Abstract
The region of the earth down to about 100 km is called the lithosphere. Rigorously speaking, lithosphere refers to the solid portion of the earth that overlays the low velocity zone or the asthenosphere, and the thickness varies from place to place depending on the tectonic setting; however, we will use this term loosely for the upper 100 km of the earth that consists of the crust and the uppermost mantle. The structure of the earth’s crust has been investigated using layered models since the discovery of the Mohorovicic discontinuity or Moho at the base of the crust Mohorovičić (1909) and the Conrad discontinuity in the mid crust Conrad (1925). The characterization of the earth as a random medium is complementary to the classical stratified medium characterization.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Abramowitz M, Stegun IA (1970) Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover, New York
Abubakirov IR, Gusev AA (1990) Estimation of scattering properties of lithosphere of Kamchatka based on Monte-Carlo simulation of record envelope of a near earthquake. Phys Earth Planet Inter 64:52–67, DOI 10.1016/0031-9201(90)90005-I
Adams DA, Abercrombie RE (1998) Seismic attenuation above 10 Hz in southern California from coda waves recorded in the Cajon Pass borehole. J Geophys Res 103:24,257–24,270, DOI 10.1029/98JB01757
Akamatsu J (1991) Coda attenuation in the Lutzow-Holm Bay region, East Antarctica. Phys Earth Planet Inter 67:65–75, DOI 10.1016/0031-9201(91)90060-U
Aki K (1957) Space and time spectra of stationary stochastic waves, with special reference to microtremors. Bull Earthq Res Inst Univ Tokyo 35:415–456
Aki K (1967) Scaling law of the seismic spectrum. J Geophys Res 72:1217–1231, DOI 10. 1029/JZ072i004p01217
Aki K (1969) Analysis of seismic coda of local earthquakes as scattered waves. J Geophys Res 74:615–631, DOI 10.1029/JB074i002p00615
Aki K (1973) Scattering of P waves under the Montana LASA. J Geophys Res 78:1334–1346, DOI 10.1029/JB078i008p01334
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, DOI 10.1016/0031-9201(80)90019-9
Aki K (1980b) Scattering and attenuation of shear waves in the lithosphere. J Geophys Res 85:6496–6504, DOI 10.1029/JB085iB11p06496
Aki K (1981) Attenuation and scattering of short-period seismic waves in the lithosphere, in Identification of Seismic Sources - Earthquake or Underground Explosion (eds. E. S. Husebye and S. Mykkeltveit), D. Reidel, Dordrecht, Holland, pp 515–541
Aki K (1982) Scattering and attenuation. Bull Seism Soc Am 72:S319–S330
Aki K (1992) Scattering conversions P to S versus S to P. Bull Seism Soc Am 82:1969–1972
Aki K (1995) Interrelation between fault zone structures and earthquake processes. Pure Appl Geophys 145:647–676, DOI 10.1007/BF00879594
Aki K (2009) Seismology of earthquake and volcano prediction (English and Chinese translation). Science Press, China
Aki K, Chouet B (1975) Origin of coda waves: Source, attenuation and scattering effects. J Geophys Res 80:3322–3342, DOI 10.1029/JB080i023p03322
Aki K, Lee WHK (1976) Determination of three-dimensional velocity anomalies under a seismic array using first P arrival times from local earthquakes, Part I. A homogeneous initial model. J Geophys Res 81:4381–4399, DOI 10.1029/JB081i023p04381
Aki K, Richards P (1980) Quantitative seismology - theory and methods, vols. 1 and 2. W. H. Freeman, San Francisco
Aki K, Tsujiura M (1959) Correlation study of near earthquake waves. Bull Earthq Res Inst Univ Tokyo 37:207–232
Aki K, Christoffersson A, Husebye ES (1976) Three-dimensional seismic structure of the lithosphere under Montana LASA. Bull Seism Soc Am 66:501–524
Aki K, Christoffersson A, Husebye ES (1977) Determination of the three-dimensional seismic structure of the lithosphere. J Geophys Res 82:277–296, DOI 10.1029/ JB082i002p00277
Akinci A, Eyidogan H (2000) Scattering and anelastic attenuation of seismic energy in the vicinity of north Anatolian fault zone, eastern Turkey. Phys Earth Planet Inter 122:229–239, DOI 10.1016/S0031-9201(00)00196-5
Akinci A, Pezzo ED, Ibanez JM (1995) Separation of scattering and intrinsic attenuation in southern Spain and western Anatolia (Turkey). Geophys J Int 121:337–353, DOI 10.1111/ j.1365-246X.1995.tb05715.x
Alford RM, Kelly K, Boore D (1974) Accuracy of finite-difference modeling of the acoustic wave equation. Geophysics 39:834–842, DOI 10.1190/1.1440470
Aminzadeh F, Burkhard N, Rocca F, Wyatt K (1994) SEG/EAEG 3-D modeling project: 2nd update. Leading Edge 13:949–952, DOI 10.1190/1.1437054
Anderson DL, Hart RS (1978) Q of the Earth. J Geophys Res 83:5869–5882, DOI 10.1029/ JB083iB12p05869
Anderson DL, Ben-Menahem A, Archambeau CB (1965) Attenuation of seismic energy in the upper mantle. J Geophys Res 70:1441–1448, DOI 10.1029/JZ070i006p01441
Antolik M, Nadeau R, Aster RC, McEvilly TV (1996) Differential analysis of coda Q using similar microearthquakes in seismic gaps. Part 2: Application to seismograms recorded by the Parkfield high resolution seismic network. Bull Seism Soc Am 86:890–910
Apresyan LA, Kravtsov YA (1996) Radiation Transfer: Statistical and Wave Aspects. Gordon and Breach Science Publishers, Amsterdam
Arfken GB, Weber HJ (1995) Mathematical methods for physicists, Fourth Edition. Academic Press, San Diego
Asano Y, Hasegawa A (2004) Imaging the fault zones of the 2000 western Tottori earthquake by a new inversion method to estimate three-dimensional distribution of the scattering coefficient. J Geophys Res 109:B06306, DOI 10.1029/2003JB002761
Aster CR, Slad G, Henton J, Antolik M (1996) Differential analysis of coda Q using similar microearthquakes in seismic gaps. Part 1: Techniques and application to seismograms recorded in the Anza Seismic Gap. Bull Seism Soc Am 86:868–889
Atkinson G, Boore D (1995) Ground-motion relations for eastern North America. Bull Seism Soc Am 85(1):17–30
van Avendonk H, Snieder R (1994) A new mechanism for shape induced seismic anisotropy. Wave Motion 20(1):89–98, DOI 10.1016/0165-2125(94)90034-5
Azimi S, Kalinin A, Kalinin V, Pivovarov B (1968) Impulse and transient characteristics of media with linear and quadratic absorption laws. Izv Phys Solid Earth 2:88–93
Badi G, Pezzo ED, Ibanez JM, Bianco F, Sabbione N, Araujo M (2009) Depth dependent seismic scattering attenuation in the Nuevo Cuyo region (southern central Andes). Geophys Res Lett 36:L24307, DOI 10.1029/2009GL041081
Baig AM, Dahlen FA, Hung SH (2003) Traveltimes of waves in three-dimensional random media. Geophys J Int 153:467–482, DOI 10.1046/j.1365-246X.2003.01905.x
Baisch S, Bokelmann G (2001) Seismic waveform attributes before and after the Loma Prieta earthquake: Scattering change near the earthquake and temporal recovery. J Geophys Res 106(B8):16,323, DOI 10.1029/2001JB000151
Bakun WH, Lindh AG (1977) Local magnitudes, seismic moments and coda durations for earthquakes near Oroville, California. Bull Seism Soc Am 67:615–629
Bakun WH, Bufe CG, Stewart RM (1976) Body-wave spectra of Central California earthquakes. Bull Seism Soc Am 66:363–384
Barabanenkov YN, Kravtsov YA, Rytov SM, Tamarskii VI (1971) Status of the theory of propagation of waves in randomly inhomogeneous medium. Soviet Phys Usp (Eng Trans) 13:551–680
Barton N (2007) Rock quality, seismic velocity, attenuation and anisotropy. Taylor & Francis Group
Battaglia J, Aki K (2003) Location of seismic events and eruptive fissures on the Piton de la Fournaise volcano using seismic amplitudes. J Geophys Res 108(B8):2364, DOI 10.1029/2002JB002193
Beaudet PR (1970) Elastic wave propagation in heterogeneous media. Bull Seism Soc Am 60: 769–784
Ben-Menahem A, Singh AJ (1981) Seismic waves and sources. Springer, New York
Benites R, Aki K, Yomogida K (1992) Multiple scattering of SH waves in 2-D media with many cavities. Pure Appl Geophys 138:353–390, DOI 10.1007/BF00876878
Benz HM, Frankel A, Boore DM (1997) Regional Lg attenuation for the continental United States. Bull Seism Soc Am 87:606–619
Beroza GC, Cole AT, Ellsworth WL (1995) Stability of coda wave attenuation during the Loma Prieta, California earthquake sequence. J Geophys Res 100:3977–3987, DOI 10.1029/94JB02574
Berteussen AK, Christoffersson A, Husebye ES, Dahle A (1975) Wave scattering theory in analysis of P-wave anomalies observed at NORSAR and LASA. Geophys J R Astron Soc 42:403–417, DOI 10.1111/j.1365-246X.1975.tb05869.x
Bianco F, Pezzo ED, Castellano M, Ibanez J, Luccio FD (2002) Separation of intrinsic and scattering seismic attenuation in the Southern Apennine zone, Italy. Geophys J Int 150(1):10–22, DOI 10.1046/j.1365-246X.2002.01696.x
Bianco F, Pezzo ED, Malagnini L, Luccio FD, Akinci A (2005) Separation of depth-dependent intrinsic and scattering seismic attenuation in the northeastern sector of the Italian Peninsula. Geophys J Int 161(1):130–142, DOI 10.1111/j.1365-246X.2005. 02555.x
Biot MA (1956a) Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range. J Acoust Soc Am 28:168–178, DOI 10.1121/1.1908239
Biot MA (1956b) Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. J Acoust Soc Am 28:179–191, DOI 10.1121/1.1908241
Birch F (1960) The velocity of compressional waves in rocks to 10 kilobars, Part 1. J Geophys Res 65:1083–1102, DOI 10.1029/JZ065i004p01083
Birch F (1961) The velocity of compressional waves in rocks to 10 kilobars, Part 2. J Geophys Res 66:2199–2224, DOI 10.1029/JZ066i007p02199
Biswas NN, Aki K (1984) Characteristics of coda waves: Central and south central Alaska. Bull Seism Soc Am 74:493–507
Block LV, Cheng CH, Fehler MC, Phillips WS (1994) Seismic imaging using microearthquakes induced by hydraulic fracturing. Geophysics 59:102–112
Boettcher AL (1977) The role of amphiboles and water in circum-Pacific volcanism, in high pressure research (eds., M. H. Manghnani and S. Akimoto), Academic Press, New York, pp 107–125
Braile L, Keller GR, Mueller S, Prodehl C (1995) Seismic techniques, in continental rifts: evolution, structure, tectonics (ed. K. Olsen), Elsevier, New York, pp 61–92
Brenguier F, Campillo M, Hadziioannou C, Shapiro N, Nadeau R, Larose E (2008) Postseismic relaxation along the San Andreas Fault at Parkfield from continuous seismological observations. Science 321(5895):1478, DOI 10.1126/science.1160943
Brockman SR, Bollinger GA (1992) Q estimates along the Wasatch front in Utah derived from Sg and Lg wave amplitudes. Bull Seism Soc Am 82:135–147
Brune JN (1970) Tectonic stress and the spectra of seismic shear waves from earthquakes. J Geophys Res 75:4997–5009, DOI 10.1029/JB075i026p04997
Butler R, McCreery CS, Frazer LN, Walker DA (1987) High-frequency seismic attenuation of oceanic P and S waves in the western Pacific. J Geophys Res 92:1383–1396, DOI 10.1029/JB092iB02p01383
Campillo M, Paul A (1992) Influence of the lower crustal structure on the early coda of regional seismograms. J Geophys Res 97:3405–3416, DOI 10.1029/91JB02714
Campillo M, Paul A (2003) Long-range correlations in the diffuse seismic coda. Science 299(5606):547–549, DOI 10.1126/science.1078551
Campillo M, Plantet JL (1991) Frequency dependence and spatial distribution of seismic attenuation in France: Experimental results and possible interpretations. Phys Earth Planet Inter 67:48–64, DOI 10.1016/0031-9201(91)90059-Q
Capon J (1974) Characterization of crust and upper mantle structure under LASA as a random medium. Bull Seism Soc Am 64:235–266
Carcolé E, 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, DOI 10.1111/j. 1365-246X.2009.04394.x
Carcolé E, Ugalde A (2008) Formulation of the multiple anisotropic scattering process in two dimensions for anisotropic source radiation. Geophys J Int 174(3):1037–1051, DOI 10.1111/ j.1365-246X.2008.03896.x
Carpenter PJ, Sanford AR (1985) Apparent Q for upper crustal rocks of the Central Rio Grande Rift. J Geophys Res 90:8661–8674, DOI 10.1029/JB090iB10p08661
Castro R, Monachesi G, Mucciarelli M, Trojani L, Pacor F (1999) P-and S-wave attenuation in the region of Marche, Italy. Tectonophysics 302(1-2):123–132, DOI 10. 1016/S0040-1951(98)00277-7
