic data functionals based upon adjoint techniques, Geophys. J. Int., 185, 775-798.
39. Fichtner, A., Bunge, H.-P. & Igel, H., 2006. The adjoint method in seismology: I. Theory, Phys. Earth planet. Inter., 157, 86-104.
40. Fichtner, A., Kennett, B.L.N., Igel, H. & Bunge, H.-P., 2008. Theoretical background for continental- and global-scale full-waveform inversion in the time-frequency domain, Geophys. J. Int., 175, 665-685.
41. Fichtner, A., Kennett, B.L.N., Igel, H. & Bunge, H.-P., 2009. Full seismic waveform tomography for upper-mantle structure in the Australasian region using adjoint methods, Geophys. J. Int., 179, 1703-1725.
42. Fichtner, A., Kennett, B.L.N., Igel, H. & Bunge, H.-P., 2010. Full waveform tomography for radially anisotropic structure: new insights into present and past states of the Australasian upper mantle, Earth planet. Sci. Lett., 290, 270-280.
43. Gauthier, O., Virieux, J. & Tarantola, A., 1986. Two-dimensional nonlinear inversion of seismic waveforms: numerical results, Geophysics, 51, 1387-1403.
44. Gee, L.S. & Jordan, T.H., 1992. Generalized seismological data functionals, Geophys. J. Int., 111, 363-390.
45. Gram, J.P., 1883. Ueber die Entwickelung reeller Functionen in Reihen mittelst der Methode der kleinsten Quadrate, Journal für die reine und angewandte Mathematik, 94, 6-73.
46. Hingee, M., Tkalčić, H., Fichtner, A. & Sambridge, M., 2011. Seismic moment tensor inversion using a 3-D structural model: applications for the Australian region, Geophys. J. Int., 184, 949-964.
47. Hu, J., Schuster, G.T. & Valasek, P.A., 2001. Poststack migration deconvolution, Geophys. J. Int., 66, 939-952.
48. Igel, H., Djikpesse, H. & Tarantola, A., 1996. Waveform inversion of marine reflection seismograms for P impedance and Poisson's ratio, Geophys. J. Int., 124, 363-371.
49. Jaynes, E.T., 2003. Probability Theory: The Logic of Science, Cambridge University Press, Cambridge.
50. Kawai, K. & Geller, R.J., 2010. Waveform inversion for localised seismic structure and an application to D″ structure beneath the Pacific, J. geophys. Res., 115, doi:.
51. Kissling, E., 1988. Geotomography with local earthquake data, Rev. Geophys., 26, 659-698.
52. Konishi, K., Kawai, K., Geller, R.J. & Fuji, N., 2009. MORB in the lowermost mantle beneath the western Pacific: evidence from waveform inversion, Earth planet. Sci. Lett., 278, 219-225.
53. Kosmas, P. & Rappaport, C.M., 2006. FDTD-based time reversal for microwave breast cancer detection: localization in three dimensions, IEEE Trans. Microw. Theo. Tech., 54, 1921-1927.
54. van Leeuwen, T. & Mulder, W.A., 2010. A correlation-based misfit criterion for wave-equation traveltime tomography, Geophys. J. Int., 182, 1383-1394.
55. Lévêque, J.J., Rivera, L. & Wittlinger, G., 1993. On the use of the checkerboard test to assess the resolution of tomographic inversions, Geophys. J. Int., 115, 313-318.
56. Liu, D.C. & Nocedal, J., 1989. On the limited-memory BFGS method for large-scale optimisation, Math. Program., 45, 503-528.
57. Liu, Q. & Tromp, J., 2006. Finite-frequency kernels based on adjoint methods, Bull. seismol. Soc. Am., 96, 2383-2397.
58. Luo, Y. & Schuster, G.T., 1991. Wave-equation traveltime inversion, Geophysics, 56, 645-653.
59. Maurer, H., Greenhalgh, S. & Latzel, S., 2009. Frequency and spatial sampling strategies for crosshole seismic waveform spectral inversion experiments, Geophysics, 74, WCC11-WCC21.
60. Meier, U., Curtis, A. & Trampert, J., 2007a. Fully nonlinear inversion of fundamental mode surface waves for a global crustal model, Geophys. Res. Lett., 34, doi:.
