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Published online by Cambridge University Press:  31 October 2024

Haruo Sato
Affiliation:
Tohoku University, Japan
Kentaro Emoto
Affiliation:
Kyushu University
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Chapter
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Seismic Wave Propagation Through Random Media
Monte Carlo Simulation Based on the Radiative Transfer Theory
, pp. 158 - 171
Publisher: Cambridge University Press
Print publication year: 2024

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References

Aki, K. 1969. Analysis of seismic coda of local earthquakes as scattered waves. J. Geophys. Res., 74, 615–631.Google Scholar
Aki, K. 1973. Scattering of P waves under the Montana LASA. J. Geophys. Res., 78, 1334–1346.Google Scholar
Aki, K. 1980a. Attenuation of shear-waves in the lithosphere for frequencies from 0.05 to 25 Hz. Phys. Earth Planet. Inter., 21, 50–60.Google Scholar
Aki, K. 1980b. Scattering and attenuation of shear waves in the lithosphere. J. Geophys. Res., 85, 6496–6504.Google Scholar
Aki, K. 1982. Scattering and attenuation. Bull. Seismol. Soc. Am., 72, S319–S330.Google Scholar
Aki, K. 1984. Short period seismology. J. Comput. Phys., 54(1), 3–17.Google Scholar
Aki, K. 1991. Summary of discussions on coda waves at the Istanbul IASPEI meeting. Phys. Earth Planet. Inter., 67(1–2), 1–3.Google Scholar
Aki, K. 2009. Seismology of Earthquake and Volcano Prediction (English and Chinese translation). Ed. Yun, X. C.. Beijing: Science Press.Google Scholar
Aki, K., and Chouet, B. 1975. Origin of coda waves: Source, attenuation and scattering effects. J. Geophys. Res., 80, 3322–3342.Google Scholar
Aki, K., and Richards, P. 2002. Quantitative Seismology. 2nd ed. California: University Science Books.Google Scholar
Allègre, C. J., and Turcotte, D. L. 1986. Implications of a two-component marble-cake mantle. Nature, 323(6084), 123.Google Scholar
Apresyan, L. A., and Kravtsov, Y. A. 1996. Radiation Transfer: Statistical and Wave Aspects. Amsterdam: Gordon and Breach.Google Scholar
Arfken, G. B., Weber, H. J., and Harris, F. E. 2013. Mathematical Methods for Physicists. 7th ed. San Diego: Academic Press.Google Scholar
Barabanenkov, Y. N., Kravtsov, Y. A., Rytov, S. M., and Tamarskii, V. I. 1971. Status of the theory of propagation of waves in randomly inhomogeneous medium. Soviet Phys. Usp. (Eng. Trans.), 13, 551–680.Google Scholar
Benites, R., Aki, K., and Yomogida, K. 1992. Multiple scattering of SH waves in 2-D media with many cavities. Pure Appl. Geophys., 138, 353–390.Google Scholar
Birch, F. 1961. The velocity of compressional waves in rocks to 10 kilobars, Part 2. J. Geophys. Res., 66, 2199–2224.Google Scholar
Bird, G. A., and Brady, J. 1994. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Vol. 5. Oxford: Clarendon Press.Google Scholar
Brown, S. R., and Scholz, C. H. 1985. Broad bandwidth study of the topography of natural rock surfaces. J. Geophys. Res. Solid Earth, 90(B14), 12575–12582.Google Scholar
Calvet, M., and Margerin, L. 2013. Lapse-time dependence of coda Q: Anisotropic multiple-scattering models and application to the Pyrenees. Bull. Seismol. Soc. Am., 103(3), 1993–2010.Google Scholar
Calvet, M., Margerin, L., and Hung, S.-H. 2023. Anomalous attenuation of high-frequency seismic waves in Taiwan: Observation, model and interpretation. J. Geophys. Res. Solid Earth, 128, e2022JB025211.Google Scholar
Calvet, M., Sylvander, M., Margerin, L., and Villaseñor, A. 2013. Spatial variations of seismic attenuation and heterogeneity in the Pyrenees: Coda Q and peak delay time analysis. Tectonophysics, 608, 428–439.Google Scholar
Campillo, M., and Paul, A. 2003. Long-range correlations in the diffuse seismic coda. Science, 299(5606), 547–549.Google Scholar
Capon, J. 1974. Characterization of crust and upper mantle structure under LASA as a random medium. Bull. Seismol. Soc. Am., 64, 235–266.Google Scholar
Carcolé, E., and Sato, H. 2010. Spatial distribution of scattering loss and intrinsic absorption of short-period S waves in the lithosphere of Japan on the basis of the Multiple Lapse Time Window Analysis of Hi-net data. Geophys. J. Int., 180, 268–290.Google Scholar
Chandrasekhar, S. 1960. Radiative Transfer. New York: Dover.Google Scholar
Chernov, L. A. 1960. Wave Propagation in a Random Medium (Engl. trans. by R. A. Silverman). New York: McGraw-Hill.Google Scholar
Chevrot, S., Montagner, J., and Snieder, R. 1998. The spectrum of tomographic earth models. Geophys. J. Int., 133(3), 783–788.Google Scholar
Christensen, N. I. 1968. Chemical changes associated with upper mantle structure. Tectonophysics, 6, 331–342.Google Scholar
Chung, T., Lees, J. M., Yoshimoto, K., Fujita, E., and Ukawa, M. 2009. Intrinsic and scattering attenuation of the Mt Fuji Region, Japan. Geophys. J. Int., 177(3), 1366–1382.Google Scholar
Cichowicz, A., and Green, R. W. E. 1989. Changes in the early part of the seismic coda due to localized scatterers: The estimation of Q in a stope environment. Pure Appl. Geophys., 129, 497–511.Google Scholar
Cormier, V. F. 1995. Time-domain modelling of PKIKP precursors for constraints on the heterogeneity in the lowermost mantle. Geophys. J. Int., 121(3), 725–736.Google Scholar
Cormier, V. F. 1999. Anisotropy of heterogeneity scale lengths in the lower mantle from PKIKP precursors. Geophys. J. Int., 136(2), 373–384.Google Scholar
Cormier, V. F., and Sanborn, C. J. 2019. Trade-offs in parameters describing crustal heterogeneity and intrinsic attenuation from radiative transport modeling of high-frequency regional seismograms. Bull. Seismol. Soc. Am., 109(1), 312–321.Google Scholar
Cormier, V. F., Tian, Y., and Zheng, Y. 2020. Heterogeneity spectrum of Earth's upper mantle obtained from the coherence of teleseismic P waves. Comm. Comput. Phys., 28(1), 74–97.Google Scholar
Cormier, V. F., Lithgow-Bertelloni, C., Stixrude, L., and Zheng, Y. 2022. Mantle phase changes detected from stochastic tomography. J. Geophys. Res. Solid Earth, 128(2), e2022JB025035.Google Scholar
Curtis, A., Gerstoft, P., Sato, H., Snieder, R., and Wapenaar, K. 2006. Seismic interferometry – Turing noise into signal. The Leading Edge, 25(9), 1082–1092.Google Scholar