Červený V (1987) Ray tracing algorithms in three-dimensional laterally varying layered structures, in Seismic Tomography (ed. G. Nolet), D. Reidel, Boston, pp 99–133
Červený V, Ravindra R (1971) Theory of seismic head waves. University Toronto Press, Tronto
Chandrasekhar S (1960) Radiative transfer. Dover, New York
Chapman CH (1987) The Radon transform and seismic tomography, in Seismic Tomography (ed. G. Nolet), D. Reidel, Boston, pp 25–48
Chen J, Schuster G (1999) Resolution limits of migrated images. Geophysics 64:1046–1053, DOI 10.1190/1.1444612
Chen X, Aki K (1991) General coherence functions for amplitude and phase fluctuations in a randomly heterogeneous medium. Geophys J Int 105:155–162, DOI 10.1111/j. 1365-246X.1991.tb03451.x
Chernov LA (1960) Wave Propagation in a Random Medium (Engl. trans. by R. A. Silverman). McGraw-Hill, New York
Chin BH, Aki K (1991) Simultaneous study of the source path and site effects on strong ground motion during the 1989 Loma Prieta earthquake: A preliminary result on pervasive nonlinear site effects. Bull Seism Soc Am 81:1859–1884
Christensen N (1996) Poisson’s ratio and crustal seismology. J Geophys Res 101:3139–3156, DOI 10.1029/95JB03446
Christensen N, Mooney W (1995) Seismic velocity structure and composition of the continental crust: A global view. J Geophys Res 100:9761–9788, DOI 10.1029/ 95JB00259
Christensen NI (1968) Chemical changes associated with upper mantle structure. Tectonophysics 6:331–342, DOI 10.1016/0040-1951(68)90048-6
Chung T, Sato H (2001) Attenuation of high-frequency P and S waves in the crust of southeastern South Korea. Bull Seism Soc Am 91(6):1867–1874, DOI 10.1785/ 0120000268
Claerbout JF (1985) Imaging the Earth’s interior. Blackwell Science, Boston
Cleary JR, Haddon RAW (1972) Seismic Wave Scattering near the Core-Mantle Boundary: a New Interpretation of Precursors to PKP. Nature 240:549–551, DOI 10.1038/ 240549a0
Conrad V (1925) Laufzeitkurven des Tauernbebens vom 28. November, 1923. Mitt Erdb Komm Wien Akad Wiss 59:1–23
Cormier V (1995) Time-domain modelling of PKIKP precursors for constraints on the heterogeneity in the lowermost mantle. Geophys J Int 121(3):725–736, DOI 10.1111/j. 1365-246X.1995.tb06434.x
Crosson R (1976) Crustal structure modeling of earthquake data 1. Simultaneous least squares estimation of hypocenter and velocity parameters. J Geophys Res 81:3036–3046, DOI 10.1029/JB081i017p03036
Curtis A, Gerstoft P, Sato H, Snieder R, Wapenaar K (2006) Seismic interferometry-turning noise into signal. Leading Edge 25(9):1082–1092, DOI 10.1190/1.2349814
Dainty AM, Toksöz M, Anderson K, Pines P, Nakamura Y, Latham G (1974) Seismic scattering and shallow structure of the Moon in Oceanus Procellarum. Earth Moon Planets 9(1):11–29, DOI 10.1007/BF00565388
Dainty AM (1984) High-frequency acoustic backscattering and seismic attenuation. J Geophys Res 89:3172–3176, DOI 10.1029/JB089iB05p03172
Dainty AM, Toksöz MN (1981) Seismic codas on the Earth and the Moon: a comparison. Phys Earth Planet Inter 26:250–260, DOI 10.1016/0031-9201(81)90029-7
Deans S (1983) The radon transform and some of its applications. Wiley, New York
Del Pezzo E (2008) Seismic wave scattering in volcanoes. In: Sato H, Fehler MC (eds) Earth heterogeneity and scattering effects on seismic waves, advances in geophysics (Series Ed. R. Dmowska), vol 50, Academic Press, New York, Chap. 13, pp 353–373
Der AZ, Marshall ME, O’Donnell A, McElfresh TW (1984) Spatial coherence structure and attenuation of the Lg phase, site effects, and interpretation of the Lg coda. Bull Seism Soc Am 74:1125–1147
Derode A, Larose E, Campillo M, Fink M (2003) How to estimate the Green’s function of a heterogeneous medium between two passive sensors? Application to acoustic waves. Appl Phys Lett 83:3054
Devaney AJ (1982) A filtered backpropagation algorithm for diffraction tomography. Ultrasonic Imaging 4:336–350, DOI 10.1016/0161-7346(82)90017-7
Dewberry SR, Crosson RS (1995) Source scaling and moment estimation for the Pacific Northwest seismograph network using S-coda amplitudes. Bull Seism Soc Am 85:1309–1326
Dubendorff B, Menke W (1986) Time-domain apparent-attenuation operators for compressional and shear waves: Experiment versus single scattering theory. J Geophys Res 91:14,023–14,032, DOI 10.1029/JB091iB14p14023
Dutta U, Biswas N, Adams D, Papageorgiou A (2004) Analysis of S-wave attenuation in South-Central Alaska. Bull Seism Soc Am 94(1):16–28, DOI 10.1785/0120030072
Duvall T, Scherrer P, Bogart R, Bush R, De forest C, Hoeksema J, Schou J, Saba J, Tarbell T, Title A, et al (1997) Time-distance helioseismology with the MDI instrument: initial results. Solar Phys 170(1):63–73, DOI 10.1023/A:1004907220393
Dziewonski A, Anderson D (1981) Preliminary reference Earth model. Phys Earth Planet Inter 25(4):297–356, DOI 10.1016/0031-9201(81)90046-7
Dziewonski AM (1979) Elastic and anelastic structure of the earth. Rev Geophys Space Phys 17:303–312, DOI 10.1029/RG017i002p00303
Einspruch NG, Witterholt EJ, Truell R (1960) Scattering of a plane transverse wave by a spherical obstacle in an elastic medium. J Appl Phys 31:806–819, DOI 10.1063/1. 1735701
Ellsworth WL (1991) Review for ”Temporal change in scattering and attenuation associated with the earthquake occurrence - A review of recent studies on coda waves (H. Sato)”, in Evaluation of Proposed Earthquake Precursors (ed. M. Wyss), AGU, Washington, D. C., pp 54–55
Emoto K, Sato H, 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:B08306, DOI 10.1029/2009JB006955
Etgen J, Gray S, Yu Z (2009) An overview of depth imaging in exploration geophysics. Geophysics 74(6):0016–8033, DOI 10.1190/1.3223188
Fang Y, Müller G (1996) Attenuation operators and complex wave velocities for scattering in random media. Pure Appl Geophys 148:269–285, DOI 10.1007/BF00882063
Fedotov SA, Boldyrev SA (1969) Frequency dependence of the body-wave absorption in the crust and the upper mantle of the Kuril Island chain. Izv Acad Sci USSR (Engl trans Phys Solid Earth) 9:17–33
Fehler M (2008) SEAM Advanced Modeling Project [SEAM]: Phase I update. Leading Edge 27:258–259
Fehler M (2010) SEG Advanced Modeling Project: completion of Phase I acoustic simulations. Leading Edge 29:640–642
Fehler M, Phillips WS (1991) Simultaneous inversion for Q and source parameters of microearthquakes accompanying hydrofracturing in granitic rock. Bull Seism Soc Am 81: 553–575
Fehler M, Roberts P, Fairbanks T (1988) A temporal change in coda wave attenuation observed during an eruption of Mount St. Helens. J Geophys Res 93:4367–4373, DOI 10.1029/JB093iB05p04367
Fehler M, Hoshiba M, Sato H, 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 108:787–800, DOI 10.1111/j.1365-246X. 1992.tb03470.x
Fehler M, Sato H, L-J H (2000) Envelope broadening of outgoing waves in 2D random media: A comparison between the Markov approximation and numerical simulations. Bull Seism Soc Am 90:914–928, DOI 10.1785/0119990143
Fei T, Fehler M, Hildebrand S (1995) Finite-difference solutions of the 3-D Eikonal equation. 65th Annual Mtg, Soc Expl Geophys, Expanded Abstracts 95:1129–1132
Flatté SM, Wu RS (1988) Small-scale structure in the lithosphere and asthenosphere deduced from arrival time and amplitude fluctuations at NORSAR. J Geophys Res 93:6601–6614, DOI 10.1029/JB093iB06p06601
Flatté SM, Dashen R, Munk WH, Watson KM, Zachariasen F (1979) Sound transmission through a fluctuating ocean. Cambridge University Press, New York
Foldy LL (1945) The multiple scattering of waves- I. General theory of isotropic scattering by randomly distributed scatterers. Phys Rev 67:107–119, DOI 10.1103/PhysRev.67. 107
Fountain DM, Christensen N (1989) Composition of the continental crust and upper mantle: A review, in Geophysical Framework of the Continental United States (eds., Pakiser, L.C. and W. Mooney), Geol. Soc. Am. Memoir 172, Geological Society of America, Boulder, Colo., pp 711–742
Frankel A (1982) The effects of attenuation and site response on the spectra of microearthquakes in the northeastern Caribbean. Bull Seism Soc Am 72:1379–1402
Frankel A (1991) Review for “Observational and physical basis for coda precursor (Jin, A. and K. Aki)” in Evaluation of Proposed Earthquake Precursors (ed. M. Wyss), AGU, Washington, D. C., pp 51–53
Frankel A, Clayton RW (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 91:6465–6489, DOI 10.1029/JB091iB06p06465
Frankel A, Wennerberg L (1987) Energy-flux model of seismic coda: Separation of scattering and intrinsic attenuation. Bull Seism Soc Am 77:1223–1251
Frankel A, McGarr A, Bicknell J, Mori J, Seeber L, Cranswickz E (1990) Attenuation of high-frequency shear waves in the crust: Measurements from New York State, South Africa and Southern California. J Geophys Res 95:17,441–17,457, DOI 10.1029/ JB095iB11p17441
Frisch U (1968) Wave Propagation in random media, in Probabilistic Method in Applied Mathematics (Vol. I, ed. A. T. Bharucha-Reid), Academic Press, New York, pp 76–198
Fukushima Y, Nishizawa H, Sato H, Ohtake M (2003) Laboratory study on scattering characteristics of shear waves in rock samples. Bull Seism Soc Am 93:253–263, DOI 10.1785/0120020074
Furumura T, Kennett BL (2008) A scattering waveguide in the heterogeneous subducting plate. In: Sato H, Fehler MC (eds) Earth Heterogeneity and Scattering Effects on Seismic Waves, Advances in Geophysics (Series Ed. R. Dmowska), vol 50, Academic Press, New York, Chap. 7, pp 195– 217
Furumura T, Kennett BLN (2005) Subduction zone guided waves and the heterogeneity structure of the subducted plate: Intensity anomalies in northern Japan. J Geophys Res 110:B10302, DOI 10.1029/2004JB003486
Gagnepain-Beyneix J (1987) Evidence of spatial variations of attenuation in the western Pyrenean range. Geophys J R Astron Soc 89:681–704, DOI 10.1111/j.1365-246X.1987. tb05187.x
Gerstoft P, Sabra K, Roux P, Kuperman W, Fehler M (2006) Green’s functions extraction and surface-wave tomography from microseisms in southern California. Geophysics 71:SI23, DOI 10.1190/1.2210607
Giampiccolo E, Gresta S, Rasconà F (2004) Intrinsic and scattering attenuation from observed seismic codas in Southeastern Sicily (Italy). Phys Earth Planet Inter 145:55–66, DOI 10.1016/ j.pepi.2004.02.004
Giampiccolo E, Tuve T, Gresta S, Patane D (2006) S-waves attenuation and separation of scattering and intrinsic absorption of seismic energy in southeastern Sicily (Italy). Geophys J Int 165:211–222, DOI 10.1111/j.1365-246X.2006.02881.x
Goff J, Holliger K (2003) Heterogeneity in the crust and upper mantle: nature, scaling, and seismic properties. Kluwer Academic/Plenum, New York
Got JL, Poupinet G, Frechet J (1990) Changes in source and site effects compared to coda Q − 1 temporal variations using microearthquakes doublets in California. Pure Appl Geophys 134:195–228, DOI 10.1007/BF00876998
Gouédard P, Stehly L, Brenguier F, Campillo M, Colin de Verdiere Y, Larose E, Margerin L, Roux P, Sánchez-Sesma FJ, Shapiro NM, Weaver RL (2008a) Cross-correlation of random fields: mathematical approach and applications. Geophys Prospecting 56(3):375–394, DOI 10.1111/j.1365-2478.2007.00684.x
Gouédard P, Roux P, Campillo M, Verdel A (2008b) Convergence of the two-point correlation function toward the Green’s function in the context of a seismic-prospecting data set. Geophysics 73(6):V47
Goutbeek FH, Dost B, van Eck T (2004) Intrinsic absorption and scattering attenuation in the southern part of the Netherlands. J Seis 8:11–23, DOI 10.1023/B:JOSE.0000009511. 27033.79
Gradshteyn IS, Ryzhik IM (1994) Table of integrals, series and products (5th Ed. in Engl., ed. A. Jeffrey). Academic Press, San Diego
Gradshteyn IS, Ryzhik IM (2007) Table of integrals, series and products (7th Ed. in Engl., ed. A. Jeffrey and D. Zwillinger). Academic Press, San Diego
Gritto R, Korneev VA, Johnson LR (1995) Low-frequency elastic-wave scattering by an inclusion: Limits of applications. Geophys J Int 120:677–692, DOI 10.1111/j. 1365-246X.1995.tb01845.