61. Meier, U., Curtis, A. & Trampert, J., 2007b. Global crustal thickness from neural network inversion of surface wave data, Geophys. J. Int., 169, 706-722.
62. Meju, M.A., 2009. Regularised extremal bounds analysis (REBA): an approach to quantifying uncertainty in nonlinear geophysical inverse problems, Geophys. Res. Lett., 36, doi:.
63. Meju, M.A. & Sakkas, V., 2007. Heterogeneous crust and upper mantle across southern Kenya and the relationship to surface deformation as inferred from magnetotelluric imaging, J. geophys. Res., 112, doi:.
64. Meles, G.A., van der Kruk, J., Greenhalgh, S.A., Ernst, J.R., Maurer, H. & Green, A.G., 2010. A new vector waveform inversion algorithm for simultaneous updating of conductivity and permittivity parameters from combination of crosshole/borehole-to-surface GPR data, IEEE Trans. Geosc. Rem. Sens., 48, 3391-3407.
65. Mora, P., 1987. Nonlinear two-dimensional elastic inversion of multioffset seismic data, Geophysics, 52, 1211-1228.
66. Mora, P., 1988. Elastic wave-field inversion of reflection and transmission data, Geophysics, 53, 750-759.
67. Mora, P., 1989. Inversion=migration+tomography, Geophysics, 54, 1575-1586.
68. Nemeth, T., Wu, C. & Schuster, G.T., 1999. Least-squares migration of incomplete reflection data, Geophysics, 64, 208-221.
69. Nolet, G. & Montelli, R., 2005. Optimal parametrization of tomographic models, Geophys. J. Int., 161, 365-372.
70. Nolet, G., Montelli, R. & Virieux, J., 1999. Explicit, approximate expressions for the resolution and a posteriori covariance of massive tomographic systems, Geophys. J. Int., 138, 36-44.
71. Pankajakshan, P., Zhang, B., Blanc-Feraud, L., Kam, Z., Olivo-Marin, J.C. & Zerubia, J., 2000. Blind deconvolution for thin-layered confocal imaging, Appl. Opt., 48, 4437-4448.
72. Pavese, A., Artioli, G. & Prencipe, M., 1995. X-ray single-crystal diffraction study of pyrope in the temperature range 30-973 k, Am. Mineral., 80, 457-464.
73. Peter, D., Boschi, L., Deschamps, F., Fry, B., Ekström, G. & Giardini, D., 2008. A new finite-frequency shear-velocity model of the European-Mediterranean region, Geophys. Res. Lett., 35, doi:.
74. Plessix, R.-E., 2006. A review of the adjoint-state method for computing the gradient of a functional with geophysical applications, Geophys. J. Int., 167, 495-503.
75. Pratt, R., Shin, C. & Hicks, G., 1998. Gauss-Newton and full Newton methods in frequency domain seismic waveform inversion, Geophys. J. Int., 133, 341-362.
76. Ravaut, C., Operto, S., Importa, L., Virieux, J., Herrero, A. & dell'Aversana, P., 2004. Multi-scale imaging of complex structures from multi-fold wide aperture seismic data by frequency-domain full-wavefield inversions: application to a thrust belt, Geophys. J. Int., 159, 1032-1056.
77. Ritsema, J. & van Heijst, H., 2002. Constraints on the correlation of P- and S-wave velocity heterogeneity in the mantle from P, PP, PPP and PKPab traveltimes, Geophys. J. Int., 149, 482-489.
78. Ritsema, J., vanHeijst, H. & Woodhouse, J.H., 1999. Complex shear wave velocity structure imaged beneath Africa and Iceland, Science, 286, 1925-1928.
79. Sambridge, M. & Mosegaard, K., 2002. Monte Carlo methods in geophysical inverse problems, Rev. Geophys., 40, doi:.
80. Samuelson, P.A., 1943. Fitting general Gram-Charlier series, Ann. Math. Stat., 14(2), 179-187.
81. Santosa, F. & Symes, W.W., 1988. Computation of the Hessian for least-squares solutions of inverse problems of reflection seismology, Inverse Probl., 4, 211-233.