da Silva, J. A., Poliannikov, O. V., Fehler, M., and Turpening, R. 2018. Modeling scattering and intrinsic attenuation of cross-well seismic data in the Michigan Basin. Geophysics, 83(3), WC15–WC27.Google Scholar
Dainty, A. M., and Toksöz, M. N. 1981. Seismic codas on the Earth and the Moon: A comparison. Phys. Earth Planet. Inter., 26(4), 250–260.Google Scholar
DLMF. 2022. NIST Digital Library of Mathematical Functions. http://dlmf.nist.gov/, Release 1.1.4 of 2022-01-15. Olver, F. W. J., Olde Daalhuis, A. B., Lozier, D. W., Schneider, B. I., Boisvert, R. F., Clark, C. W., Miller, B. R., Saunders, B. V., Cohl, H. S., and McClain, M. A., (Eds).Google Scholar
Dubendorff, B., and Menke, W. 1986. Time-domain apparent-attenuation operators for compressional and shear waves: Experiment versus single scattering theory. J. Geophys. Res., 91(B14), 14023–14032.Google Scholar
Emoto, K., Sato, H., and Nishimura, T. 2010. Synthesis of vector-wave envelopes on the free surface of a random medium for the vertical incidence of a plane wavelet based on the Markov approximation. J. Geophys. Res., 115(B8).Google Scholar
Emoto, K., Sato, H., and Nishimura, T. 2012. Synthesis and applicable condition of vector wave envelopes in layered random elastic media with anisotropic autocorrelation function based on the Markov approximation. Geophys. J. Int., 188(1), 325–335.Google Scholar
Emoto, K., Sato, H., and Nishimura, T. 2013. Envelope synthesis of a cylindrical outgoing wavelet in layered random elastic media based on the Markov approximation. Geophys. J. Int., 194(2), 899–910.Google Scholar
Emoto, K., Saito, T., and Shiomi, K. 2017. Statistical parameters of random heterogeneity estimated by analyzing coda waves based on finite difference method. Geophys. J. Int., 211(3), 1575–1584.Google Scholar
Emoto, K., and Sato, H. 2018. Statistical characteristics of scattered waves in three-dimensional random media: Comparison of the finite difference simulation and statistical methods. Geophys. J. Int., 215(1), 585–599.Google Scholar
Eulenfeld, T., and Wegler, U. 2017. Crustal intrinsic and scattering attenuation of high-frequency shear waves in the contiguous United States. J. Geophys. Res. Solid Earth, 122(6), 4676–4690.Google Scholar
Fang, Y., and Müller, G. 1996. Attenuation operators and complex wave velocities for scattering in random media. Pure Appl. Geophys., 148(1–2), 269–285.Google Scholar
Fehler, M., Hoshiba, M., Sato, H., and Obara, K. 1992. Separation of scattering and intrinsic attenuation for the Kanto-Tokai region, Japan, using measurements of S-wave energy versus hypocentral distance. Geophys. J. Int., 108(3), 787–800.Google Scholar
Fehler, M., Roberts, P., and Fairbanks, T. 1988. A temporal change in coda wave attenuation observed during an eruption of Mount St. Helens. J. Geophys. Res., 93(B5), 4367–4373.Google Scholar
Fehler, M., Sato, H., and Huang, L.-J. 2000. Envelope broadening of outgoing waves in 2D random media: A comparison between the Markov approximation and numerical simulations. Bull. Seismol. Soc. Am., 90(4), 914–928.Google Scholar
Fehler, M., and Sato, H. 2003. Coda. Pure Appl. Geophys., 160(3–4), 541–554.Google Scholar
Feustel, A. J. 1998. Seismic attenuation in underground mines: a comparative evaluation of methods and result. Tectonophysics, 289(1–3), 31–49.Google Scholar
Flatté, S. M., and Wu, R. S. 1988. Small-scale structure in the lithosphere and asthenosphere deduced from arrival time and amplitude fluctuations at NORSAR. J. Geophys. Res., 93(B6), 6601–6614.Google Scholar
Flatté, S. M., Dashen, R., Munk, W. H., Watson, K. M., and Zachariasen, F. 1979. Sound Transmission through a Fluctuating Ocean. New York: Cambridge University Press.Google Scholar
Foldy, L. L. 1945. The multiple scattering of waves-I. General theory of isotropic scattering by randomly distributed scatterers. Phys. Rev., 67(3–4), 107–119.Google Scholar
Frankel, A., and Clayton, R. W. 1986. Finite difference simulations of seismic scattering: Implications for the propagation of short-period seismic waves in the crust and models of crustal heterogeneity. J. Geophys. Res., 91(B6), 6465–6489.Google Scholar
Frankel, A., and Wennerberg, L. 1987. Energy-flux model of seismic coda: Separation of scattering and intrinsic attenuation. Bull. Seismol. Soc. Am., 77(4), 1223–1251.Google Scholar
Frisch, U. 1968. Wave Propagation in Random Media, in Probabilistic Method in Applied Mathematics, Vol. I. Ed. Bharucha-Reid, A. T.. New York: Academic Press, pp. 76–198.Google Scholar
Fukushima, Y., Nishizawa, H., Sato, H., and Ohtake, M. 2003. Laboratory study on scattering characteristics of shear waves in rock samples. Bull. Seismol. Soc. Am., 93(1), 253–263.Google Scholar
Furumura, T., and Kennett, B. L. N. 2005. Subduction zone guided waves and the heterogeneity structure of the subducted plate: Intensity anomalies in northern Japan. J. Geophys. Res., 110(B10), B10302.Google Scholar
Furutsu, K. 1964. On the Statistical Theory of Electromagnetic Waves in a Fluctuating Medium (II). Vol. 79. Washington, DC: US Government Printing Office.Google Scholar
Gillet, K., Margerin, L., Calvet, M., and Monnereau, M. 2017. Scattering attenuation profile of the Moon: Implications for shallow moonquakes and the structure of the megaregolith. Phys. Earth Planet. Inter., 262, 28–40.Google Scholar
Gradshteyn, I. S., and Ryzhik, I. M. 2007. Table of Integrals, Series and Products (7th Ed. in Engl. Ed. Jeffrey, A. and Zwillinger, D.). San Diego: Academic Press.Google Scholar
Guo, J., Shuai, D., Wei, J., Ding, P., and Gurevich, B. 2018. P-wave dispersion and attenuation due to scattering by aligned fluid saturated fractures with finite thickness: Theory and experiment. Geophys. J. Int., 215(3), 2114–2133.Google Scholar
Gusev, A. A., and Abubakirov, I. R. 1987. Monte Carlo simulation of record envelope of a near earthquake. Phys. Earth Planet. Inter., 49(1–2), 30–36.Google Scholar
Gusev, A. A., and Lemzikov, V. K. 1985. Properties of scattered elastic waves in the lithosphere of Kamchatka: Parameters and temporal variations. Tectonophysics, 112(1–4), 137–153.Google Scholar