Gupta SC, Teotia SS, Rai SS, Gautam N (1998) Coda Q estimates in the Koyna region, India. Pure Appl Geophys 153:713–731, DOI 10.1007/s000240050216
Gupta SC, Kumar A, Shukla AK, Suresh G, Baidya PR (2006) Coda Q in the Kachchh basin, western India using aftershocks of the Bhuj earthquake of January 26, 2001. Pure Appl Geophys 136:1583–1595, DOI 10.1007/s00024-006-0086-2
Gusev AA (1995a) Baylike and continuous variations of the relative level of the late coda during 24 years of observation on Kamchatka. J Geophys Res 100:20,311–20,319, DOI 10.1029/95JB01571
Gusev AA (1995b) Vertical profile of turbidity and coda Q. Geophys J Int 123:665–672, DOI 10.1111/j.1365-246X.1995.tb06882.x
Gusev AA, Abubakirov IR (1987) Monte-Carlo simulation of record envelope of a near earthquake. Phys Earth Planet Inter 49:30–36, DOI 10.1016/0031-9201(87)90130-0
Gusev AA, Lemzikov VK (1985) Properties of scattered elastic waves in the lithosphere of Kamchatka: Parameters and temporal variations. Tectonophysics 112:137–153, DOI 10. 1016/0040-1951(85)90177-5
Gusev AA, Pavlov VM (1991) Deconvolution of squared velocity waveform as applied to study of non-coherent short-period radiator in earthquake source. Pure Appl Geophys 136:236–244, DOI 10.1007/BF00876375
Gutenberg B (1956) The energy of earthquakes. Quart J Geol Soc London 112:1–14
Haddon RAW, Husebye ES (1978) Joint interpretation of P-wave time and amplitude anomalies in terms of lithospheric heterogeneities. Geophys J R Astron Soc 55:19–43, DOI 10.1111/j.1365-246X.1978.tb04746.x
Hadley K (1976) Comparison of calculated and observed crack densities and seismic velocities in Westerly granite. J Geophys Res 81:3484–3494, DOI 10.1029/ JB081i020p03484
Halliday D, Curtis A (2009) Seismic interferometry of scattered surface waves in attenuative media. Geophys J Int 178(1):419–446, DOI 10.1111/j.1365-246X.2009.04153.x
Haney MM, van Wijk K (2007) Modified Kubelka-Munk equations for localized waves inside a layered medium. Phys Rev E 75(3):36,601, DOI 10.1103/PhysRevE.75.036601
Hardy J, Pomeau Y, de Pazzis O (1973) Time evolution of two-dimensional model system, I: Invariant states and time correlation functions. J Math Phys 14:1746–1759, DOI 10.1063/1.1666248
Hartse H, Phillips WS, Fehler MC, House LS (1995) Single-station spectral discrimination using coda waves. Bull Seism Soc Am 85:1464–1474
Hartse HE, Sanford AR, Knapp JS (1992) Incorporating Socorro magma body reflections into the earthquake location process. Bull Seism Soc Am 82:2511–2532
Hassani S (1999) Mathematical physics: a modern introduction to its foundations. Springer, New York
Hatzidimitriou PM (1993) Attenuation of coda waves in northern Greece. Pure Appl Geophys 140:63–78, DOI 10.1007/BF00876871
Hatzidimitriou PM (1994) Scattering and anelastic attenuation of seismic energy in northern Greece. Pure Appl Geophys 143:587–601, DOI 10.1007/BF00879499
Hedlin M, Shearer P (2000) An analysis of large-scale variations in small-scale mantle heterogeneity using Global Seismographic Network recordings of precursors to PKP. J Geophys Res 105(B6):13,655, DOI 10.1029/2000JB900019
Hedlin M, Shearer P, Earle P (1997) Seismic evidence for small-scale heterogeneity throughout the Earth’s mantle. Nature 387(6629):145–150, DOI 10.1038/387145a0
Helbig K, Thomsen L (2005) 75-plus years of anisotropy in exploration geophysics and reservoir seismics: A historical review of concepts and method, Japan. Geophysics 70:9ND–23ND, DOI 10.1190/1.2122407
Hemmer PC (1961) Generalization of Smoluchowskis diffusion equation. Physica 27:79–82
Hennino R, Tregoures N, Shapiro NM, Margerin L, Campillo M, Van Tiggelen BA, Weaver RL (2001) Observation of equipartition of seismic waves. Phys Rev Lett 86(15):3447–3450, DOI 10.1103/PhysRevLett.86.3447
Hestholm SO, Husebye ES, Ruud BO (1994) Seismic wave propagation in complex crust-upper mantle media using 2-D finite-difference synthetics. Geophys J Int 118:643–670, DOI 10.1046/j.1365-246x.1999.00994.x
Hiramatsu Y, Hayashi N, Furumoto M, 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, DOI 10.1029/1999JB900432
Hoang-Trong P (1983) Some medium properties of the Hohenzollerngraben (Swabian Jura, W. Germany) inferred from Qp/Qs analysis. Phys Earth Planet Inter 31:119–131, DOI 10.1016/0031-9201(83)90104-8
Hock S, Korn M, the TOR Working group (2000) Random heterogeneity of the lithosphere across the Trans-European Structure Zone. Geophys J Int 141:57–70, DOI 10.1046/j. 1365-246X.2000.00078.x
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, DOI 10.1111/j.1365-246X.1996. tb06025.x
Holliger K, Levander A (1992) A stochastic view of lower crustal fabric based on evidence from the Ivrea zone. Geophys Res Lett 19:1153–1156, DOI 10.1029/92GL00919
Holliger K, Levander A, Goff J (1993) Stochastic modeling of the reflective lower crust: Petrophysical and geological evidence from the Ivrea zone (Northern Italy). J Geophys Res 98:11,967–11,980, DOI 10.1029/93JB00351
Holme R, Rothman D (1992) Lattice-gas and lattice-Boltzman models of miscible fluids. J Stat Phys 68:409–429, DOI 10.1007/BF01341756
de Hoop A (1988) Time-domain reciprocity theorems for acoustic wave fields in fluids with relaxation. Acoust Soc Am J 84:1877–1882
Hoshiba M (1991) Simulation of multiple-scattered coda wave excitation based on the energy conservation law. Phys Earth Planet Inter 67:123–136, DOI 10.1016/ 0031-9201(91)90066-Q
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 98:15,809–15,824, DOI 10.1029/93JB00347
Hoshiba M (1994) Simulation of coda wave envelope in depth dependent scattering and absorption structure. Geophys Res Lett 21:2853–2856, DOI 10.1029/94GL02718
Hoshiba M, Sato H, 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 42:65–91
Hough SE, Anderson JG, Brune J, Vernon III F, Berger J, Fletcher J, Haar L, Hanks T, Baker L (1988) Attenuation near Anza, California. Bull Seism Soc Am 78:672–691
Howe MS (1971a) Wave propagation in random media. J Fluid Mech 45:769–783, DOI 10. 1017/S0022112071000326
Howe MS (1971b) On wave scattering by random inhomogeneities, with application to the theory of weak bores. J Fluid Mech 45:785–805, DOI 10.1017/S0022112071000338
Howe MS (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 331:479–496
Howe MS (1974) A kinetic equation for wave propagation in random media. Q J Mech Appl Math XXVII:237–253
Huang L (2007) A lattice Boltzmann approach to acoustic-wave propagation. In: Wu R, Maupin V (eds) Advances in Wave Propagation in Heterogeneous Earth, Advances in Geophysics (Series Ed.: R. Dmowska), vol 48, Academic Press, New York, Chap. 9, pp 517–561
Huang LJ, Mora P (1994) The phononic lattice solid by interpolation for modeling P waves in heterogeneous media. Geophys J Int 119:766–778, DOI 10.1111/j.1365-246X.1994. tb04015.x
Huang LJ, Mora P (1996) Numerical simulation of wave propagation in strongly heterogeneous media using a lattice solid approach. Proc Soc Photo-Optical Inst Eng 2822:170–179, DOI 10.1117/12.255205
Husebye ES (ed) (1981) Contribution of scattering to the complexity of seismograms. Phys Earth Planet Inter 26:233–291
Husebye ES, Christoffersson A, Aki K, Powell C (1976) Preliminary results on the 3-dimensional seismic structure under the USGS central California seismic array. Geophys J R Astron Soc 46:319–340, DOI 10.1111/j.1365-246X.1976.tb04161.x
Ibanez J, Del Pezzo E, De Miguel F, Herraiz M, Alguacil G, Morales J (1990) Depth-dependent seismic attenuation in the Granada zone (Southern Spain). Bull Seism Soc Am 80:1232–1244
Ishimaru A (1978) Wave Propagation and Scattering in Random Media, Vols. 1 and 2. Academic Press, New York
Ishimaru A (1997) Wave Propagation and Scattering in Random Media. IEEE Press and Oxford University Press
Izutani Y (2000) Q S -value in southern Kyushu evaluated from double spectral ratio of strong motion records. Proc JSCE 640:225–230
Jackson DD, Anderson DL (1970) Physical mechanisms of seismic-wave attenuation. Rev Geophys Space Phys 8:1–63, DOI 10.1029/RG008i001p00001
Jacobson RS (1987) An investigation into the fundamental relationships between attenuation, phase dispersion, and frequency using seismic refraction profiles over sedimentary structures. Geophysics 52:72–87, DOI 10.1190/1.1442242
Jannaud LR, P MA, Jacquin CG (1991) Spectral analysis and inversion of codas. J Geophys Res 96:18,215–18,231, DOI 10.1029/91JB01427
Jin A, Aki K (1986) Temporal change in coda Q before the Tangshan earthquake of 1976 and the Haicheng earthquake of 1975. J Geophys Res 91:665–673, DOI 10.1029/ JB091iB01p00665
Jin A, Aki K (1988) Spatial and temporal correlation between coda Q and seismicity in China. Bull Seism Soc Am 78:741–769
Jin A, Aki K (1989) Spatial and temporal correlation between coda Q − 1 and seismicity and its physical mechanism. J Geophys Res 94:14,041–14,059, DOI 10.1029/JB094iB10p14041
Jin A, Aki K (1991) Observational and physical basis for coda precursor, in Evaluation of Proposed Earthquake Precursors (ed. M. Wyss), AGU, Washington, D. C., pp 33–46
Jin A, Aki K (1993) Temporal correlation between coda Q − 1 and seismicity: Evidence for a structural unit in the brittle-ductile transition zone. J Geodyn 17:95–119, DOI 10.1016/0264-3707(93)90001-M
Jin A, 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
Jin A, Mayeda K, Adams D, Aki K (1994) Separation of intrinsic and scattering attenuation in southern California using TERRAscope data. J Geophys Res 99:17,835–17,848, DOI 10.1029/94JB01468
Jin A, Aki K, Liu Z, Keilis-Borok V (2004) Seismological evidence for the brittle-ductile interaction hypothesis on earthquake loading. Earth Planets Space 56(8):823–830
Kakehi Y, Irikura K (1996) Estimation of high-frequency wave radiation areas on the fault plane by the envelope inversion of acceleration seismograms. Geophys J Int 125:892–900, DOI 10.1111/j.1365-246X.1996.tb06032.x
Kanamori H, Mizutani H (1965) Ultrasonic measurements of elastic constants of rocks under high pressures. Bull Earthq Res Inst Univ Tokyo 43:173–194
Kanao M, Ito K (1990) Attenuation property of coda waves in the middle and northern parts of Kinki district (in Japanese with English abstract). Zisin (in Japanese) 43:311–320
Karal FC, Keller JB (1964) Elastic, electromagnetic and other waves in a random medium. J Math Phys 5:537–547, DOI 10.1063/1.1704145
Karato S (2008) Deformation of earth materials: an introduction to the rheology of solid earth. Cambridge Univsity Press, Cambridge
Karato S, Spetzler H (1990) Defect microdynamics in minerals and solid-state mechanisms of seismic wave attenuation and velocity dispersion in the mantle. Rev Geophysics 28(4):399–421
Kato K, Aki K, Takemura M (1995) Site amplification from coda waves: Validation and application to S-wave site response. Bull Seism Soc Am 85:467–477
Kato K, Takemura M, Yashiro K (1998) Regional variation of source spectra in high-frequency range determined from strong motion records (in Japanese with English abstract). Zisin (in Japanese) 51:123–138
Kawahara J (2002) Cutoff scattering angles for random acoustic media. J Geophys Res 107(B1), DOI 10.1029/2001JB000429
Kawahara J, Yamashita T (1992) Scattering of elastic waves by a fracture zone containing randomly distributed cracks. Pure Appl Geophys 139:121–144, DOI 10. 1007/BF00876828
Kawahara J, Ohno T, Yomogida K (2009) Attenuation and dispersion of antiplane shear waves due to scattering by many two-dimensional cavities. J Acoust Soc Am 125:3589, DOI 10.1121/ 1.3124779