82. Sargan, J.D., 1975. Gram-Charlier approximations applied to t ratios of k-class estimators, Econometrica, 43, 327-347.
83. Sauer, P.W. & Heydt, G.T., 1979. Convenient multivariate Gram-Charlier type-A series, IEEE Trans. Comm., 27, 247-248.
84. Schäfer, J., Boschi, L. & Kissling, E., 2011. Adaptively parametrized surface wave tomography: methodology and a new model of the European upper mantle, Geophys. J. Int., 186, 1431-1453.
85. Schivardi, R. & Morelli, A., 2011. EPmantle: a 3-D transversely isotropic model of the upper mantle under the European Plate, Geophys. J. Int., 185, 469-484.
86. Schuster, G.T. & Hu, J., 2000. Green's function for migration: continuous recording geometry, Geophysics, 65, 167-175.
87. Sirgue, L. & Pratt, R.G., 2004. Efficient waveform inversion and imaging: a strategy for selecting temporal frequencies, Geophysics, 69, 231-248.
88. Smithyman, B., Pratt, R.G., Hayles, J. & Wittebolle, R., 2009. Detecting near-surface objects with seismic waveform tomography, Geophysics, 74, WCC119-WCC127.
89. Spakman, W., 1991. Delay-time tomography of the upper mantle below Europe, the Mediterranean and Asia Minor, Geophys. J. Int., 107, 309-332.
90. Takam Takougang, E.M. & Calvert, A., 2011. Application of waveform tomography to marine seismic reflection data from the Queen Charlotte Basin of western Canada, Geophysics, 76, B55-B70.
91. Takeuchi, H. & Saito, M., 1972. Seismic surface waves, in Methods in Computational Physics, Vol. 11, pp. 217-295, ed. Bolt B.A., Academic Press, New York, NY.
92. Tape, C., Liu, Q. & Tromp, J., 2007. Finite-frequency tomography using adjoint methods: methodology and examples using membrane surface waves, Geophys. J. Int., 168, 1105-1129.
93. Tape, C., Liu, Q., Maggi, A. & Tromp, J., 2009. Adjoint tomography of the southern California crust, Science, 325, 988-992.
94. Tape, C., Liu, Q., Maggi, A. & Tromp, J., 2010. Seismic tomography of the southern California crust based upon spectral-element and adjoint methods, Geophys. J. Int., 180, 433-462.
95. Tarantola, A., 1984. Inversion of seismic reflection data in the acoustic approximation, Geophysics, 49, 1259-1266.
96. Tarantola, A., 1988. Theoretical background for the inversion of seismic waveforms, including elasticity and attenuation, Pure appl. Geophys., 128, 365-399.
97. Tarantola, A., 2005. Inverse Problem Theory and Methods for Model Parameter Estimation, 2nd edn., Society for Industrial and Applied Mathematics, Philadephia, PA.
98. Tromp, J., Tape, C. & Liu, Q., 2005. Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels, Geophys. J. Int., 160, 195-216.
99. Trujillo, I., Aguerri, J.A.L. & Gutierrez, C.M., 2001. The effects of seeing on Sérsic profiles, Mon. Not. R. astr. Soc., 321, 269-276.
100. Widiyantoro, S. & van der Hilst, R., 1997. Mantle structure beneath Indonesia inferred from high-resolution tomographic imaging, Geophys. J. Int., 130, 167-182.
101. Wu, R.-S. & Toksöz, M.N., 1987. Diffraction tomography and multisource holography applied to seismic imaging, Geophysics, 52, 11-25.
102. Yu, J.H., Wang, Y. & Schuster, G.T., 2002. Deconvolution of the psf of a seismic lens, in Image Reconstruction from Incomplete Data II, Proc. SPIE Vol. 4792, pp. 135-145, eds Bones, P.J., Fiddy, M.A. & Millane, R.P., SPIE, Bellingham, WA.
103. Zhang, B., Zerubia, J. & Olivo-Marin, J.C., 2007. Gaussian approximation of fluorescence microscope point-spread function models, Appl. Opt., 46, 1819-1829.
104. Zielhuis, A. & Nolet, G., 1994. Shear-wave velocity variations in the upper mantle beneath central Europe, Geophys. J. Int., 117, 695-715.