Havskov, J., Sørensen, M. B., Vales, D., Özyazıcıog˘lu, M., Sánchez, G., and Li, B. 2016. Coda Q in different tectonic areas, influence of processing parameters. Bull. Seismol. Soc. Am., 106(3), 956–970.Google Scholar
Heller, G., Margerin, L., Sèbe, O., Mayor, J., and Calvet, M. 2022. Revisiting multiplescattering principles in a crustal waveguide: Equipartition, depolarization and coda normalization. Pure Appl. Geophys., 179(6–7), 1–35.Google Scholar
Hennino, R., Tregoures, N., Shapiro, N. M., Margerin, L., Campillo, M., Van Tiggelen, B. A., and Weaver, R. L. 2001. Observation of equipartition of seismic waves. Phys. Rev. Lett., 86(15), 3447–3450.Google Scholar
Hiramatsu, Y., Hayashi, N., Furumoto, M., and Katao, H. 2000. Temporal changes in coda Q-1 and b value due to the static stress change associated with the 1995 Hyogo-ken Nanbu earthquake. J. Geophys. Res., 105(B3), 6141–6151.Google Scholar
Hirata, T., and Imoto, S. 1991. Multifractal analysis of spatial distribution of microearthquakes in the Kanto region. Geophys. J. Int., 107(1), 155–162.Google Scholar
Hock, S., Korn, M., Ritter, J. R. R., and Rothert, E. 2004. Mapping random lithospheric heterogeneities in northern and central Europe. Geophys. J. Int., 157(1), 251–264.Google Scholar
Holliger, K. 1996. Upper-crustal seismic velocity heterogeneity as derived from a variety of P-wave sonic logs. Geophys. J. Int., 125(3), 813–829.Google Scholar
Holliger, K., and Levander, A. 1992. A stochastic view of lower crustal fabric based on evidence from the Ivrea zone. Geophys. Res. Lett., 19(11), 1153–1156.Google Scholar
Hoshiba, M. 1991. Simulation of multiple-scattered coda wave excitation based on the energy conservation law. Phys. Earth Planet. Inter., 67(1–2), 123–136.Google Scholar
Hoshiba, M. 1993. Separation of scattering attenuation and intrinsic absorption in Japan using the multiple lapse time window analysis of full seismogram envelope. J. Geophys. Res., 98(B9), 15809–15824.Google Scholar
Hoshiba, M., Sato, H., and Fehler, M. 1991. Numerical basis of the separation of scattering and intrinsic absorption from full seismogram envelope – A Monte-Carlo simulation of multiple isotropic scattering. Pa. Meteorol. Geophys., Meteorol. Res. Inst., 42(2), 65–91.Google Scholar
Howe, M. S. 1973. Conservation of energy in random media, with application to the theory of sound absorption by an inhomogeneous flexible plate. Proc. R. Soc. Lond. A., 331(1587), 479–496.Google Scholar
Howe, M. S. 1974. A kinetic equation for wave propagation in random media. Q. J. Mech. Appl. Math., 27(2), 237–253.Google Scholar
van de Hulst, H. C. 1981. Light Scattering by Small Particles. New York, Dover: Courier Corporation.Google Scholar
Igel, H. 2017. Computational Seismology: A Practical Introduction. Oxford: Oxford University Press.Google Scholar
Ishimaru, A. 1997. Wave Propagation and Scattering in Random Media. Piscataway: IEEE Press and Oxford University Press.Google Scholar
Jin, A., and Aki, K. 1986. Temporal change in coda Q before the Tangshan earthquake of 1976 and the Haicheng earthquake of 1975. J. Geophys. Res., 91(B1), 665–673.Google Scholar
Jin, A., and Aki, K. 1988. Spatial and temporal correlation between coda Q and seismicity in China. Bull. Seismol. Soc. Am., 78(2), 741–769.Google Scholar
Jin, A., and Aki, K. 1989. Spatial and temporal correlation between coda Q−1 and seismicity and its physical mechanism. J. Geophys. Res., 94(B10), 14041–14059.Google Scholar
Jin, A., and Aki, K. 2005. High-resolution maps of Coda Q in Japan and their interpretation by the brittle-ductile interaction hypothesis. Earth Planets Space, 57(5), 403–409.Google Scholar
Jin, A., Aki, K., Liu, Z., and Keilis-Borok, V. 2004. Seismological evidence for the brittle-ductile interaction hypothesis on earthquake loading. Earth Planets Space, 56(8), 823–830.Google Scholar
Jing, Y., Zeng, Y., and Lin, G. 2014. High-frequency seismogram envelope inversion using a multiple nonisotropic scattering model: Application to aftershocks of the 2008 Wells earthquake. Bull. Seismol. Soc. Am., 104(2), 823–839.Google Scholar
Kanamori, H., and Mizutani, H. 1965. Ultrasonic measurements of elastic constants of rocks under high pressures. Bull. Earthq. Res. Inst. Univ. Tokyo, 43, 173–194.Google Scholar
Kato, K., Aki, K., and Takemura, M. 1995. Site amplification from coda waves: Validation and application to S-wave site response. Bull. Seismol. Soc. Am., 85(2), 467–477.Google Scholar
Kawahara, J., and Yamashita, T. 1992. Scattering of elastic waves by a fracture zone containing randomly distributed cracks. Pure Appl. Geophys., 139(1), 121–144.Google Scholar
Kawahara, J., Ohno, T., and Yomogida, K. 2009. Attenuation and dispersion of antiplane shear waves due to scattering by many two-dimensional cavities. J. Acoust. Soc. Am., 125(6), 3589–3596.Google Scholar
Kenter, J., Braaksma, H., Verwer, K., and van Lanen, X. 2007. Acoustic behavior of sedimentary rocks: Geologic properties versus Poisson's ratios. Lead. Edge., 26(4), 436–444.Google Scholar
Kikuchi, M. 1981. Dispersion and attenuation of elastic waves due to multiple scattering from cracks. Phys. Earth Planet. Inter., 27(2), 100–105.Google Scholar
Kobayashi, M., Takemura, S., and Yoshimoto, K. 2015. Frequency and distance changes in the apparent P-wave radiation pattern: Effects of seismic wave scattering in the crust inferred from dense seismic observations and numerical simulations. Geophys. J. Int., 202(3), 1895–1907.Google Scholar
Koper, K. D., Wiens, D. A., Dorman, L., Hildebrand, J., and Webb, S. 1999. Constraints on the origin of slab and mantle wedge anomalies in Tonga from the ratio of S to P velocities. J. Geophys. Res. Solid Earth, 104(B7), 15089–15104.Google Scholar
Kopnichev, Y. F. 1975. A model of generation of the tail of the seismogram. Dok. Akad. Nauk, SSSR (Engl. trans.), 222, 333–335.Google Scholar
Korn, M., and Sato, H. 2005. Synthesis of plane vector wave envelopes in two-dimensional random elastic media based on the Markov approximation and comparison with finite-difference simulations. Geophys. J. Int., 161(3), 839–848.Google Scholar