Keenan JH, Keys FG, Hill PG, Moore JG (1969) Steam tables - thermodynamic properties of water including vapor, liquid, and solid phases. Wiley, New York
Keller JB (1964) Stochastic equations and wave propagation in random media. In: Stochastic Processes in Mathematical Physics and Engineering: Proceedings of a Symposium in Applied Mathematics of the American Mathematical Society: Held in New York City, April 30-May 2, 1963, American Mathematical Society, pp 145–170
Kennett BLN (1985) Seismic wave propagation in stratified media. Cambridge University Press, Cambridge, UK
Kenter J, Braaksma H, Verwer K, van Lanen X (2007) Acoustic behavior of sedimentary rocks: Geologic properties versus Poisson’s ratios. Leading Edge 26(4):436–444
Kikuchi M (1981) Dispersion and attenuation of elastic waves due to multiple scattering from cracks. Phys Earth Planet Inter 27:100–105, DOI 10.1016/0031-9201(81)90037-6
Kinoshita S (1994) Frequency-dependent attenuation of shear waves in the crust of the southern Kanto, Japan. Bull Seism Soc Am 84:1387–1396
Kinoshita S, Ohike M (2002) Scaling relations of earthquakes that occured in the upper part of the Philippine Sea Plate beneath the Kanto region, Japan, estimated by means of borehole recordings. Bull Seism Soc Am 92:611–624, DOI 10.1785/0120010134
Klimeš L (2002) Correlation functions of random media. Pure Appl Geophys 159:1811–1831, DOI 10.1007/s00024-002-8710-2
Knopoff L (1964) Q. Rev Geophys 2:625–660, DOI 10.1029/RG002i004p00625
Knopoff L, Hudson JA (1964) Scattering of elastic waves by small inhomogeneities. J Acoust Soc Am 36(2):338–343, DOI 10.1121/1.1918957
Kopnichev YF (1975) A model of generation of the tail of the seismogram. Dok Akad Nauk, SSSR (Engl trans) 222:333–335
Kopnichev YF (1985) Short-period seismic wave fields (in Russian). Nauka, Moscow
Korn M (1990) A modified energy flux model for lithospheric scattering of teleseismic body waves. Geophys J Int 102:165–175, DOI 10.1111/j.1365-246X.1990.tb00538.x
Korn M (1993) Determination of site-dependent scattering Q from P-wave coda analysis with an energy-flux model. Geophys J Int 113:54–72, DOI 10.1111/j.1365-246X.1993. tb02528.x
Korn M, 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, DOI 10.1111/j.1365-246X.2005.02624.x
Korn M, Sato H and Scherbaum F (eds) (1997) Stochastic Seismology: Stochastic Seismic Wave Fields and Realistic Media. Phys Earth Planet Inter 104:1–281, DOI 10.1016/ S0031-9201(97)00040-X
Korneev VA, Johnson LR (1993a) Scattering of elastic wave by a spherical inclusion - I. Theory and numerical results. Geophys J Int 115:230–250, DOI 10.1111/j.1365-246X. 1993.tb05601.x
Korneev VA, Johnson LR (1993b) Scattering of elastic wave by a spherical inclusion - II. Limitations of asymptotic solutions. Geophys J Int 115:251–263, DOI 10.1111/j. 1365-246X.1993.tb05602.x
Korneev VA, Johnson LR (1996) Scattering of P and S waves by a spherically symmetric inclusion. Pure Appl Geophys 147:675–718, DOI 10.1007/BF01089697
Kosuga M (1992) Dependence of coda Q on frequency and lapse time in the western Nagano region, central Japan. J Phys Earth 40:421–445
Kubanza M, Nishimura T, 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:e45–e48
Kubanza M, Nishimura T, 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, DOI 10.1111/j.1365-246X.2007.03544.x
Kubelka P, Munk F (1931) Bin beitrag zur optik der farbanstriche. Z Techn Phys 11a:593–601
Kumagai H, Palacios P, Maeda T, Castillo D, Nakano M (2009) Seismic tracking of lahars using tremor signals. J Volcanol Geoth Res 183(1-2):112–121, DOI 10.1016/j.jvolgeores. 2009.03.010
Kumagai H, Nakano M, Maeda T, Yepes H, Palacios P, Ruiz M, Arraiz S, Vaca M (2010) Broadband seismic monitoring of active volcanoes using deterministic and stochastic approaches. J Geophys Res 115, B08303, DOI 10.1029/2009JB006889
Kurita T (1975) Attenuation of shear waves along the San Andreas fault zone in central California. Bull Seism Soc Am 65:277–292
Kuwahara Y, Ito H, Kawakatsu H, Ohminato T, Kiguchi T (1997) Crustal heterogeneity as inferred from seismic coda wave: Decomposition by small-aperture array observations. Phys Earth Planet Inter 104:247–256, DOI 10.1016/S0031-9201(97)00057-5
Kvamme LB, Havskov J (1989) Q in southern Norway. Bull Seism Soc Am 79:1575–1588
Lacombe C, Campillo M, Paul A, Margerin L (2003) Separation of intrinsic absorption and scattering attenuation from Lg coda decay in central France using acoustic radiative transfer theory. Geophys J Int 154:417–425, DOI 10.1046/j.1365-246X.2003.01976.x
Lacoss T, Kelly EJ, Toksöz MN (1969) Estimation of seismic noise structure using arrays. Geophysics 34:21–38, DOI 10.1190/1.1439995
Landau L, Lifshitz E (2003) Quantum mechanics (3rd Ed., Engl. trans. by J. B. Sykes and J. S. Bell). Butterworth-Heinemann
Langston C (1979) Structure under Mount Rainier, Washington, inferred from teleseismic body waves. J Geophys Res 84:4749–4762, DOI 10.1029/JB084iB09p04749
Langston CA (1989) Scattering of teleseismic body waves under Pasadena, California. J Geophys Res 94:1935–1951, DOI 10.1029/JB094iB02p01935
Larose E, Margerin L, Van Tiggelen B, Campillo M (2004) Weak localization of seismic waves. Phys Rev Lett 93(4):48,501, DOI 10.1103/PhysRevLett.93.048501
Larose E, Margerin L, Derode A, van Tiggelen B, Campillo M, Shapiro N, Paul A, Stehly L, Tanter M (2006) Correlation of random wavefields: An interdisciplinary review. Geophysics 71:SI11–SI21, DOI 10.1190/1.2213356
Lay T, Wallace TC (1995) Modern global seismology. Academic Press, San Diego
Leary P, Abercrombie R (1994) Frequency dependent crustal scattering and absorption at 5-160 Hz from coda decay observed at 2.5 km depth. Geophys Res Lett 21:971–974, DOI 10.1029/94GL00977
Lee LC, Jokipii JR (1975a) Strong scintillations in astrophysics. I. The Markov approximation, its validity and application to angular broadening. Astrophys J 196:695–707
Lee LC, Jokipii JR (1975b) Strong scintillations in astrophysics. II. A theory of temporal broadening of pulses. Astrophys J 201:532–543
Lee W, Sato H (2006) Power-law decay characteristic of coda envelopes revealed from the analysis of regional earthquakes. Geophys Res Lett 33:L07317, DOI 10.1029/ 2006GL025840
Lee WHK, Stewart S (1981) Principles and applications of microearthquake networks. Academic Press, New York
Lee WS, Sato H, Lee K (2003) Estimation of S-wave scattering coefficient in the mantle from envelope characteristics before and after the ScS arrival. Geophys Res Lett 30(24):2248, DOI 10.1029/2003GL018413
Lee WS, Sato H, Lee K (2006) Scattering coefficients in the mantle revealed from the seismogram envelope analysis based on the multiple isotropic scattering model. Earth Planet Sci Lett 241:888–900, DOI 10.1016/j.epsl.2005.10.035
Lee WS, Yun S, Do JY (2010) Scattering and intrinsic attenuation of short-period S-waves in the Gyeongsang Basin, South Korea, revealed from S-wave seismogram envelopes based on the radiative transfer theory. Bull Seism Soc Am 100:833–840, DOI 10.1785/0120090149
Liu P H, Anderson DL, Kanamori H (1976) Velocity dispersion due to anelasticity; Implications for seismology and mantle composition. Geophys J R Astron Soc 47:41–58, DOI 10.1111/j.1365-246X.1976.tb01261.x
Lobkis O, Weaver R (2001) On the emergence of the Green’s function in the correlations of a diffuse field. J Acoust Soc Am 110:3011, DOI 10.1121/1.1417528
Lu L, Ding Z, Zeng R, He Z (2011) Retrieval of Green’s function and generalized optical theorem for the scattering of complete dyadic fields. J Acoustical Soc Am 129:1935
Lundquist GM, Cormier VC (1980) Constraints on the absorption band model of Q. J Geophys Res 85:5244–5256, DOI 10.1029/JB085iB10p05244
Maeda T, Obara K (2009) Spatiotemporal distribution of seismic energy radiation from low-frequency tremor in western Shikoku, Japan. J Geophys Res 114:B00A09, DOI 10.1029/2008JB006043
Maeda T, Sato H, 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, DOI 10.1029/2002GL016629
Maeda T, Sato H, Ohtake M (2006) Constituents of vertical-component coda waves at long periods. Pure Appl Geophys 163:549–566, DOI 10.1007/s00024-005-0031-9
Maeda T, Sato H, 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 172:130–154, DOI 10.1111/j.1365-246X.2007.03603.x
Maeda T, Obara K, Yukutake Y (2010) Seismic velocity decrease and recovery related to earthquake swarms in a geothermal area. Earth Planets Space 62(9):685–691, DOI 10.5047/eps.2010.08.006
Malin PE (1980) A first order scattering solution for modeling elastic wave codas - I. The acoustic case. Geophys J R Astron Soc 63:361–380, DOI 10.1111/j.1365-246X.1980. tb02626.x
Malin PE, Phinney RA (1985) On the relative scattering of P- and S-waves. Geophys J R Astron Soc 80:603–618, DOI 10.1111/j.1365-246X.1985.tb05113.x
Manghnani MH, Ramananantoandro R, S P Clark J (1974) Compressional and shear wave velocities in granulite faces rocks and eclogites to 10 kb. J Geophys Res 79:5427–5446, DOI 10.1029/JB079i035p05427
Margerin L (2005) Introduction to radiative transfer of seismic waves, in “Seismic Earth: Array Analysis of Broadband Seismograms” (Eds. A. Levander and G. Nolet), vol 157, Geophysical Monograph-Ameerican Geophysical Union, pp 229–252
Margerin L (2006) Attenuation, transport and diffusion of scalar waves in textured random media. Tectonophysics 416(1-4):229–244
Margerin L (2008) Coherent Back-Scattering and Weak Localization of Seismic Waves. In: Sato H, Fehler MC (eds) Earth heterogeneity and scattering effects on seismic waves, advances in geophysics (Series Ed. R. Dmowska), vol 50, Academic Press, New York, Chap. 1, pp 1–20
Margerin L, Nolet G (2003b) 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, DOI 10.1029/2003JB002455
Margerin L, Nollet G (2003a) Multiple scattering of high-frequency seismic in the deep Earth:Modeling and numerical examples. J Geophys Res 108(B5):2234, DOI 10.1029/ 2002JB001974
Margerin L, Sato H (2011a) Reconstruction of multiply-scattered arrivals from the cross-correlation of waves excited by random noise sources in a a heterogeneous dissipative medium. Wave Motion 48:146–160, DOI 10.1016/j.wavemoti.2010.10.001
Margerin L, Sato H (2011b) Generalized optical theorems for the reconstruction of Green’s function of an inhomogeneous elastic medium. J. Acoust. Soc. Am. in press, DOI 10.1121/1.3652856
Margerin L, Campillo M, Van Tiggelen BA (1998) Radiative transfer and diffusion of waves in a layered medium: new insight into coda Q. Geophys J Int 134(2):596–612
Margerin L, Campillo M, Shapiro NM, Van Tiggelen B (1999) Residence time of diffuse waves in the crust as a physical interpretation of coda Q: application to seismograms recorded in Mexico. Geophys J Int 138(2):343–352, DOI 10.1046/j.1365-246X.1999. 00897.x
Margerin L, Campillo M, Tiggelen BV (2000) Monte Carlo simulation of multiple scattering of elastic waves. J Geophys Res 105:7873–7893, DOI 10.1029/1999JB900359
Matsumoto S, Hasegawa A (1996) Distinct S wave reflector in the midcrust beneath Nikko-Shirane volcano in the northeastern Japan arc. J Geophys Res 101:3067–3083, DOI 10.1029/95JB02883
Matsumoto S, Obara K, Yoshimoto K, Saito T, Hasegawa A, Ito A (1999) Imaging of crustal inhomogeneous structure of the crust beneath Ou Backbone Range, northeastern Japan, based on small aperture seismic array obsevations. Zisin (in Japanese) 52:293–297
