Review article
11 Apr 2019
Review article | 11 Apr 2019
Green's theorem in seismic imaging across the scales
Kees Wapenaar et al.
Related authors
Related subject area
Lithospheric image of the Central Iberian Zone (Iberian Massif) using global-phase seismic interferometry
Juvenal Andrés, Deyan Draganov, Martin Schimmel, Puy Ayarza, Imma Palomeras, Mario Ruiz, and Ramon Carbonell
Solid Earth, 10, 1937–1950, https://doi.org/10.5194/se-10-1937-2019,https://doi.org/10.5194/se-10-1937-2019, 2019
Visual analytics of aftershock point cloud data in complex fault systems
Chisheng Wang, Junzhuo Ke, Jincheng Jiang, Min Lu, Wenqun Xiu, Peng Liu, and Qingquan Li
Solid Earth, 10, 1397–1407, https://doi.org/10.5194/se-10-1397-2019,https://doi.org/10.5194/se-10-1397-2019, 2019
Short summary
A multi-technology analysis of the 2017 North Korean nuclear test
Peter Gaebler, Lars Ceranna, Nima Nooshiri, Andreas Barth, Simone Cesca, Michaela Frei, Ilona Grünberg, Gernot Hartmann, Karl Koch, Christoph Pilger, J. Ole Ross, and Torsten Dahm
Solid Earth, 10, 59–78, https://doi.org/10.5194/se-10-59-2019,https://doi.org/10.5194/se-10-59-2019, 2019
Short summary
Cited articles
Abe, S., Kurashimo, E., Sato, H., Hirata, N., Iwasaki, T., and Kawanaka, T.:
Interferometric seismic imaging of crustal structure using scattered
teleseismic waves, Geophys. Res. Lett., 34, L19305,
https://doi.org/10.1029/2007GL030633, 2007.
a
Aki, K.: Space and time spectra of stationary stochastic waves, with special
reference to micro-tremors, Bull. Earthq. Res.
Inst., 35, 415–457, 1957. a
Almagro Vidal, C., van der Neut, J., Verdel, A., Hartstra, I. E., and Wapenaar,
K.: Passive body-wave interferometric imaging with directionally constrained
migration, Geophys. J. Int., 215, 1022–1036, 2018. a
Anderson, B. E., Guyer, R. A., Ulrich, T. J., Le Bas, P.-Y., Larmat, C.,
Griffa, M., and Johnson, P. A.: Energy current imaging method for time
reversal in elastic media, Appl. Phys. Lett., 95, 021907,
https://doi.org/10.1063/1.3180811, 2009.
a
Bensen, G. D., Ritzwoller, M. H., Barmin, M. P., Levshin, A. L., Lin, F.,
Moschetti, M. P., Shapiro, N. M., and Yang, Y.: Processing seismic ambient
noise data to obtain reliable broad-band surface wave dispersion
measurements, Geophys. J. Int., 169, 1239–1260, 2007. a
Bensen, G. D., Ritzwoller, M. H., and Shapiro, N. M.: Broadband ambient noise
surface wave tomography across the United States, J. Geophys. Res., 113, B05306,
https://doi.org/10.1029/2007JB005248, 2008.
a
Berkhout, A. J.: Seismic Migration. Imaging of acoustic energy by wave
field extrapolation. A. Theoretical aspects, Elsevier, Amsterdam, the Netherlands, 1982.
a,
b,
c
Berryhill, J. R.: Wave-equation datuming before stack, Geophysics, 49,
2064–2066, 1984. a
Bleistein, N.: On the imaging of reflectors in the Earth, Geophysics, 52,
931–942, 1987. a
Blondel, T., Chaput, J., Derode, A., Campillo, M., and Aubry, A.: Matrix
approach of seismic imaging: Application to the Erebus Volcano,
Antarctica, J. Geophys. Res., 123, 10936–10950, 2018. a
Boué, P., Poli, P., Campillo, M., and Roux, P.: Reverberations, coda waves
and ambient noise: Correlations at the global scale and retrieval of deep
phases, Earth Planet. Sci. Lett., 391, 137–145, 2014. a
Boullenger, B., Verdel, A., Paap, B., Thorbecke, J., and Draganov, D.: Studying
CO
2 storage with ambient-noise seismic interferometry: A combined
numerical feasibility study and field-data example for Ketzin, Germany,
Geophysics, 80, Q1–Q13, 2015. a
Brackenhoff, J., Thorbecke, J., and Wapenaar, K.: Monitoring induced distributed double-couple
sources using Marchenko-based virtual receivers, Solid Earth Discuss.,
https://doi.org/10.5194/se-2018-142,
in review, 2019.