Kubanza, M., Nishimura, T., and Sato, H. 2006. Spatial variation of lithospheric heterogeneity on the globe as revealed from transverse amplitudes of short-period teleseismic P-waves. Earth Planets Space, 58(10), e45e48.Google Scholar
Kubanza, M., Nishimura, T., and Sato, H. 2007. Evaluation of strength of heterogeneity in the lithosphere from peak amplitude analyses of teleseismic short-period vector P waves. Geophys. J. Int., 171(1), 390–398.Google Scholar
Landau, L. D., and Lifshitz, E. M. 2003. Quantum Mechanics (3rd Ed., Engl. trans. By, J. B. Sykes and Bell, J. S.). Amsterdam: Butterworth-Heinemann.Google Scholar
Lee, L. C., and Jokipii, J. R. 1975a. Strong scintillations in astrophysics. I. The Markov approximation, its validity and application to angular broadening. Astrophys. J., 196(3), 695–707.Google Scholar
Lee, L. C., and Jokipii, J. R. 1975b. Strong scintillations in astrophysics. II. A theory of temporal broadening of pulses. Astrophys. J., 201(2), 532–543.Google Scholar
Lee, W., and Sato, H. 2006. Power-law decay characteristic of coda envelopes revealed from the analysis of regional earthquakes. Geophys. Res. Lett., 33(7), L07317.Google Scholar
Lenoble, J., and Sekera, Z. 1961. Equation of radiative transfer in a planetary spherical atmosphere. Proc. Natl. Acad. Sci., 47(3), 372–378.Google Scholar
Liemert, A., and Kienle, A. 2012. Infinite space Green's function of the time-dependent radiative transfer equation. Biomed. Opt. Express, 3(3), 543–551.Google Scholar
Maeda, T., Sato, H., and Ohtake, M. 2003. Synthesis of Rayleigh-wave envelope on the spherical Earth: Analytic solution of the single isotropic-scattering model for a circular source radiation. Geophys. Res. Lett., 30(6), 1286.Google Scholar
Maeda, T., Sato, H., and Ohtake, M. 2006. Constituents of vertical-component coda waves at long periods. Pure Appl. Geophys., 163(2–3), 549–566.Google Scholar
Maeda, T., Sato, H., and Nishimura, T. 2008. Synthesis of coda wave envelopes in randomly inhomogeneous elastic media in a half-space: Single scattering model including Rayleigh waves. Geophys. J. Int., 172(1), 130–154.Google Scholar
Maeda, T., Sato, H., and Nishimura, T. 2013. Erratum: Synthesis of coda wave envelopes in randomly inhomogeneous elastic media in a half-space: Single scattering model including Rayleigh waves. Geophys. J. Int., 193(2), 105–1051.Google Scholar
Maeda, T., Takemura, S., and Furumura, T. 2017. OpenSWPC: An open-source integrated parallel simulation code for modeling seismic wave propagation in 3D heterogeneous viscoelastic media. Earth Planets Space, 69, Article 102.Google Scholar
Mancinelli, N., Shearer, P., and Liu, Q. 2016a. Constraints on the heterogeneity spectrum of Earth's upper mantle. J. Geophys. Res. Solid Earth, 121(5), 3703–3721.Google Scholar
Mancinelli, N., Shearer, P., and Thomas, C. 2016b. On the frequency dependence and spatial coherence of PKP precursor amplitudes. J. Geophys. Res. Solid Earth, 121(3), 1873–1889.Google Scholar
Manghnani, M. H., Ramananantoandro, R., and Clark, S. P. Jr. 1974. Compressional and shear wave velocities in granulite faces rocks and eclogites to 10 kb. J. Geophys. Res., 79(35), 5427–5446.Google Scholar
Margerin, L. 2005. Introduction to radiative transfer of seismic waves, in “Seismic Earth: Array Analysis of Broadband Seismograms.” Vol. 157. Eds. Levander, A. and Nolet, G.. Washington, DC: Geophysical Monograph-American Geophysical Union, 229–252.Google Scholar
Margerin, L. 2006. Attenuation, transport and diffusion of scalar waves in textured random media. Tectonophysics, 416(1–4), 229–244.Google Scholar
Margerin, L. 2017. Computation of Green's function of 3-D radiative transport equation for non-isotropic scattering of P and unpolarized S waves. Pure Appl. Geophys., 174(11), 4057–4075.Google Scholar
Margerin, L., and Nolet, G. 2003a. Multiple scattering of high-frequency seismic waves in the deep Earth: PKP precursor analysis and inversion for mantle granularity. J. Geophys. Res., 108(B11), 2514.Google Scholar
Margerin, L., and Nollet, G. 2003b. Multiple scattering of high-frequency seismic in the deep Earth: Modeling and numerical examples. J. Geophys. Res., 108(B5), 2234.Google Scholar
Margerin, L., Campillo, M., and Tiggelen, B. V. 2000. Monte Carlo simulation of multiple scattering of elastic waves. J. Geophys. Res., 105(B4), 7873–7893.Google Scholar
Mathews, J., and Walker, R. L. 1970. Mathematical Methods of Physics. 2nd ed. New York: WA Benjamin.Google Scholar
Matsumoto, M., and Nishimura, T. 1998. Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comp. Sim., 8(1), 3–30.Google Scholar
Matsumoto, S., and Hasegawa, A. 1989. Two-dimensional coda Q structure beneath Tohoku, NE Japan. Geophys. J. Int., 99(1), 101–108.Google Scholar
Mayeda, K., Koyanagi, S., Hoshiba, M., Aki, K., and Zeng, Y. 1992. A comparative study of scattering, intrinsic, and coda Q−1 for Hawaii, Long Valley and Central California between 1.5 and 15 Hz. J. Geophys. Res., 97(B5), 6643–6659.Google Scholar
Menina, S., Margerin, L., Kawamura, T., Lognonné, P., Marti, J., Drilleau, M., Calvet, M., Compaire, N., Garcia, R., Karakostas, F., et al. 2021. Energy envelope and attenuation characteristics of high-frequency (HF) and very-high-frequency (VF) Martian events. Bull. Seismol. Soc. Am., 111(6), 3016–3034.Google Scholar
Mitra, S., Wanchoo, S. K., and Priestley, K. 2022. Seismic coda-wave attenuation tomography of the Jammu and Kashmir Himalaya. J. Geophys. Res. Solid Earth, 127(9), e2022JB024917.Google Scholar
Moczo, P., Kristek, J., and Gális, M. 2014. The Finite-Difference Modelling of Earthquake Motions: Waves and Ruptures. Cambridge: Cambridge University Press.Google Scholar
Morgan, K. S., Siu, K. K. W., and Paganin, D. 2010. The projection approximation and edge contrast for x-ray propagation-based phase contrast imaging of a cylindrical edge. Optics Express, 18(10), 9865–9878.Google Scholar
Morioka, H., Kumagai, H., and Maeda, T. 2017. Theoretical basis of the amplitude source location method for volcano-seismic signals. J. Geophys. Res. Solid Earth, 122(8), 6538–6551.Google Scholar