Matsumura S (1981) Three-dimensional expression of seismic particle motions by the trajectory ellipsoid and its application to the seismic data observed in the Kanto district, Japan. J Phys Earth 29:221–239
Matsunami K (1990) Laboratory measurements of spatial fluctuation and attenuation of elastic waves by scattering due to random heterogeneities. Pure Appl Geophys 132:197–220, DOI 10.1007/BF00874363
Matsunami K (1991) Laboratory tests of excitation and attenuation of coda waves using 2-D models of scattering media. Phys Earth Planet Inter 67:36–47, DOI 10.1016/ 0031-9201(91)90058-P
Mavko G, Kjartansson E, Winkler K (1979) Seismic wave attenuation in rocks. Rev Geophys Space Phys 17:1155–1164, DOI 10.1029/RG017i006p01155
Mavko GM, Nur A (1979) Wave attenuation in partially saturated rocks. Geophysics 44:161–178, DOI 10.1190/1.1440958
Mayeda K, Walter WR (1996) Moment, energy, stress drop, and source spectra of western United States earthquakes from regional coda envelopes. J Geophys Res 101:11,195–11,208, DOI 10.1029/96JB00112
Mayeda K, Koyanagi S, Hoshiba M, Aki K, 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 97:6643–6659, DOI 10.1029/91JB03094
McLaughlin KL, Anderson LM (1987) Stochastic dispersion of short-period P-waves due to scattering and multipathing. Geophys J R Astron Soc 89:933–963, DOI 10.1111/j. 1365-246X.1987.tb05202.x
Menke W (1984a) Asymptotic formulas for the apparent Q of weakly scattering three-dimensional media. Bull Seism Soc Am 74:1079–1081
Menke W (1984b) Geophysical data analysis: discrete inverse theory. Academic Press, New York
Menke W, Chen R (1984) Numerical studies of the coda falloff rate of multiply scattered waves in randomly layered media. Bull Seism Soc Am 74:1605–1614
Mikada H, Watanabe H, Sakashita S (1997) Evidence for subsurface magma bodies beneath Izu-Oshima volcano inferred from a seismic scattering analysis and possible interpretation of the magma plumbing system of the 1986 eruptive activity. Phys Earth Planet Inter 104:257–269, DOI 10.1016/S0031-9201(97)00060-5
Miles JW (1960) Scattering of elastic waves by small inhomogeneities. Geophysics 15:642–648, DOI 10.1190/1.1438745
Mishchenko M, Travis L, Lacis A (2006) Multiple scattering of light by particles: Radiative transfer and coherent backscattering. Cambridge University Press, Cambridge
Mitchell BJ (1995) Anelastic structure and evolution of the continental crust and upper mantle from seismic surface wave attenuation. Rev Geophys 33:441–462, DOI 10.1029/ 95RG02074
Modiano T, Hatzfeld D (1982) Experimental study of the spectral content for shallow earthquakes. Bull Seism Soc Am 72:1739–1758
Mohorovičić A (1909) Das Beben vom 8. X. Jahrb Meterol Obs Zagreb 9:1–63
Mooney W (1989) Seismic methods for determining earthquake source parameters and lithospheric structure, in Geophysical Framework of the Continental United States (eds., L. Pakiser and W. Mooney), Geol. Soc. Am. Memoir 172, Geological Society of America, Boulder, Colo., pp 11–34
Mora P (1992) The lattice Boltzman phononic lattice solid. J Stat Phys 68:591–609, DOI 10.1007/BF01341765
Mori J, Frankel A (1992) Correlation of P wave amplitudes and travel time residuals for teleseisms recorded on the southern California seismic network. J Geophys Res 97:6661–6674, DOI 10.1029/91JB02578
Mori J, Shimazaki K (1985) Inversion of intermediate-period Rayleigh waves for source characteristics of the 1968 Tokachi-Oki earthquake. J Geophys Res 90:11,374–11,382, DOI 10.1029/JB090iB13p11374
Morse PM, Feshbach H (1953) Methods of theoretical physics, vols. I and II. McGraw-Hill, New York
Müller G, Roth M, Korn M (1992) Seismic wave traveltimes in random media. Geophys J Int 110:29–41, DOI 10.1111/j.1365-246X.1992.tb00710.x
Murai Y, Kawahara J, Yamashita T (1995) Multiple scattering of SH waves in 2-D elastic media with distributed cracks. Geophys J Int 122:925–937, DOI 10.1111/j.1365-246X. 1995.tb06846.x
Nakahara H (2006b) A systematic study of theoretical relations between spatial correlation and Green’s function in one-, two-and three-dimensional random scalar wavefields. Geophys J Int 167(3):1097–1105, DOI 10.1111/j.1365-246X.2006.03170.x
Nakahara H (2008) Seismogram envelope inversion for high-frequency seismic energy radiation from moderate-to-large earthquakes. In: Sato H, Fehler MC (eds) Earth heterogeneity and scattering effects on seismic waves, advances in geophysics (Series Ed. R. Dmowska), vol 50, Academic Press, New York, Chap. 15, pp 402–426
Nakahara H, Nishimura T, Sato H, 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 103:855–867, DOI 10.1029/97JB02676
Nakajima J, Hasegawa A (2003) Estimation of thermal structure in the mantle wedge of northeastern Japan from seismic attenuation data. Geophys Res Lett 30(14):1760, DOI 10.1029/2003GL017185
Nakamura Y (1977a) Seismic energy transmission in an intensively scattering environment. J Geophys 43:389–399
Nakamura Y (1977b) HFT events: Shallow moonquakes? Phys Earth Planet Inter 14:217–223, DOI 10.1016/0031-9201(77)90174-1
Neidell NS, Taner MT (1971) Semblance and other coherency measures for multi-channel data. Geophysics 36:482–497, DOI 10.1190/1.1440186
Nielsen L, Thybo H (2003) The origin of teleseismic Pn waves: Multiple crustal scattering of upper mantle whispering gallery phases. J Geophysical Res 108(B10):2460
Nikolaev AV (1975) The Seismics of Heterogeneous and Turbid Media (Engl. trans. by R. Hardin). Israel Program for Science translations, Jerusalem
Nishigami K (1991) A new inversion method of coda waveforms to determine spatial distribution of coda scatterers in the crust and uppermost mantle. Geophys Res Lett 18:2225–2228, DOI 10.1029/91GL02823
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 105:7983–7998, DOI 10.1029/1999JB900381
Nishimura T, Nakahara H, Sato H, Ohtake M (1996) Source process of the 1994 far east off Sanriku earthquake, Japan, as inferred from a broad-band seismogram. Sci Rep Tohoku Univ 34: 121–134
Nishimura T, Fehler M, Baldridge W, Roberts P, Steck L (1997) Heterogeneous structure around the Jemez Volcanic field, New Mexico, USA, as inferred from envelope inversion of active experiment seismic data. Geophys J Int 131:667–681, DOI 10.1111/j.1365-246X.1997. tb06605.x
Nishimura T, Yoshimoto K, Ohtaki T, Kanjo K, Purwana I (2002) Spatial distribution of lateral heterogeneity in the upper mantle around the western Pacific region as inferred from analysis of transverse components of teleseismic P-coda. Geophys Res Lett 29(23):2137, DOI 10.1029/2002GL015606
Nishimura T, Tanaka S, Yamawaki T, Yamamoto H, Sano T, Sato M, Nakahara H, Uchida N, Hori S, Sato H (2005) Temporal changes in seismic velocity of the crust around Iwate volcano, Japan, as inferred from analyses of repeated active seismic experiment data from 1998 to 2003. Earth Planets Space 57(6):491–505
Nishizawa O, Fukushima Y (2008) Laboratory Experiments of Seismic Wave Propagation in Random Heterogeneous Media. In: Sato H, Fehler M (eds) Earth Heterogeneity and Scattering Effects on Seismic Waves, Advances in Geophysics (Series Ed. R. Dmowska), vol 50, Academic Press, New York, Chap. 8, pp 219–246
Nishizawa O, Pearson C, Albright J (1983) Properties of seismic wave scattering around water injection well at Fenton Hill hot dry rock geothermal site. Geophys Res Lett 10:101–104, DOI 10.1029/GL010i001p00101
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
Nolet G (1987) Seismic wave propagation and seismic tomography, in Seismic Tomography (ed. G. Nolet), D. Reidel, Boston, pp 11–23
Novelo-Casanova DA, Berg E, Hsu V, Helsley E (1985) Time-space variations of seismic S-wave coda attenuation Qc − 1 and magnitude distribution (b-value) for the Petatlan earthquake. Geophys Res Lett 12:789–792, DOI 10.1029/GL012i011p00789
Nur A (1971) Viscous phase in rocks and the low-velocity zone. J Geophys Res 76:1270–1277, DOI 10.1029/JB076i005p01270
Nur A, Simmons G (1969) The effect of saturation on velocity in low porosity rocks. Earth Planet Sci Lett 7:183–193, DOI 10.1016/0012-821X(69)90035-1
Obara K (1989) Regional extent of the S wave reflector beneath the Kanto district, Japan. Geophys Res Lett 16:839–842, DOI 10.1029/GL016i008p00839
Obara K (2002) Nonvolcanic deep tremor associated with subduction in sourthwest Japan. Science 296(5573):1679–1681, DOI 10.1126/science.1070378
Obara K, Maeda T (2009) Reverse propagation of T waves from the Emperor seamount chain. Geophys Res Lett 36:L08304, DOI 10.1029/2009GL037454
Obara K, Sato H (1988) Existence of an S wave reflector near the upper plane of the double seismic zone beneath the southern Kanto district, Japan. J Geophys Res 93:15,037–15,045, DOI 10.1029/JB093iB12p15037
Obara K, 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 100:2103–2121, DOI 10.1029/94JB02644
O’Connell RJ, Budiansky B (1977) Viscoelastic properties of fluid-saturated cracked solids. J Geophys Res 82:5719–5735, DOI 10.1029/JB082i036p05719
Ojeda A, Ottemöller L (2002) Q Lg tomography in Colombia. Phys Earth Planet Inter 130:253–270, DOI 10.1016/ S0031-9201(02)00010-9
Okal EA (2008) The generation of T waves by earthquakes. In: Advances in Geophysics, vol 49, Academic Press, New York, pp 1–58
Olson AH, Anderson JG (1988) Implications of frequency-domain inversion of earthquake ground motions for resolving the space-time dependence of slip on an extended fault. Geophys J Int 94:443–455, DOI 10.1111/j.1365-246X.1988.tb02267.x
Ordaz M, Singh SK (1992) Source spectra and spectral attenuation of seismic waves from Mexican earthquakes, and evidence of amplification in the hill zone of Mexico city. Bull Seism Soc Am 82:24–43
Paasschens JCJ (1997) Solution of the time-dependent Boltzmann equation. Phys Rev E 56(1):1135–1141, DOI 10.1103/PhysRevE.56.1135
Padhy S (2009) Characteristics of body-wave attenuation in the Bhuj crust. Bull Seism Soc Am 99:3300–3313, DOI 10.1785/0120080337
Papanicolaou GC, Ryzhik LV, Keller JB (1996) Stability of the P to S wave energy ratio in the diffusive regime. Bull Seism Soc Am 86:1107–1115
Pavlenko O, Irikura K (2002) Changes in shear moduli of liquefied and nonliquefied soils during the 1995 Kobe earthquake and its aftershocks at three vertical-array sites. Bull Seism Soc Am 92(5):1952, DOI 10.1785/0120010143
Peng Z, Ben-Zion Y (2006) Temporal changes of shallow seismic velocity around the Karadere-Düzce branch of the north Anatolian fault and strong ground motion. Pure Appl Geophysics 163(2):567–600
Perry F, Baldridge WS, DePaolo DJ, Shafiqullah M (1990) Evolution of a magmatic system during continental extension: The Mount Taylor volcanic field, New Mexico. J Geophys Res 95:19,327–19,348, DOI 10.1029/JB095iB12p19327
Petukhin A, Gusev A (2003) The duration-distance relationship and average envelope shapes of small Kamchatka earthquakes. Pure Appl Geophys 160(9):1717–1743, DOI 10.1007/s00024-003-2373-5
Phillips WS, Aki K (1986) Site amplification of coda waves from local earthquakes in central California. Bull Seism Soc Am 76:627–648
Phillips WS, Stead RJ, Randall GE, Hartse HE, MMayeda K (2008) Source Effects From Broad Area Network Calibration of Regional Distance Coda Waves. In: Sato H, Fehler MC (eds) Earth heterogeneity and scattering effects on seismic waves, advances in geophysics (Series Ed. R. Dmowska), vol 50, Academic Press, Chap. 12, pp 319–352