a,
b,
c
Campillo, M. and Paul, A.: Long-range correlations in the diffuse seismic coda,
Science, 299, 547–549, 2003.
a,
b
Cassereau, D. and Fink, M.: Time-reversal of ultrasonic fields - Part III:
Theory of the closed time-reversal cavity, IEEE Trans. Ultrason., Ferroelect., and Freq. Control, 39, 579–592, 1992. a
Claerbout, J. F.: Synthesis of a layered medium from its acoustic transmission
response, Geophysics, 33, 264–269, 1968. a
Curtis, A. and Halliday, D.: Directional balancing for seismic and general
wavefield interferometry, Geophysics, 75, SA1–SA14, 2010a. a
Derode, A., Roux, P., and Fink, M.: Robust acoustic time reversal with
high-order multiple scattering, Phys. Rev. Lett., 75, 4206–4209,
1995.
a,
b,
c
Derode, A., Larose, E., Tanter, M., de Rosny, J., Tourin, A., Campillo, M.,
and Fink, M.: Recovering the Green's function from field-field correlations
in an open scattering medium (L), J. Acoust. Soc. Am., 113, 2973–2976, 2003.
a,
b
Draeger, C. and Fink, M.: One-channel time-reversal in chaotic cavities:
Theoretical limits, J. Acoust. Soc. Am., 105,
611–617, 1999.
a,
b
Draganov, D., Wapenaar, K., Mulder, W., Singer, J., and Verdel, A.: Retrieval
of reflections from seismic background-noise measurements, Geophys. Res. Lett., 34, L04305,
https://doi.org/10.1029/2006GL028735, 2007.
a
Draganov, D., Campman, X., Thorbecke, J., Verdel, A., and Wapenaar, K.:
Reflection images from ambient seismic noise, Geophysics, 74, A63–A67, 2009. a
Draganov, D., Campman, X., Thorbecke, J., Verdel, A., and Wapenaar, K.: Seismic
exploration-scale velocities and structure from ambient seismic noise (
>1 Hz), J. Geophys. Res., 118, 4345–4360, 2013. a
Duvall, T. L., Jefferies, S. M., Harvey, J. W., and Pomerantz, M. A.:
Time-distance helioseismology, Nature, 362, 430–432, 1993. a
Fichtner, A., Stehly, L., Ermert, L., and Boehm, C.: Generalized interferometry
− I: theory for interstation correlations, Geophys. J. Int., 208, 603–638, 2017. a
Fink, M.: Time-reversal of ultrasonic fields: Basic principles, IEEE Trans. Ultrason., Ferroelect., and Freq. Control,
39, 555–566, 1992.
a,
b
Fink, M.: Time-reversal acoustics in complex environments, Geophysics, 71,
SI151–SI164, 2006.
a,
b,
c,
d
Forghani, F. and Snieder, R.: Underestimation of body waves and feasibility of
surface-wave reconstruction by seismic interferometry, The Leading Edge, 29,
790–794, 2010. a
Green, G.: An essay on the application of mathematical analysis to the theories
of electricity and magnetism, available at:
arXiv:0807.0088v1 [physics.hist-ph], originally published as book in Nottingham, 1828 (reprinted in
three parts in Journal für die reine und angewandte Mathematik, 39, 73–89, 1850; 44, 356–374, 1852, and 47, 161–221, 1854). a
Halliday, D. and Curtis, A.: Seismic interferometry, surface waves and source
distribution, Geophys. J. Int., 175, 1067–1087, 2008.
a,
b
Hokstad, K.: Multicomponent Kirchhoff migration, Geophysics, 65, 861–873,
2000. a
Jakubowicz, H.: Wave equation prediction and removal of interbed multiples, in:
SEG, Expanded Abstracts, Annual Meeting 1998, Society of Exploration Geophysicists, Tulsa, Oklahoma, USA, pp. 1527–1530, 1998. a
Kimman, W. P. and Trampert, J.: Approximations in seismic interferometry and
their effects on surface waves, Geophys. J. Int., 182,
461–476, 2010.