Nakahara, H., Nishimura, T., Sato, H., and Ohtake, M. 1998. Seismogram envelope inversion for the spatial distribution of high-frequency energy radiation from the earthquake fault: Application to the 1994 far east off Sanriku earthquake, Japan. J. Geophys. Res., 103(B1), 855–867.Google Scholar
Nakamura, Y. 1977b. HFT events: Shallow moonquakes? Phys. Earth Planet. Inter., 14(3), 217–223.Google Scholar
Nakata, N., and Beroza, G. C. 2015. Stochastic characterization of mesoscale seismic velocity heterogeneity in Long Beach, California. Geophys. J. Int., 203(3), 2049–2054.Google Scholar
Nikolaev, A. V. 1975. The Seismics of Heterogeneous and Turbid Media (Engl. trans. By R. Hardin). Jerusalem: Israel Program for Science translations.Google Scholar
Nishigami, K. 2000. Deep crustal heterogeneity along and around the San Andreas fault system in central California and its relation to the segmentation. J. Geophys. Res., 105(B4), 7983–7998.Google Scholar
Noguchi, S. 1990. Regional difference in maximum velocity amplitude decay with distance and earthquake magnitude (in Japanese). Res. Notes Nat. Res. Ctr. Disast. Prev., 86, 1–40.Google Scholar
Noguchi, S. 2001. Fractal properties of the distribution of earthquake hypocenters in the Kanto district, Japan (in Japanese). Rep. NIED, 61, 107–118.Google Scholar
Obara, K., and Sato, H. 1995. Regional differences of random inhomogeneities around the volcanic front in the Kanto-Tokai area, Japan, revealed from the broadening of S wave seismogram envelopes. J. Geophys. Res., 100(B2), 2103–2121.Google Scholar
Obermann, A., Planès, T., Larose, E., Sens-Schönfelder, C., and Campillo, M. 2013. Depth sensitivity of seismic coda waves to velocity perturbations in an elastic heterogeneous medium. Geophys. J. Int., 194(1), 372–382.Google Scholar
Ogata, Y., and Katsura, K. 1991. Maximum likelihood estimates of the fractal dimension for random spatial patterns. Biometrika, 78(3), 463–474.Google Scholar
Onodera, K., Maeda, T., Nishida, K., Kawamura, T., Margerin, L., Menina, S., Lognonné, P., and Barnedt, W. B. 2023. Seismic scattering and absorption properties of Mars estimated through coda analysis on a long-period surface wave of S1222a marsquake. Geophys. Res. Lett., 50(13), e2022GL102716.Google Scholar
Paasschens, J. C. J. 1997. Solution of the time-dependent Boltzmann equation. Phys. Rev. E, 56(1), 1135–1141.Google Scholar
Pacheco, C., and Snieder, R. 2006. Time-lapse traveltime change of singly scattered acoustic waves. Geophys. J. Int., 165(2), 485–500.Google Scholar
Petukhin, A., and Gusev, A. 2003. The duration-distance relationship and average envelope shapes of small Kamchatka earthquakes. Pure Appl. Geophys., 160(9), 1717–1743.Google Scholar
Phillips, W. S., and Aki, K. 1986. Site amplification of coda waves from local earthquakes in central California. Bull. Seismol. Soc. Am., 76(3), 627–648.Google Scholar
Pitarka, A. 1999. 3D elastic finite-difference modeling of seismic motion using staggered grids with nonuniform spacing. Bull. Seismol. Soc. Am., 89(1), 54–68.Google Scholar
Poupinet, G., and Kennett, B. 2004. On the observation of high frequency PKiKP and its coda in Australia. Phys. Earth Planet. Inter., 146(3–4), 497–511.Google Scholar
Powell, C. A., and Meltzer, A. S. 1984. Scattering of P-waves beneath SCARLET in southern California. Geophys. Res. Lett., 11(5), 481–484.Google Scholar
Przybilla, J., and Korn, M. 2008. Monte Carlo simulation of radiative energy transfer in continuous elastic random media-three-component envelopes and numerical validation. Geophys. J. Int., 173(2), 566–576.Google Scholar
Przybilla, J., Korn, M., and Wegler, U. 2006. Radiative transfer of elastic waves versus finite difference simulations in two-dimensional random media. J. Geophys. Res., 111(B4), B04305.Google Scholar
Przybilla, J., Wegler, U., and Korn, M. 2009. Estimation of crustal scattering parameters with elastic radiative transfer theory. Geophys. J. Int., 178(2), 1105–1111.Google Scholar
Rachman, A. N., and Chung, T. W. 2016. Depth-dependent crustal scattering attenuation revealed using single or few events in South Korea. Bull. Seismol. Soc. Am., 106(4), 1499–1508.Google Scholar
Rautian, T. G., and Khalturin, V. I. 1978. The use of the coda for determination of the earthquake source spectrum. Bull. Seismol. Soc. Am., 68(4), 923–948.Google Scholar
Rautian, T. G., Khalturin, V. I., Martinov, V. G., and Molnar, P. 1978. Preliminary analysis of the spectral content of P and S waves from local earthquakes in the Garm, Tadjikistan region. Bull. Seismol. Soc. Am., 68(4), 949–971.Google Scholar
Rautian, T. G., Khalturin, V. I., Zakirov, M. S., Zemchova, A. G., Proskurin, A. P., Pustovitenko, B. G., Pustovitenko, A. N., Sinelinikova, L. G., Filina, A. G., and Tchengelia, I. S. 1981. Experimental Studies of Seismic Coda (in Russian). Moscow: Nauka.Google Scholar
Research Group for Aftershocks. 1971. General Report on the Tokachi-oki Earthquake of 1968 Ed. Suzuki, Z.. Tokyo: Keigaku Publishing Company. Chap. General description of the special observations in case of the Tokachi-oki earthquake of 1968, pages 85–114.Google Scholar
Robertson, M., Sammis, C., Sahimi, M., and Martin, A. 1995. Fractal analysis of three-dimensional spatial distributions of earthquakes with a percolation interpretation. J. Geophys. Res., 100(B1), 609–620.Google Scholar
Roth, M., and Korn, M. 1993. Single scattering theory versus numerical modelling in 2-D random media. Geophys. J. Int., 112(1), 124–140.Google Scholar
Rytov, S. M., Kravtsov, Y. A., and Tatarskii, V. I. 1989. Principles of Statistical Radiophysics (Vol. 4) Wave Propagation Through Random Media. Berlin: Springer-Verlag.Google Scholar
Ryzhik, L. V., Papanicolaou, G. C., and Keller, J. B. 1996. Transport equations for elastic and other waves in random media. Wave Motion, 24(4), 327–370.Google Scholar
Sadovskiy, M. A., Golbeva, T. V., Pisarenko, V. F., and Shnirman, M. G. 1984. Characteristics dimensions of rock and hierarchical properties of seismicity. Izv. Acad. Sci. USSR (Engl. trans. Phys. Solid Earth), 20(2), 87–96.Google Scholar