Poupinet G, Kennett B (2004) On the observation of high frequency PKiKP and its coda in Australia. Phys Earth Planet Inter 146(3-4):497–511, DOI 10.1016/j.pepi.2004.05.003
Poupinet G, Ellsworth VL, Frechet J (1984) Monitoring velocity variations in the crust using earthquake doublets: An application to the Calaveras fault, California. J Geophys Res 89:5719–5732, DOI 10.1029/JB089iB07p05719
Poupinet G, GOT J, Brenguier F (2008) Monitoring Temporal Variations of Physical Properties in the Crust by Cross-Correlating the Waveforms of Seismic Doublets. In: Sato H, Fehler MC (eds) Earth heterogeneity and scattering effects on seismic waves, advances in geophysics (Series Ed. R. Dmowska), vol 50, Academic Press, New York, Chap. 14, pp 374–401
Powell CA, Meltzer AS (1984) Scattering of P-waves beneath SCARLET in southern California. Geophys Res Lett 11:481–484, DOI 10.1029/GL011i005p00481
Pratt R (1999) Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model. Geophysics 64(3):888–901, DOI 10.1190/1. 1444597
Press F (1966) Seismic Velocities, in Handbook of Physical Constants (ed., S. P. Clark), Geol. Soc. Am. Memoir 97, Geological Society of America, New York, pp 195–218
Prokhorov A, Bunkin F, Gochelashvily K, Shishov V (1975) Laser irradiance propagation in turbulent media. Proc IEEE 63(5):790–811, DOI 10.1109/PROC.1975.9828
Przybilla J, 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, DOI 10.1111/j.1365-246X.2008.03747.x
Przybilla J, Korn M, Wegler U (2006) Radiative transfer of elastic waves versus finite difference simulations in two-dimensional random media. J Geophys Res 111, DOI 10. 1029/2005JB003952
Przybilla J, Wegler U, Korn M (2009) Estimation of crustal scattering parameters with elastic radiative transfer theory. Geophys J Int 178(2):1105–1111, DOI 10.1111/j. 1365-246X.2009.04204.x
Pujol J (1996) An integrated 3D velocity inversion - joint hypocentral determination relocation analysis of events in the Northridge area. Bull Seism Soc Am 86:s138–s155
Radon J (1917) Uber die bestimmung von funktionen durch ihre integralwerte langs gewisser mannigfaltigkeiten. Ber Verh Sachs Akad Wiss Leipzig, Math Phys Kl 69:262–267
Raoof M, Hermann RB, Malagnini L (1999) Attenuation and Excitation of Three-Component Ground Motion in Southern California. Bull Seism Soc Am 89:888–902
Ratdomopurdo A, Poupinet G (1995) Monitoring a temporal change of seismic velocity in a volcano: application to the 1992 eruption of Mt. Merapi (Indonesia). Geophys Res Lett 22(7):775–778, DOI 10.1029/95GL00302
Rautian TG, Khalturin VI (1978) The use of the coda for determination of the earthquake source spectrum. Bull Seism Soc Am 68:923–948
Rautian TG, Khalturin VI, Martinov VG, Molnar P (1978) Preliminary analysis of the spectral content of P and S waves from local earthquakes in the Garm, Tadjikistan region. Bull Seism Soc Am 68:949–971
Rautian TG, Khalturin VI, Zakirov MS, Zemchova AG, Proskurin AP, Pustovitenko BG, Pustovitenko AN, Sinelinikova LG, Filina AG, Tchengelia IS (1981) Experimental Studies of Seismic Coda (in Russian). Nauka, Moscow
Revenaugh J (1995a) The contribution of topographic scattering to teleseismic coda in Southern California. Geophys Res Lett 22(5):543–546, DOI 10.1029/95GL00162
Revenaugh J (1995b) A scattered-wave image of subduction beneath the Transverse Ranges. Science 268(5219):1888–1892, DOI 10.1126/science.268.5219.1888
Richtmyer R (1978) Principles of advances mathematical physics. Springer, New York
Roecker SW, Tucker B, King J, Hatzfeld D (1982) Estimation of Q in central Asia as a function of frequency and depth using the coda of locally recorded earthquakes. Bull Seism Soc Am 72:129–149
Rondenay S, Bostock M, Shragge J (2001) Multiparameter two-dimensional inversion of scattered teleseismic body waves 3. Application to the Cascadia 1993 data set. J Geophys Res 106(30):795–808, DOI 10.1029/2000JB000039
Roth M (1997) Statistical interpretation of traveltime fluctuations. Phys Earth Planet Inter 104:213–228, DOI 10.1016/S0031-9201(97)00048-4
Roth M, Korn M (1993) Single scattering theory versus numerical modelling in 2-D random media. Geophys J Int 112:124–140, DOI 10.1111/j.1365-246X.1993.tb01442.x
Roth M, Müller G, Snieder R (1993) Velocity shift in random media. Geophys J Int 115:552–563, DOI 10.1111/j.1365-246X.1993.tb01206.x
Rothman D (1988) Cellular-automaton fluids: A model for flow in porous media. Geophysics 53:509–518, DOI 10.1190/1.1442482
Roux P, Sabra K, Kuperman W, Roux A (2005a) Ambient noise cross correlation in free space: Theoretical approach. J Acoust Soc Am 117:79–84, DOI 10.1121/1.1830673
Roux P, Sabra KG, Gerstoft P, Kuperman WA, Fehler MC (2005b) P-waves from cross-correlation of seismic noise. Geophys Res Lett 32, DOI 10.1029/2005GL023803
Rovelli A (1983) Frequency relationship for seismic Q of central southern Italy from accelerograms for the Irpinia earthquake (1980). Phys Earth Planet Inter 32:209–217, DOI 10.1016/0031-9201(83)90126-7
Rovelli A (1984) Seismic Q for the lithosphere of the Montenegro region (Yugoslavia): Frequency, depth and time windowing effect. Phys Earth Planet Inter 34:159–172, DOI 10.1016/0031-9201(84)90004-9
Rubinstein J, Beroza G (2004) Evidence for widespread nonlinear strong ground motion in the Mw 6.9 Loma Prieta earthquake. Bull Seism Soc Am 94(5):1595, DOI 10.1785/ 012004009
Rubinstein J, Beroza G (2005) Depth constraints on nonlinear strong ground motion from the 2004 Parkfield earthquake. Geophys Res Lett 32(14):L14,313, DOI 10.1029/ 2005GL023189
Rubinstein J, Uchida N, Beroza G (2007) Seismic velocity reductions caused by the 2003 Tokachi-Oki earthquake. J Geophys Res 112(B5):B05,315, DOI 10.1029/2006JB004440
Rytov SM, Kravstov YA, Tatarskii VI (1989) Principles of statistical radiophysics (Vol. 4) Wave propagation through random media. Springer-Verlag, Berlin
Ryzhik LV, Papanicolaou GC, Keller JB (1996) Transport equations for elastic and other waves in random media. Wave Motion 24:327–370, DOI 10.1016/S0165-2125(96) 00021-2
Sabra K, Gerstoft P, Roux P, Kuperman W, Fehler M (2005a) Extracting time-domain Green’s function estimates from ambient seismic noise. Geophys Res Lett 32:L03310, DOI 10.1029/2004GL021862
Sabra K, Gerstoft P, Roux P, Kuperman W, Fehler M (2005b) Surface wave tomography from microseisms in Southern California. Geophys Res Lett 32:L14311, DOI 10.1029/ 2005GL023155
Sahin S, Erduran M, Alptekin O, Cakir O (2007) Intrinsic and scattering seismic attenuation in southewestern Anatolia. Pure Appl Geophys 164:2255–2270, DOI 10. 1007/s00024-007-0263-y
Saito T (2006a) Synthesis of scalar-wave envelopes in two-dimensional weakly anisotropic random media by using the Markov approximation. Geophys J Int 165(2):501–515, DOI 10.1111/j.1365-246X.2006.02896.x
Saito T (2006b) Velocity shift in two-dimensional anisotropic random media using the Rytov method. Geophys J Int 166:293–308, DOI 10.1111/j.1365-246X.2006.02976.x
Saito T, Sato H, Ohtake M (2002) Envelope broadening of spherically outgoing waves in three-dimensional random media having power-law spectra. J Geophys Res 107(10.1029), DOI 10.1029/2001JB000264
Saito T, Sato H, Fehler M, Ohtake M (2003) Simulating the envelope of scalar waves in 2D random media having power-law spectra of velocity fluctuation. Bull Seism Soc Am 93(1):240–252, DOI 10.1785/0120020105
Saito T, Sato H, Ohtake M, 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: Forearc side of the volcanic front in northeastern Honshu, Japan. J Geophys Res 110, DOI 10.1029/2004JB003225
Saito T, Sato H, 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 3:63–84
Samuelides Y (1998) Velocity shift using the Rytov approximation. J Acoust Soc Am 104:2596
Sanchez-Sesma F, Campillo M (2006) Retrieval of the Green’s function from cross correlation: the canonical elastic problem. Bull Seism Soc Am 96(3):1182, DOI 10. 1785/0120050181
Sanford A, Long LT (1965) Microearthquake crustal reflections, Socorro, New Mexico. Bull Seism Soc Am 55:579–586
Sato H (1977a) Energy propagation including scattering effects: Single isotropic scattering approximation. J Phys Earth 25:27–41
Sato H (1977b) Single isotropic scattering model including wave conversions: Simple theoretical model of the short period body wave propagation. J Phys Earth 25:163–176
Sato H (1978) Mean free path of S-waves under the Kanto district of Japan. J Phys Earth 26:185–198
Sato H (1979) Wave propagation in one dimensional inhomogeneous elastic media. J Phys Earth 27:455–466
Sato H (1982a) Amplitude attenuation of impulsive waves in random media based on travel time corrected mean wave formalism. J Acoust Soc Am 71:559–564, DOI 10.1121/1. 387525
Sato H (1982b) Attenuation of S waves in the lithosphere due to scattering by its random velocity structure. J Geophys Res 87:7779–7785, DOI 10.1029/JB087iB09p07779
Sato H (1984a) Attenuation and envelope formation of three-component seismograms of small local earthquakes in randomly inhomogeneous lithosphere. J Geophys Res 89:1221–1241, DOI 10.1029/JB089iB02p01221
Sato H (1984b) Scattering and attenuation of seismic waves in the lithosphere: Single scattering theory in a randomly inhomogeneous lithosphere (in Japanese). Rep Nat Res Ctr Disast Prev 33:101–186
Sato H (1986) Temporal change in attenuation intensity before and after the eastern Yamanashi earthquake of 1983 in central Japan. J Geophys Res 91:2049–2061, DOI 10. 1029/JB091iB02p02049
Sato H (1987) A precursorlike change in coda excitation before the western Nagano earthquake (Ms=6.8) of 1984 in central Japan. J Geophys Res 92:1356–1360, DOI 10. 1029/JB092iB02p01356
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 126:465–497, DOI 10.1007/BF00879007
Sato H (1989) Broadening of seismogram envelopes in the randomly inhomogeneous lithosphere based on the parabolic approximation: Southeastern Honshu, Japan. J Geophys Res 94:17,735–17,747, DOI 10.1029/JB094iB12p17735
Sato H (1990) Unified approach to amplitude attenuation and coda excitation in the randomly inhomogeneous lithosphere. Pure Appl Geophys 132:93–121, DOI 10.1007/ BF00874359
Sato H (1991a) Study of seismogram envelopes based on scattering by random inhomogeneities in the lithosphere: A review. Phys Earth Planet Inter 67:4–19, DOI 10. 1016/0031-9201(91)90056-N
Sato H (ed) (1991b) Scattering and attenuation of seismic waves. Phys. Earth Planet. Inter. 67:1–210
Sato H (1993) Energy transportation in one- and two-dimensional scattering media: Analytic solutions of the multiple isotropic scattering model. Geophys J Int 112:141–146, DOI 10.1111/j.1365-246X.1993.tb01443.x
Sato H (1994a) Multiple isotropic scattering model including P-S conversions for the seismogram envelope formation. Geophys J Int 117:487–494, DOI 10.1111/j.1365-246X. 1994.tb03946.x
Sato H (1995a) Formulation of the multiple non-isotropic scattering process in 3-D space on the basis of energy transport theory. Geophys J Int 121:523–531, DOI 10.1111/j. 1365-246X.1995.tb05730.x
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):B06,306, DOI 10.1029/ 2005JB004036
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):B01,301, DOI 10.1029/ 2006JB004437
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):B08,304, DOI 10.1029/2007JB005524
Sato H (2009a) Retrieval of Green’s function having coda from the cross-correlation function in a scattering medium illuminated by surrounding noise sources on the basis of the first order Born approximation. Geophys J Int 179(1):408–412, DOI 10.1111/j. 1365-246X.2009.04296.x