a,
b
Kuo, J. T. and Dai, T. F.: Kirchhoff elastic wave migration for the case of
noncoincident source and receiver, Geophysics, 49, 1223–1238, 1984. a
Langenberg, K. J., Berger, M., Kreutter, T., Mayer, K., and Schmitz, V.:
Synthetic aperture focusing technique signal processing, NDT International,
19, 177–189, 1986. a
Larose, E., Margerin, L., Derode, A., van Tiggelen, B., Campillo, M., Shapiro,
N., Paul, A., Stehly, L., and Tanter, M.: Correlation of random wave fields:
An interdisciplinary review, Geophysics, 71, SI11–SI21, 2006. a
Lindsey, C. and Braun, D. C.: Principles of seismic holography for diagnostics
of the shallow subphotosphere, The Astrophys. J. Suppl. Series,
155, 209–225, 2004. a
Lobkis, O. I. and Weaver, R. L.: On the emergence of the Green's function in
the correlations of a diffuse field, J. Acoust. Soc. Am., 110, 3011–3017, 2001. a
McMechan, G. A.: Determination of source parameters by wavefield extrapolation,
Geophys. J. R. Astr. Soc., 71, 613–628, 1982. a
McMechan, G. A.: Migration by extrapolation of time-dependent boundary values,
Geophys. Prosp., 31, 413–420, 1983. a
Meles, G. A., Löer, K., Ravasi, M., Curtis, A., and da Costa Filho, C. A.:
Internal multiple prediction and removal using Marchenko autofocusing and
seismic interferometry, Geophysics, 80, A7–A11, 2015. a
Oren, C. and Nowack, R. L.: Seismic body-wave interferometry using noise
autocorrelations for crustal structure, Geophys. J. Int.,
208, 321–332, 2017. a
Oristaglio, M. L.: An inverse scattering formula that uses all the data,
Inverse Probl., 5, 1097–1105, 1989. a
Panea, I., Draganov, D., Almagro Vidal, C., and Mocanu, V.: Retrieval of
reflections from ambient noise record in the Mizil area, Romania,
Geophysics, 79, Q31–Q42, 2014. a
Porter, R. P.: Diffraction-limited, scalar image formation with holograms of
arbitrary shape, J. Opt. Soc. Am., 60, 1051–1059,
1970.
a,
b
Porter, R. P. and Devaney, A. J.: Holography and the inverse source problem,
J. Opt. Soc. Am., 72, 327–330, 1982.
a,
b
Ravasi, M., Vasconcelos, I., Kritski, A., Curtis, A., da Costa Filho, C. A.,
and Meles, G. A.: Target-oriented Marchenko imaging of a North Sea
field, Geophys. J. Int., 205, 99–104, 2016. a
Rayleigh, J. W. S.: The theory of sound. Volume II, Dover Publications,
Inc., New York, USA, 1878 (reprint 1945). a
Rickett, J. and Claerbout, J.: Acoustic daylight imaging via spectral
factorization: Helioseismology and reservoir monitoring, The Leading Edge,
18, 957–960, 1999. a
Roux, P., Sabra, K. G., Kuperman, W. A., and Roux, A.: Ambient noise cross
correlation in free space: Theoretical approach, J. Acoust. Soc. Am., 117, 79–84, 2005. a
Ruigrok, E., Campman, X., Draganov, D., and Wapenaar, K.: High-resolution
lithospheric imaging with seismic interferometry, Geophys. J. Int., 183, 339–357, 2010. a
Ryberg, T.: Body wave observations from cross-correlations of ambient seismic
noise: A case study from the Karoo, RSA, Geophys. Res. Lett.,
38, L13311,
https://doi.org/10.1029/2011GL047665, 2011.
a
Sabra, K. G., Gerstoft, P., Roux, P., Kuperman, W. A., and Fehler, M. C.:
Surface wave tomography from microseisms in Southern California,
Geophys. Res. Lett., 32, L14311,
https://doi.org/10.1029/2005GL023155, 2005a.
a,
b
Sabra, K. G., Gerstoft, P., Roux, P., Kuperman, W. A., and Fehler, M. C.:
Extracting time-domain Green's function estimates from ambient seismic
noise, Geophys. Res. Lett., 32, L03310,
https://doi.org/10.1029/2004GL021862, 2005b.