Saito, T., Sato, H., and Ohtake, M. 2002a. Correction to “Envelope broadening of spherically outgoing waves in three-dimensional random media having power-law spectra.” J. Geophys. Res., 107(B9), ESE 8–1 –ESE 8–1.Google Scholar
Saito, T., Sato, H., and Ohtake, M. 2002b. Envelope broadening of spherically outgoing waves in three-dimensional random media having power-law spectra. J. Geophys. Res., 107(B5), ESE 3–1 –ESE 3–15.Google Scholar
Saito, T., Sato, H., Fehler, M., and Ohtake, M. 2003. Simulating the envelope of scalar waves in 2D random media having power-law spectra of velocity fluctuation. Bull. Seismol. Soc. Am., 93(1), 240–252.Google Scholar
Saito, T., Sato, H., Ohtake, M., and Obara, K. 2005. Unified explanation of envelope broadening and maximum-amplitude decay of high-frequency seismograms based on the envelope simulation using the Markov approximation: Fore-arc side of the volcanic front in northeastern Honshu, Japan. J. Geophys. Res., 110(B1), B01304.Google Scholar
Saito, T., Sato, H., and Takahashi, T. 2008. Direct simulation methods for scalar-wave envelopes in two-dimensional layered random media based on the small-angle scattering approximation. Commun. Comput. Phys., 3(1), 63–84.Google Scholar
Sanborn, C. J. 2017. Simulations with Radiative3D: A software tool for radiative transport in 3-D Earth models. PhD thesis, University of Connecticut.Google Scholar
Sanborn, C. J., Cormier, V. F., and Fitzpatrick, M. 2017. Combined effects of deterministic and statistical structure on high-frequency regional seismograms. Geophys. J. Int., 210(2), 1143–1159.Google Scholar
Sato, H. 1977. Energy propagation including scattering effects: Single isotropic scattering approximation. J. Phys. Earth, 25(1), 27–41.Google Scholar
Sato, H. 1982a. Amplitude attenuation of impulsive waves in random media based on travel time corrected mean wave formalism. J. Acoust. Soc. Am., 71(3), 559–564.Google Scholar
Sato, H. 1982b. Coda wave excitation due to nonisotropic scattering and nonspherical source radiation. J. Geophys. Res., 87(B10), 8665–8674.Google Scholar
Sato, H. 1984. Attenuation and envelope formation of three-component seismograms of small local earthquakes in randomly inhomogeneous lithosphere. J. Geophys. Res., 89(B2), 1221–1241.Google Scholar
Sato, H. 1987. A precursor-like change in coda excitation before the western Nagano earthquake (Ms=6.8) of 1984 in central Japan. J. Geophys. Res., 92(B2), 1356–1360.Google Scholar
Sato, H. 1988a. Fractal interpretation of the linear relation between logarithms of maximum amplitude and hypocentral distance. Geophys. Res. Lett., 15(4), 373–375.Google Scholar
Sato, H. 1988b. Temporal change in scattering and attenuation associated with the earthquake occurrence – A review of recent studies on coda waves. Pure Appl. Geophys., 126(2–4), 465–497.Google Scholar
Sato, H. 1989. Broadening of seismogram envelopes in the randomly inhomogeneous lithosphere based on the parabolic approximation: Southeastern Honshu, Japan. J. Geophys. Res., 94(B12), 17735–17747.Google Scholar
Sato, H. 1991. Study of seismogram envelopes based on scattering by random inhomogeneities in the lithosphere: A review. Phys. Earth Planet. Inter., 67(1–2), 4–19.Google Scholar
Sato, H. 1993. Energy transportation in oneand two-dimensional scattering media: Analytic solutions of the multiple isotropic scattering model. Geophys. J. Int., 112(1), 141–146.Google Scholar
Sato, H. 1994. Multiple isotropic scattering model including P-S conversions for the seismogram envelope formation. Geophys. J. Int., 117(2), 487–494.Google Scholar
Sato, H. 1995. Formulation of the multiple non-isotropic scattering process in 3-D space on the basis of energy transport theory. Geophys. J. Int., 121(2), 523–531.Google Scholar
Sato, H. 2006. Synthesis of vector wave envelopes in three-dimensional random elastic media characterized by a Gaussian autocorrelation function based on the Markov approximation: Plane wave case. J. Geophys. Res., 111(B6), B06306.Google Scholar
Sato, H. 2007. Synthesis of vector wave envelopes in three-dimensional random elastic media characterized by a Gaussian autocorrelation function based on the Markov approximation: Spherical wave case. J. Geophys. Res., 112(B1), B01301.Google Scholar
Sato, H. 2008. Synthesis of vector-wave envelopes in 3-D random media characterized by a nonisotropic Gaussian ACF based on the Markov approximation. J. Geophys. Res., 113(B8), B08304.Google Scholar
Sato, H. 2009. Green's function retrieval from the CCF of coda waves in a scattering medium. Geophys. J. Int., 179(3), 1580–1583.Google Scholar
Sato, H. 2016. Envelope broadening and scattering attenuation of a scalar wavelet in random media having power-law spectra. Geophys. J. Int., 204(1), 386–398.Google Scholar
Sato, H. 2019a. Isotropic scattering coefficient of the solid earth. Geophys. J. Int., 218(3), 2079–2088.Google Scholar
Sato, H. 2019b. Power spectra of random heterogeneities in the solid earth. Solid Earth, 10(1), 275–292.Google Scholar
Sato, H. 2021. SH wavelet propagation through the random distribution of aligned line cracks based on the radiative transfer theory. Pure Appl. Geophys., 178(3), 1047–1061.Google Scholar
Sato, H., and Emoto, K. 2017. Synthesis of a scalar wavelet intensity propagating through von Kármán-type random media: Joint use of the radiative transfer equation with the Born approximation and the Markov approximation. Geophys. J. Int., 211(1), 512–527.Google Scholar
Sato, H., and Emoto, K. 2018. Synthesis of a scalar wavelet intensity propagating through von Kármán-type random media: Radiative transfer theory using the Born and phasescreen approximations. Geophys. J. Int., 215(2), 909–923.Google Scholar
Sato, H., and Fukushima, R. 2013. Radiative transfer theory for the fractal structure and power-law decay characteristics of short-period seismograms. Geophys. J. Int., 195(3), 1831–1842.Google Scholar
Sato, H., and Korn, M. 2007. Envelope syntheses of cylindrical vector-waves in 2-D random elastic media based on the Markov approximation. Earth Planets Space, 59(4), 209–219.Google Scholar
Sato, H., and Nishino, M. 2002. Multiple isotropic-scattering model on the spherical Earth for the synthesis of Rayleigh-wave envelopes. J. Geophys. Res., 107(B12), 2343.Google Scholar