Sato H (2009b) Green’s function retrieval from the CCF of coda waves in a scattering medium. Geophys J Int 179:1580–1583, DOI 10.1111/j.1365-246X.2009.04398.x
Sato H (2010) Retrieval of Green’s function having coda waves from the cross-correlation function in a scattering medium illuminated by a randomly homogeneous distribution of noise sources on the basis of the first order Born approximation. Geophys J Int 180:759–764, DOI 10.1111/j.1365-246X.2009.04432.x
Sato H, Fehler M (1998) Seismic wave propagation and scattering in the heterogeneous earth. AIP Press/Springer, New York
Sato H, Fehler M (2007) Synthesis of seismigram envelopes in heterogeneous media. In: Wu R, Maupin V (eds) Advances in wave propagation in heterogeneous earth, advances in geophysics (Series Ed.: R. Dmowska), vol 48, Academic Press, New York, Chap. 10, pp 561–596
Sato H, Fehler M (eds) (2008) Advances in geophysics (Series Ed.: R. Dmowska): Earth heterogeneity and scattering effects on seismic waves, vol 50. Academic Press, New York
Sato H, Korn M (2007) Envelope syntheses of cylindrical vector-waves in 2-D random elastic media based on the Markov approximation. Earth Planets Space 59:4209–219
Sato H, Korn M (2008) Synthesis of vector-wave envelopes in random elastic media on the basis of the Markov approximation. In: Sato H, Fehler MC (eds) Earth heterogeneity and scattering effects on seismic waves, advances in geophysics (Series Ed. R. Dmowska), vol 50, Academic Press, New York, Chap. 3, pp 43– 94
Sato H, Matsumura S (1980) Q − 1 value for S-waves (2-32 Hz) under the Kanto district in Japan. Zisin (in Japanese) 33:541–543
Sato H, Nishino M (2002) Multiple isotropic-scattering model on the spherical Earth for the synthesis of Rayleigh-wave envelopes. J Geophys Res 107(B12):2343, DOI 10.1029/ 2001JB000915
Sato H, Nohechi M (2001) Envelope formation of long-period Rayleigh waves in vertical component seismograms: Single isotropic scattering model. J Geophys Res 106:6589–6594, DOI 10.1029/2000JB900383
Sato H, Nakahara H, Ohtake M (1997) Synthesis of scattered energy density for non-spherical radiation from a point shear dislocation source based on the radiative transfer theory. Phys Earth Planet Inter 104:1–13, DOI 10.1016/S0031-9201(97) 00050-2
Sato H, Fehler M, Saito T (2004) Hybrid synthesis of scalar wave enveloopes in two-dimensional random media having rich short-wavelength spectra. J Geophys Res 109:B06303, DOI 10.1029/2003JB002673
Savage JC (1965) Attenuation of elastic waves in granular medium. J Geophys Res 70:3935–3942, DOI 10.1029/JZ070i016p03935
Savage JC (1966) Thermoelastic attenuation of elastic waves by cracks. J Geophys Res 71:3929–3938, DOI 10.1029/JZ071i016p03929
Sawazaki K, Sato H, Nakahara H, Nishimura T (2006) Temporal change in site response caused by earthquake strong motion as revealed from coda spectral ratio measurement. Geophys Res Lett 33(L21303), DOI 10.1029/2006GL027938
Sawazaki K, Sato H, Nakahara H, Nishimura T (2009) Time-lapse changes of seismic velocity in the shallow ground caused by strong ground motion shock of the 2000 Western-Tottori earthquake, Japan, as revealed from coda deconvolution analysis. Bull Seism Soc Am 99(1):352, DOI 10.1785/0120080058
Scherbaum F, Sato H (1991) Inversion of full seismogram envelopes based on the parabolic approximation: Estimation of randomness and attenuation in southeast Honshu, Japan. J Geophys Res 96:2223–2232, DOI 10.1029/90JB01538
Scherbaum F, Gillard D, Deichmann N (1991) Slowness power spectrum analysis of the coda composition of two microearthquake clusters in northern Switzerland. Phys Earth Planet Inter 67:137–161, DOI 10.1016/0031-9201(91)90067-R
Schilt S, Oliver J, Brown L, Kaufman S, Albauch D, Brewer J, Cook F, Jensen L, Krumhansl P, Long G, Steiner D (1979) The heterogeneity of the continental crust: Results from deep crustal reflection profiling using the Vibroseis technique. Rev Geophys Space Phys 17:354–368, DOI 10.1029/RG017i002p00354
Schneider WA (1978) Integral formulation for migration in two and three dimensions. Geophysics 43:49–76, DOI 10.1190/1.1440828
Schuster GT (2009) Seismic interferometry. Cambridge University Press, Cambridge, UK
Sens-Schönfelder C, Wegler U (2006) Radiative transfer theory for estimation of the seismic moment. Geophys J Int 167:1363–1372, DOI 10.1111/j.1365-246X.2006.03139.x
Sens-Schönfelder C, Margerin L, Campillo M (2009) Laterally heterogeneous scattering explains Lg blockage in the Pyrenees. J Geophys Res 114:B07,309, DOI 10.1029/ 2008JB006107
Shang T, Gao L (1988) Transportation theory of multiple scattering and its application to seismic coda waves of impulsive source. Scientia Sinica (series B, China) 31:1503–1514
Shapiro NM, Campillo M, Stehly L, Ritzwoller MH (2005) High-resolution surface-wave tomography from ambient seismic noise. Science 307(11):1615–1618, DOI 10.1126/ science.1108339
Shapiro S, Hubral P (1999) Elastic waves in random media. Lecture Notes in Earth Sciences, Springer, Berlin 80
Shapiro SA, Kneib G (1993) Seismic attenuation by scattering: Theory and numerical results. Geophys J Int 114:373–391, DOI 10.1111/j.1365-246X.1993.tb03925.x
Shapiro SA, Schwarz R, Gold N (1996) The effect of random isotropic inhomogeneities on the phase velocity of seismic waves. Geophys J Int 127:783–794, DOI 10.1111/j. 1365-246X.1996.tb04057.x
Shearer P (2007) Seismic scattering in the deep Earth. Treatise on geophysics, vol 1: Deep Earth Structure, Schubert, G (ed) pp 695–730
Shearer PM, Earle PS (2004) The global short-period wavefield modelled with a Monte Carlo seismic phonon method. Geophys J Int 158:1103–1117, DOI 10.1111/j. 1365-246X.2004.02378.x
Shearer PM, Earle PS (2008) Observing and Modeling Elastic Scattering in the Deep Earth. In: Sato H, Fehler MC (eds) Earth heterogeneity and scattering effects on seismic waves, advances in geophysics (Series Ed. R. Dmowska), vol 50, Academic Press, New York, Chap. 6, pp 167–195
Sheng P (2006) Introduction to wave scattering, localization and mesoscopic phenomena. Springer, Berlin
Shiomi K, Sato H, Ohtake M (1997) Broad-band power-law spectra of well-log data in Japan. Geophys J Int 130:57–64, DOI 10.1111/j.1365-246X.1997.tb00987.x
Shiomi K, Sato H, Obara K, Ohtake M (2004) Configuration of subducting Philippine Sea plate beneath southwest Japan revealed from receiver function analysis based on the multivariate autoregressive model. J Geophys Res 109(B4):B04,308, DOI 10.1029/ 2003JB002774
Shiomi K, Matsubara M, Ito Y, Obara K (2008) Simple relationship between seismic activity along Philippine Sea slab and geometry of oceanic Moho beneath southwest Japan. Geophys J Int 173:1018–1029, DOI 10.1111/j.1365-246X.2008.03786.x
Shishov VI (1974) Effect of refraction on scintillation characteristics and average pulse shape of pulsars. Sov Astron 17:598–602
Shriner JF, Thompson WJ (1993) Angular momentum coupling coefficients: New and improved algorithm. Comp Phys 7:144–148
Simmons G, Nur A (1968) Granites - Relation of properties in situ to laboratory measurements. Science 162:789–791, DOI 10.1126/science.162.3855.789
Simmons G, Wang H (1971) Single crystal elastic constants and calculated aggregate properties: a handbook. MIT Press, Cambridge, Mass.
Singh S, Herrmann RB (1983) Regionalization of crustal coda Q in the continental United States. J Geophys Res 88:527–538, DOI 10.1029/JB088iB01p00527
Singh SK, Apsel RJ, Fried J, Brune JN (1982) Spectral attenuation of SH waves along the Imperial fault. Bull Seism Soc Am 72:2003–2016
Sivaji C, Nishizawa O, Kitagawa G, 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, DOI 10.1046/j.1365-246x.2002.01606.x
Snieder R (1986a) The influence of topography on the propagation and scattering of surface waves. Phys Earth Planet Inter 44:226–241, DOI 10.1016/0031-9201(86)90072-5
Snieder R (2004a) Extracting the Green’s function from the correlation of coda waves: A derivation based on stationary phase. Phys Rev E 69:046610, DOI 10.1103/PhysRevE. 69.046610
Snieder R, Fleury C (2010) Cancellation of spurious arrivals in the Green’s function retrieval of multiple scattered waves. J Acoust Soc Am 128:1598–1605, DOI 10.1121/ 1.348372
Snieder R, Grêt A, Douma H, Scales J (2002) Coda wave interferometry for estimating nonlinear behavior in seismic velocity. Science 295(5563):2253–2255, DOI 10.1126/ science.1070015
Snieder R, Wapenaar K, Wegler U (2007) Unified Green’s function retrieval by cross-correlation; connection with energy principles. Phys Rev E 75(3):36,103, DOI 10. 1103/PhysRevE.75.036103
Snieder R, Sánchez-Sesma FJ, Wapenaar K (2009) Field fluctuations, imaging with backscattered waves, a generalized energy theorem, and the optical theorem. SIAM J Img Sci 2:763–776
Solov’ev SL (1965) Seismicity of sakhalin. Bull Earthq Res Inst Univ Tokyo 43:95–102
Souriau A (2007) Deep Earth structure - The Earth’s cores. In: Dziewonski A, Romanowicz B (eds) Seismology and Structure of the Earth, Treatise on Geophysics (Ed. G. Schubert), vol 1, Academic Press, New York, Chap. 1.19, pp 655–693
Spencer JJW (1981) Stress relaxation at low frequencies in fluid-saturated rocks: Attenuation and modulus dispersion. J Geophys Res 86:1803–1812, DOI 10.1029/ JB086iB03p01803
Spudich P, Bostwick T (1987) Studies of the seismic coda using an earthquake cluster as a deeply buried seismograph array. J Geophys Res 92:10,526–10,546, DOI 10.1029/ JB092iB10p10526
Sreenivasiah I, Ishimaru A, Hong ST (1976) Two-frequency mutual coherence function and pulse propagation in a random medium: An analytic solution to the plane wave case. Radio Sci 11:775–778, DOI 10.1029/RS011i010p00775
Stehly L, Campillo M, Froment B, Weaver R (2008) Reconstructing Green’s function by correlation of the coda of the correlation (C3) of ambient seismic noise. J Geophys Res 113:B11,306, DOI 10.1029/2008JB005693
Su F, Aki K, Biswas N (1991) Discriminating quarry blasts from earthquakes using coda waves. Bull Seism Soc Am 81:162–178
Sugimura A (1960) Zonal arrangement of some geophysical and petrological features in Japan and its environs. J Fac Sci Univ Tokyo (Sect. 2) 12:133–153
Suzuki H, Ikeda R, Mikoshiba T, Kinoshita S, Sato H, Takahashi H (1981) Deep well logs in the Kanto-Tokai area (in Japanese). Rev Nat Res Ctr Disast Prev 65:1–162
Takagi N, Sato H, Nishimura T, Obara K (2006) Rayleigh-wave group velocity in Japan revealed from the cross-correlation analysis of microseisms excited by typhoons. Proc 8th SEGJ Symp pp 207–210
Takahara M, Yomogida K (1992) Estimation of coda Q using the maximum likelihood method. Pure Appl Geophys 139:255–268, DOI 10.1007/BF00876330
Takahashi T, Sato H, Ohtake M, Obara K (2005) Scale Dependence of Apparent Stress for Earthquakes along the Subducting Pacific Plate in Northeastern Honshu, Japan. Bull Seism Soc Am 95(4):1334, DOI 10.1785/0120040075
Takahashi T, Sato H, 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 168:90–99, DOI 10.1111/j. 1365-246X.2006.03197.x
Takahashi T, Sato H, 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, DOI 10.1111/j.1365-246X.2008. 03739.x
Takahashi T, Sato H, Nishimura T, 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, DOI 10.1111/j. 1365-246X.2009.04227.x
Takemura S, Furumura T, Saito T (2009) Distortion of the apparent S-wave radiation pattern in the high-frequency wavefield: Tottori-Ken Seibu, Japan, earthquake of 2000. Geophys J Int 178(2):950–961, DOI 10.1111/j.1365-246X.2009.04210.x