a
Scalerandi, M., Griffa, M., and Johnson, P. A.: Robustness of computational
time reversal imaging in media with
elastic constant uncertainties, J. Appl. Phys., 106, 114911,
https://doi.org/10.1063/1.3269718, 2009.
a
Schneider, W. A.: Integral formulation for migration in two and three
dimensions, Geophysics, 43, 49–76, 1978. a
Schuster, G. T.: Theory of daylight/interferometric imaging: tutorial, in:
EAGE, Extended Abstracts, Annual Meeting 2001, European Association of Geoscientists and Engineers, Houten, the Netherlands, p. A32, 2001. a
Schuster, G. T.: Seismic interferometry, Cambridge University Press, Cambridge, UK, 2009. a
Schuster, G. T. and Zhou, M.: A theoretical overview of model-based and
correlation-based redatuming methods, Geophysics, 71, SI103–SI110, 2006. a
Schuster, G. T., Yu, J., Sheng, J., and Rickett, J.: Interferometric/daylight
seismic imaging, Geophys. J. Int., 157, 838–852, 2004.
a,
b
Shapiro, N. M. and Campillo, M.: Emergence of broadband Rayleigh waves from
correlations of the ambient seismic noise, Geophys. Res. Lett., 31,
L07614,
https://doi.org/10.1029/2004GL019491, 2004.
a
Shapiro, N. M., Campillo, M., Stehly, L., and Ritzwoller, M. H.:
High-resolution surface-wave tomography from ambient seismic noise, Science,
307, 1615–1618, 2005. a
Slob, E., Wapenaar, K., Broggini, F., and Snieder, R.: Seismic reflector
imaging using internal multiples with Marchenko-type equations, Geophysics,
79, S63–S76, 2014. a
Staring, M., Pereira, R., Douma, H., van der Neut, J., and Wapenaar, K.:
Source-receiver Marchenko redatuming on field data using an adaptive
double-focusing method, Geophysics, 83, S579–S590, 2018. a
Stehly, L., Campillo, M., Froment, B., and Weaver, R. L.: Reconstructing
Green's function by correlation of the coda of the correlation (C
3)
of ambient seismic noise, J. Geophys. Res., 113, B11306,
https://doi.org/10.1029/2008JB005693,
2008.
a
Tanter, M. and Fink, M.: Ultrafast imaging in biomedical ultrasound, IEEE Trans. Ultrason., Ferroelect., and Freq. Control, 61,
102–119, 2014. a
Ten Kroode, F.: Prediction of internal multiples, Wave Motion, 35, 315–338,
2002. a
Tonegawa, T., Nishida, K., Watanabe, T., and Shiomi, K.: Seismic interferometry
of teleseismic S-wave coda for retrieval of body waves: an application to
the Philippine Sea slab underneath the Japanese Islands, Geophys. J. Int., 178, 1574–1586, 2009. a
Tonegawa, T., Fukao, Y., Nishida, K., Sugioka, H., and Ito, A.: A temporal
change of shear wave anisotropy within the marine sedimentary layer
associated with the 2011 Tohoku-Oki earthquake, J. Geophys. Res., 118, 607–615, 2013. a
van der Neut, J., Tatanova, M., Thorbecke, J., Slob, E., and Wapenaar, K.:
Deghosting, demultiple, and deblurring in controlled-source seismic
interferometry, Int. J. Geophys., 2011, 870819,
https://doi.org/10.1155/2011/870819, 2011.
a
van der Neut, J., Wapenaar, K., Thorbecke, J., and Vasconcelos, I.: Internal
multiple suppression by adaptive Marchenko redatuming, in: SEG, Annual Meeting 2014, Expanded
Abstracts, Society of Exploration Geophysicists, Tulsa, Oklahoma, USA, pp. 4055–4059, 2014. a
van der Neut, J., Johnson, J. L., van Wijk, K., Singh, S., Slob, E., and
Wapenaar, K.: A Marchenko equation for acoustic inverse source problems,
J. Acoust. Soc. Am., 141, 4332–4346, 2017. a
van Manen, D.-J., Robertsson, J. O. A., and Curtis, A.: Modeling of wave
propagation in inhomogeneous media, Phys. Rev. Lett., 94, 164301,
https://doi.org/10.1103/PhysRevLett.94.164301,
2005.