Sato, H., and Nohechi, M. 2001. Envelope formation of long-period Rayleigh waves in vertical component seismograms: Single isotropic scattering model. J. Geophys. Res., 106(B4), 6589–6594.Google Scholar
Sato, H., Fehler, M. C., and Saito, T. 2004. Hybrid synthesis of scalar wave envelopes in two-dimensional random media having rich short-wavelength spectra. J. Geophys. Res., 109(B6), B06303.Google Scholar
Sato, H., Fehler, M. C., and Maeda, T. 2012. Seismic wave propagation and scattering in the heterogeneous earth. 2nd ed. Heidelberg: Springer.Google Scholar
Sato, H., and Emoto, K. 2023. Propagation of a vector wavelet through von Kármán-type random elastic media: Monte Carlo simulation by using the spectrum division method. Geophys. J. Int., 234(3), 1655–1680.Google Scholar
Sato, H., and Fehler, M. C. (Eds). 2008. Earth Heterogeneity and Scattering Effects on Seismic Waves. Advances in Geophysics (Series Ed.: Dmowska, R.), vol. 50. Amsterdam: Academic Press.Google Scholar
Sato, H., and Fehler, M. C. 2016. Synthesis of wavelet envelope in 2-D random media having power-law spectra: comparison with FD simulations. Geophys. J. Int., 207(1), 333–342.Google Scholar
Sawazaki, K., Sato, H., and Nishimura, T. 2011. Envelope synthesis of short-period seismograms in 3-D random media for a point shear dislocation source based on the forward scattering approximation: Application to small strike-slip earthquakes in southwestern Japan. J. Geophys. Res. Solid Earth, 116(B8), B08305.Google Scholar
Sayles, R. S., and Thomas, T. R. 1978. Surface topography as a non-stationary random process. Nature, 271(5644), 431.Google Scholar
Sens-Schönfelder, C., Margerin, L., and Campillo, M. 2009. Laterally heterogeneous scattering explains Lg blockage in the Pyrenees. J. Geophys. Res., 114(B7), B07309.Google Scholar
Shang, T., and Gao, L. 1988. Transportation theory of multiple scattering and its application to seismic coda waves of impulsive source. Scientia Sinica (series B, China), 31(12), 1503–1514.Google Scholar
Shapiro, S. A., and Kneib, G. 1993. Seismic attenuation by scattering: Theory and numerical results. Geophys. J. Int., 114(2), 373–391.Google Scholar
Shearer, P. M., and Earle, P. S. 2004. The global short-period wavefield modelled with a Monte Carlo seismic phonon method. Geophys. J. Int., 158(3), 1103–1117.Google Scholar
Shearer, P. M. 2015. Deep Earth structure–seismic scattering in the Deep Earth. Treatise on Geophysics, 2nd Ed., Vol. 1: 24.1.24 Deep Earth Structure. Ed. Schubert, G., pages 695–730.Google Scholar
Shearer, P. M. 2019. Introduction to Seismology. Cambridge: Cambridge University Press.Google Scholar
Shiomi, K., Sato, H., and Ohtake, M. 1997. Broad-band power-law spectra of well-log data in Japan. Geophys. J. Int., 130(1), 57–64.Google Scholar
Shishov, V. I. 1974. Effect of refraction on scintillation characteristics and average pulse shape of pulsars. Sov. Astron., 17(5), 598–602.Google Scholar
Shito, A., Matsumoto, S., Ohkura, T., Shimizu, H., Sakai, S., Iio, Y., Takahashi, H., Yakiwara, H., Watanabe, T., Kosuga, M., et al. 2020. 3-D intrinsic and scattering seismic attenuation structures beneath Kyushu, Japan. J. Geophys. Res. Solid Earth, 125(8), e2019JB018742.Google Scholar
Sivaji, C., Nishizawa, O., Kitagawa, G., and Fukushima, Y. 2002. A physical-model study of the statistics of seismic waveform fluctuations in random heterogeneous media. Geophys. J. Int., 148(3), 575–595.Google Scholar
Snieder, R. 2004. Extracting the Green's function from the correlation of coda waves: A derivation based on stationary phase. Phys. Rev. E, 69(4), 046610.Google Scholar
Snieder, R., and Kasper, V. W. 2015. A Guided Tour of Mathematical Methods for the Physical Sciences. Cambridge: Cambridge University Press.Google Scholar
Solov’ev, S. L. 1965. Seismicity of Sakhalin. Bull. Earthq. Res. Inst. Univ. Tokyo, 43(1), 95–102.Google Scholar
Suzuki, H., Ikeda, R., Mikoshiba, T., Kinoshita, S., Sato, H., and Takahashi, H. 1981. Deep well logs in the Kanto-Tokai area (in Japanese). Rev. Nat. Res. Ctr. Disast. Prev., 65, 1–162.Google Scholar
Takahashi, T., Sato, H., Ohtake, M., and Obara, K. 2005. Scale dependence of apparent stress for earthquakes along the subducting Pacific plate in Northeastern Honshu, Japan. Bull. Seismol. Soc. Am., 95(4), 1334.Google Scholar
Takahashi, T., Sato, H., and Nishimura, T. 2007. Strong inhomogeneity beneath Quaternary volcanoes revealed from the peak delay analysis of S-wave seismograms of microearthquakes in northeastern, Japan. Geophys. J. Int., 168(1), 90–99.Google Scholar
Takahashi, T., Sato, H., and Nishimura, T. 2008. Recursive formula for the peak delay time with travel distance in von Karman type non-uniform random media on the basis of the Markov approximation. Geophys. J. Int., 173(2), 534–545.Google Scholar
Takahashi, T., Sato, H., Nishimura, T., and Obara, K. 2009. Tomographic inversion of the peak delay times to reveal random velocity fluctuations in the lithosphere: method and application to northeastern Japan. Geophys. J. Int., 178(47), 1437–1455.Google Scholar
Takemura, S., Kobayashi, M., and Yoshimoto, K. 2016. Prediction of maximum P-and S-wave amplitude distributions incorporating frequency-and distance-dependent characteristics of the observed apparent radiation patterns. Earth, Planets and Space, 68(1), 1–9.Google Scholar
Takemura, S., Emoto, K., and Yamaya, L. 2023. High-frequency S and S-coda waves at ocean-bottom seismometers. Earth Planet Space, 75(1), 20.Google Scholar
Takeuchi, N. 2016. Differential Monte Carlo method for computing seismogram envelopes and their partial derivatives. J. Geophys. Res. Solid Earth, 121(5), 3428–3444.Google Scholar
Tatarskii, V. I. 1971. The Effects of the Turbulent Atmosphere on Wave Propagation. Jerusalem: Israel Program for Science translations.Google Scholar
Tripathi, J., Sato, H., and Yamamoto, M. 2010. Envelope broadening characteristics of crustal earthquakes in northeastern Honshu, Japan. Geophys. J. Int., 182(2), 988–1000.Google Scholar
Tsuboi, C. 1954. Determination of the Gutenberg-Richter's magnitude of earthquakes occurring in and near Japan. Zisin (in Japanese), 7(3), 185–193.Google Scholar
Tsujiura, M. 1978. Spectral analysis of the coda waves from local earthquakes. Bull. Earthq. Res. Inst. Univ. Tokyo, 53(1), 1–48.Google Scholar
Tsumura, K. 1967. Determination of earthquake magnitude from total duration of oscillation. Bull. Earthq. Res. Inst. Univ. Tokyo, 45(1), 7–18.Google Scholar
Turner, J. A., and Weaver, R. L. 1994. Radiative transfer and multiple scattering of diffuse ultrasound in polycrystalline media. J. Acoust. Soc. Am., 96(6), 3675–3683.Google Scholar
Ugalde, A. 2013. S-wave envelope broadening characteristics of micro-earthquakes in the Canary Islands. J. Seismol., 17(2), 771–782.Google Scholar
Ukawa, M., and Fukao, Y. 1981. Poisson's ratios of the upper and lower crust and the sub-Moho mantle beneath central Honshu, Japan. Tectonophysics, 77(3–4), 233–256.Google Scholar
Wang, W., and Shearer, P. 2017. Using direct and coda wave envelopes to resolve the scattering and intrinsic attenuation structure of Southern California. J. Geophys. Res. Solid Earth, 122(9), 7236–7251.Google Scholar
Wapenaar, K., Slob, E., and Snieder, R. 2010. On seismic interferometry, the generalized optical theorem, and the scattering matrix of a point scatterer. Geophysics, 75(3), SA27– SA35.Google Scholar
Watanabe, H. 1971. Determination of earthquake magnitude at regional distance in and near Japan. Zisin (in Japanese), 24(3), 189–200.Google Scholar
Weaver, R. L. 1982. On diffuse waves in solid media. J. Acoust. Soc. Am., 71(6), 1608.Google Scholar
Weaver, R. L. 1990. Diffusivity of ultrasound in polycrystals. J. Mech. Phys. Solids, 38(1), 55–86.Google Scholar
Wegler, U., and Luhr, B. G. 2001. Scattering behaviour at Merapi volcano (Java) revealed from an active seismic experiment. Geophys. J. Int., 145(3), 579–592.Google Scholar
Wegler, U., Korn, M., and Przybilla, J. 2006. Modeling full seismogram envelopes using radiative transfer theory with Born scattering coefficients. Pure Appl. Geophys., 163 (2–3), 503–531.Google Scholar
Wesley, J. P. 1965. Diffusion of seismic energy in the near range. J. Geophys. Res., 70(20), 5099–5106.Google Scholar
Williamson, I. P. 1972. Pulse broadening due to multiple scattering in the interstellar medium. Mon. Not. R. Astron. Soc., 157(1), 55–71.Google Scholar
Williamson, I. P. 1975. The broadening of pulses due to multi-path propagation of radiation. Proc. R. Soc. Lond. A., 342(1628), 131–147.Google Scholar
Wolfram-Research. 2023. The Mathematical Function Site. https://functions.wolfram.com, As of June 5, 2023.Google Scholar
Wu, R. S. 1982. Attenuation of short period seismic waves due to scattering. Geophys. Res. Lett., 9(1), 9–12.Google Scholar
Wu, R. S. 1985. Multiple scattering and energy transfer of seismic waves – separation of scattering effect from intrinsic attenuation – I. Theoretical modeling. Geophys. J. R. Astron. Soc., 82(1), 57–80.Google Scholar
Wu, R. S., and Aki, K. 1985. Elastic wave scattering by a random medium and the smallscale inhomogeneities in the lithosphere. J. Geophys. Res., 90(B12), 10261–10273.Google Scholar
Wu, R. S., and Aki, K. 1988. Multiple scattering and energy transfer of seismic waves – Separation of scattering effect from intrinsic attenuation. II. Application of the theory to Hindu-Kush region. Pure Appl. Geophys., 128(1–2), 49–80.Google Scholar
Wu, R. S., Xu, Z., and Li, X. P. 1994. Heterogeneity spectrum and scale-anisotropy in the upper crust revealed by the German Continental Deep-Drilling (KTB) holes. Geophys. Res. Lett., 21(10), 911–914.Google Scholar
Xu, Z., Margerin, L., and Mikesell, T. D. 2021. Monte Carlo simulations of coupled body and Rayleigh-wave multiple scattering in elastic media. Geophys. J. Int., 228(2), 1213–1236.Google Scholar
Yamamoto, M., and Sato, H. 2010. Multiple scattering and mode conversion revealed by an active seismic experiment at Asama volcano, Japan. J. Geophys. Res., 115(B7), B07304.Google Scholar
Yamashita, T. 1990. Attenuation and dispersion of SH waves due to scattering by randomly distributed cracks. Pure Appl. Geophys., 132(3), 545–568.Google Scholar
Yomogida, K., and Benites, R. 2002. Scattering of seismic waves by cracks with the boundary integral method. Pure Appl. Geophys., 159(7), 1771–1789.Google Scholar
Yoshimoto, K. 2000. Monte-Carlo simulation of seismogram envelope in scattering media. J. Geophys. Res., 105(B3), 6153–6161.Google Scholar
Yoshimoto, K., and Jin, A. 2008. Coda energy distribution and attenuation. (eds) Sato, H., and Fehler, M. C., Earth Heterogeneity and Scattering Effects on Seismic Waves. Advances in Geophysics (Series Ed. Dmowska, R.), Vol. 50. Amsterdam: Academic Press. pages 265–300Google Scholar
Yoshimoto, K., Sato, H., and Ohtake, M. 1993. Frequency-dependent attenuation of P and S waves in the Kanto area, Japan, based on the coda-normalization method. Geophys. J. Int., 114(1), 165–174.Google Scholar
Yoshimoto, K., Sato, H., and Ohtake, M. 1997a. Short-wavelength crustal heterogeneities in the Nikko area, central Japan, revealed from the three-component seismogram envelope analysis. Phys. Earth Planet. Inter., 104(1–3), 63–73.Google Scholar
Yoshimoto, K., Sato, H., and Ohtake, M. 1997b. Three-component seismogram envelope synthesis in randomly inhomogeneous semi-infinite media based on the single scattering approximation. Phys. Earth Planet. Inter., 104(1–3), 37–61.Google Scholar
Yoshimoto, K., Takemura, S., and Kobayashi, M. 2015. Application of scattering theory to P-wave amplitude fluctuations in the crust. Earth Planet Space, 67(1), 199.Google Scholar
Zeng, Y. 2017. Modeling of high-frequency seismic-wave scattering and propagation using radiative transfer theory. Bull. Seismol. Soc. Am., 107(6), 2948–2962.Google Scholar
Zeng, Y., Su, F., and Aki, K. 1991. Scattering wave energy propagation in a random isotropic scattering medium 1. Theory. J. Geophys. Res., 96(B1), 607–619.Google Scholar
Zhou, H., Jia, X., Fu, L., and Tourin, A. 2021. Monte Carlo simulations of ultrasound scattering and absorption in finite-size heterogeneous materials. Phys. Rev. Appl., 16(3), 034009.Google Scholar

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