a
Wapenaar, C. P. A., Peels, G. L., Budejicky, V., and Berkhout, A. J.: Inverse
extrapolation of primary seismic waves, Geophysics, 54, 853–863, 1989. a
Wapenaar, K. and Thorbecke, J.: Review paper: Virtual sources and their
responses, Part I: time-reversal acoustics and seismic interferometry,
Geophys. Prosp., 65, 1411–1429, 2017. a
Wapenaar, K., Draganov, D., Thorbecke, J., and Fokkema, J.: Theory of acoustic
daylight imaging revisited, in: SEG, Annual Meeting 2002, Expanded Abstracts, Society of Exploration Geophysicists, Tulsa, Oklahoma, USA, pp. 2269–2272,
2002.
a,
b
Wapenaar, K., Draganov, D., Snieder, R., Campman, X., and Verdel, A.: Tutorial
on seismic interferometry: Part 1 – Basic principles and applications,
Geophysics, 75, 75A195–75A209, 2010. a
Wapenaar, K., van der Neut, J., Ruigrok, E., Draganov, D., Hunziker, J., Slob,
E., Thorbecke, J., and Snieder, R.: Seismic interferometry by
crosscorrelation and by multidimensional deconvolution: a systematic
comparison, Geophys. J. Int., 185, 1335–1364, 2011. a
Wapenaar, K., Thorbecke, J., van der Neut, J., Broggini, F., Slob, E., and
Snieder, R.: Marchenko imaging, Geophysics, 79, WA39–WA57,
2014a.
a,
b
Wapenaar, K., Thorbecke, J., van der Neut, J., Vasconcelos, I., and Slob, E.:
Marchenko imaging below an overburden with random scatterers, in: EAGE, Annual Meeting 2014,
Extended Abstracts, European Association of Geoscientists and Engineers, Houten, the
Netherlands, Th–E102–10,
https://doi.org/10.3997/2214-4609.20141368, 2014b.
a
Wapenaar, K., Thorbecke, J., and van der Neut, J.: A single-sided homogeneous
Green's function representation for holographic imaging, inverse
scattering, time-reversal acoustics and interferometric Green's function
retrieval, Geophys. J. Int., 205, 531–535,
2016a. a
Wapenaar, K., van der Neut, J., and Slob, E.: Unified double- and single-sided
homogeneous Green's function representations, P. Roy. Soc. A-Math. Phy., 472, 20160162,
https://doi.org/10.1098/rspa.2016.0162, 2016b.
a
Weaver, R. L. and Lobkis, O. I.: On the emergence of the Green's function in
the correlations of a diffuse field: pulse-echo using thermal phonons,
Ultrasonics, 40, 435–439, 2002. a
Weaver, R. L. and Lobkis, O. I.: Diffuse fields in open systems and the
emergence of the Green's function (L), J. Acoust. Soc. Am., 116, 2731–2734, 2004. a
Weglein, A. B., Gasparotto, F. A., Carvalho, P. M., and Stolt, R. H.: An
inverse-scattering series method for attenuating multiples in seismic
reflection data, Geophysics, 62, 1975–1989, 1997. a
Weglein, A. B., Hsu, S. Y., Terenghi, P., Li, X., and Stolt, R. H.: Multiple
attenuation: Recent advances and the road ahead (2011), The Leading Edge,
30, 864–875, 2011. a
Whitmore, N. D.: Iterative depth migration by backward time propagation, in:
SEG, Annual Meeting 1983, Expanded Abstracts, Society of Exploration Geophysicists, Tulsa, Oklahoma, USA, pp. 382–385, 1983. a
Wiggins, J. W.: Kirchhoff integral extrapolation and migration of nonplanar
data, Geophysics, 49, 1239–1248, 1984.
a,
b
Zhang, L., Thorbecke, J., Wapenaar, K., and Slob, E.: Transmission compensated
primary reflection retrieval in data domain and consequences for imaging,
Geophysics, 84, in press,
https://doi.org/10.1190/geo2018-0340.1, 2019.
a
Zhang, Y. and Sun, J.: Practical issues in reverse time migration: true
amplitude gathers, noise removal and harmonic source encoding, First Break,
27, 53–59, 2009. a
Zheng, Y., He, Y., and Fehler, M. C.: Crosscorrelation kernels in acoustic
Green's function retrieval by wavefield correlation for point sources on a
plane and a sphere, Geophys. J. Int., 184, 853–859, 2011. a