Tanimoto T (1987) The three-dimensional shear wave structure in the mantle by overtone waveform inversion - I. Radial seismogram inversion. Geophys J R Astron Soc 89:713–740, DOI 10.1111/j.1365-246X.1987.tb05189.x
Tarantola A (1987) Inverse problem theory. Elsevier Science, Amsterdam
Tatarski VI, Gertensshtein ME (1963) Propagation of waves in a medium with strong fluctuations of the refractive index. Zh Ekspelim i Teor Fiz 44:676–685
Tatarskii VI (1971) The effects of the turbulent atmosphere on wave propagation. Israel Program for Science translations, Jerusalem
Tatsukawa M (1983) Determination of earthquake magnitude from total duration time of seismic waves based on the automatic recording for the Kanto-Tokai observation net. Rep Natl Res Ctr Disast Prev 31:89–100
Tatsumi Y (1986) Formation of the volcanic front in subduction zones. Geophys Res Lett 13:717–720, DOI 10.1029/GL013i008p00717
Taylor SR, Bonner BP, Zandt G (1986) Attenuation and scattering of broadband P and S waves across North America. J Geophys Res 91:7309–7325, DOI 10.1029/ JB091iB07p07309
Telford W, Geldart L, Sheriff R, Keys D (1976) Applied geophysics. Cambridge University Press, Cambridge, UK
Thatcher W, Hanks TC (1973) Source parameters of southern California earthquakes. J Geophys Res 78:8547–8576, DOI 10.1029/JB078i035p08547
Thurber C (1993) Local earthquake tomography: Velocities and Vp/Vs - theory, in Seismic Tomography: Theory and Practice (eds. H. M. Iyer and K. Hirahara), Chapmann & Hall, London, pp 563–583
Tittmann BR (1977) Internal friction measurements and their implications in seismic Q structure model of the crust, in The Earth’s Crust, AGU monograph, pp 197–213
Tittmann BR, Ahlberg L, Curnow J (1976) Internal friction and velocity measurements. Proc 7th Lunar Sci Conf pp 3123–3132
Tittmann BR, Clark VA, Richardson JM (1980) Possible mechanism for seismic attenuation in rocks containing small amount of volatiles. J Geophys Res 85:5199–5208, DOI 10. 1029/JB085iB10p05199
Toksöz MN, Dainty AM, Charrette EE (1991) Coherency of ground motion at regional distances and scattering. Phys Earth Planet Inter 67:162–179, DOI 10.1016/ 0031-9201(91)90068-S
Toksöz N, Johnston DH (1981) Seismic wave attenuation. Soc. Expl. Geophys., Tulsa, Okla
Tonegawa T, K Nishida TW, Shiomi K (2009) 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, DOI 10.1111/j.1365-246X.2009. 04249.x
Trifunac M, Brady A (1975) A study on the duration of strong earthquake ground motion. Bull Seism Soc Am 65(3):581
Tripathi J, Sato H, Yamamoto M (2010) Envelope broadening characteristics of crustal earthquakes in northeastern Honshu, Japan. Geophys J Int 182(2):988–1000, DOI 10. 1111/j.1365-246X.2010.04657.x
Tsujiura M (1978) Spectral analysis of the coda waves from local earthquakes. Bull Earthq Res Inst Univ Tokyo 53:1–48
Tsukuda T (1988) Coda before and after the 1983 Misasa earthquake of M 6.2, Tottori Prefecture, Japan. Pure Appl Geophys 128:261–280, DOI 10.1007/BF01772600
Tsumura K (1967) Determination of Earthquake Magnitude from Total Duration of Oscillation. Bull Earthquake Res Inst 45:7–18
Tsumura N, Matsumoto S, Horiuchi S, Hasegawa A (2000) Three-dimensional attenuation structure beneath the northeastern Japan arc estimated from spectra of small earthquakes. Tectonophysics 319(4):241–260, DOI 10.1016/S0040-1951(99)00297-8
Tsvankin I, Gaiser J, Grechka V, van der Baan M, Thomsen L (2010) Seismic anisotropy in exploration and reservoir characterization: An overview. Geophysics 75(5):75A15–75A29, DOI 10.1190/1.3481775
Tucker B, Brune J (1977) Source mechanism and mb-Ms analysis of aftershocks of the San Fernando earthquake. Geophys J R Astron Soc 49:371–426, DOI 10.1111/j.1365-246X. 1977.tb03714.x
Turner J (1998) Scattering and diffusion of seismic waves. Bull Seism Soc Am 88(1):276–283
Turner J, Weaver R (1994) Radiative transfer and multiple scattering of diffuse ultrasound in polycrystalline media. J Acoust Soc Am 96(6):3675–3683, DOI 10.1121/1.407739
Tuvč T, Bianco F, Ibáńez J, Patanč D, Del Pezzo E, Bottari A (2006) Attenuation study in the Straits of Messina area (southern Italy). Tectonophysics 421(3-4):173–185, DOI 10.1016/j.tecto.2006.04.005
Ugalde A, Carcolé E (2009) Comments on “Separation of Qi and Qs from passive data at Mt. Vesuvius: A reappraisal of the seismic attenuation estimates” by E. Del Pezzo et al. (2006). Phys Earth Planet Inter 173(1-2):191–194, DOI 10.1016/j.pepi.2008.10.001
Ugalde A, Pujades LG, Canas JA, Villasenor A (1998) Estimation of the intrinsic absorption and scattering attenuation in northeastern Venezuela (southeastern Caribbean) using coda waves. Pure Appl Geophys 153:685–702, DOI 10.1007/ s000240050214
Um J, Thurber C (1987) A fast algorithm for two-point seismic ray tracing. Bull Seism Soc Am 77:972–986
Uyeda S, Horai K (1964) Terrestrial heat flow in Japan. J Geophys Res 69:2121–2141, DOI 10.1029/JZ069i010p02121
Varadan VK, Varadan VV, Pao YH (1978) Multiple scattering of elastic waves by cylinders of arbitrary cross section. I. SH waves. J Acoust Soc Am 63:1310–1319, DOI 10.1121/1.381883
Vargas CA, Ugalde A, Pujades LG, Canas JA (2004) Spatial variation of coda wave attenuation in northwestern Colombia. Geophys J Int 158:609–624, DOI 10.1111/j. 1365-246X.2004.02307.x
Vasco DW, Johnson LR, Pulliam RJ, Earle P (1994) Robust inversion of IASP91 travel time residuals for mantle P and S velocity structure, earthquake mislocations, and station corrections. J Geophys Res 99:13,727–13,755, DOI 10.1029/93JB02023
Vidale J (1988) Finite-difference calculation of travel times. Bull Seism Soc Am 78:2062–2076, DOI 10.1038/35005059
Vidale J, Earle P (2000) Fine-scale heterogeneity in the Earth’s inner core. Nature 404(6775):273–275, DOI 10.1038/35005059
Vinogradov SD, Troitskiy PA, Solov’yeva MS (1992) Study of propagation of elastic waves in medium with oriented cracks. Izv Acad Sci USSR (Engl trans Phys Solid Earth) 28:367–384
Wagner GS, Owens TJ (1993) Broadband bearing-time records of three-component seismic array data and their application to the study of local earthquake coda. Geophys Res Lett 20:1823–1826, DOI 10.1029/93GL01884
Walsh JB (1965) The effects of cracks on the compressibility of rocks. J Geophys Res 70:381–389, DOI 10.1029/JZ070i002p00381
Walsh JB (1966) Seismic wave attenuation in rock due to friction. J Geophys Res 71:2591–2599, DOI 10.1029/JZ071i010p02591
Walsh JB (1969) New analysis of attenuation in partially melted rock. J Geophys Res 74:4333–4337, DOI 10.1029/JB074i017p04333
Wapenaar K, Fokkema J (2006) Green’s function representations for seismic interferometry. Geophysics 71:SI33–SI46, DOI 10.1190/1.2213955
Wapenaar K, Slob E, Snieder R (2010) On seismic interferometry, the generalized optical theorem, and the scattering matrix of a point scatterer. Geophysics 75:SA27–SA35, DOI 10.1190/1.3374359
Warner M (1990a) Absolute reflection coefficients from deep seismic reflections. Tectonophysics 173:15–23, DOI 10.1016/0040-1951(90)90199-I
Warner M (1990b) Basalts, water, or shear zones in the lower continental crust? Tectonophysics 173:163–174, DOI 10.1016/0040-1951(90)90214-S
Watanabe H (1971) Determination of earthquake magnitude at regional distance in and near Japan. Zisin (in Japanese) 24:189–200
Weaver R (1982) On diffuse waves in solid media. J Acoust Soc Am 71:1608, DOI 10.1121/ 1.387816
Weaver R (1990) Diffusivity of ultrasound in polycrystals. J Mech Phys Solids 38(1):55–86, DOI 10.1016/0022-5096(90)90021-U
Weaver R (2008) Ward identities and the retrieval of Green’s functions in the correlations of a diffuse field. Wave Motion 45(5):596–604
Weaver R, Lobkis O (2004) Diffuse fields in open systems and the emergence of the Green’s function (L). J Acoust Soc Am 116:2731, DOI 10.1121/1.1810232
Weaver R, Froment B, Campillo M (2009) On the correlation of non-isotropically distributed ballistic scalar diffuse waves. J Acoust Soc Am 126(4):1817–1826, DOI 10. 1121/1.3203359
Wegler U (2004) Diffusion of seismic waves in a thick layer: Theory and application to Vesvius volcano. J Geophys Res 109:B07303, DOI 10.1029/2004JB003048
Wegler U (2005) Diffusion of seismic waves in layered media: boundary conditions and analytical solutions. Geophys J Int 163(3):1123–1135, DOI 10.1111/j.1365-246X.2005. 02798.x
Wegler U, Luhr B (2001) Scattering behaviour at Merapi volcano (Java) revealed from an active seismic experiment. Geophys J Int 145(3):579–592, DOI 10.1046/j.1365-246x. 2001.01390.x
Wegler U, Sens-Schönfelder C (2007) Fault zone monitoring with passive image interferometry. Geophys J Int 168(3):1029–1033, DOI 10.1111/j.1365-246X.2006. 03284.x
Wegler U, Korn M, Przybilla J (2006a) Modeling full seismogram envelopes using radiative transfer theory with Born scattering coefficients. Pure Appl Geophys 163:503–531, DOI 10.1007/s00024-005-0027-5
Wegler U, Lühr B, Snieder R, Ratdomopurbo A (2006b) Increase of shear wave velocity before the 1998 eruption of Merapi volcano (Indonesia). Geophys Res Lett 33:L09303, DOI 10.1029/2006GL025928
Wegler U, Nakahara H, Sens-Schönfelder C, Korn M, Shiomi K (2009) Sudden drop of seismic velocity after the 2004 Mw 6.6 Mid-Niigata earthquake, Japan, observed with passive image interferometry. J Geophys Res 114(B6):B06,305, DOI 10.1029/ 2008JB005869
Weiland CM, Steck LK, Dawson PB, Korneev V (1995) Nonlinear teleseismic tomography at Long Valley Caldera, using three-dimensional minimum travel time ray tracing. J Geophys Res 100:20,379–20,390, DOI 10.1029/95JB01147
Wesley JP (1965) Diffusion of seismic energy in the near range. J Geophys Res 70:5099–5106, DOI 10.1029/JZ070i020p05099
White JE (1965) Seismic waves; radiation, transmission, and attenuation. McGraw-Hill, New York
Williamson IP (1975) The broadening of pulses due to multi-path propagation of radiation. Proc R Soc Lond A 342:131–147
Williamson PR (1991) A guide to the limits of resolution imposed by scattering in ray tomography. Geophysics 56:202–207, DOI 10.1190/1.1443032
Wolfram S (1991) Mathematica: a system for doing mathematics by computer (2nd edn.). Addison-Wesley, Redwood, Calif.
Woodgold CRD (1994) Coda Qin the Charlevoix, Quebec, region: Lapse-time dependence and spatial and temporal comparisons. Bull Seism Soc Am 84:1123–1131
Wu R, Maupin V (eds) (2007) Advances in wave propagation in heterogeneous earth, Advances in geophysics (Series Ed.: R. Dmowska), vol 48. Academic Press
Wu R, Jin S, Xie X (2000) Seismic wave propagation and scattering in heterogeneous crustal waveguides using screen propagators: I SH waves. Bull Seism Soc Am 90(2):401, DOI 10.1785/0119990102
Wu RS (1982a) Attenuation of short period seismic waves due to scattering. Geophys Res Lett 9:9–12, DOI 10.1029/GL009i001p00009
Wu RS (1982b) Mean field attenuation and amplitude attenuation due to wave scattering. Wave Motion 4:305–316, DOI 10.1016/0165-2125(82)90026-9
Wu RS (1985) Multiple scattering and energy transfer of seismic waves - separation of scattering effect from intrinsic attenuation - I. Theoretical modeling. Geophys J R Astron Soc 82:57–80, DOI 10.1111/j.1365-246X.1985.tb05128.x
Wu RS (1989) The perturbation method in elastic wave scattering. Pure Appl Geophys 131:605–638, DOI 10.1007/BF00876266
Wu RS, Aki K (1985) Elastic wave scattering by a random medium and the small-scale inhomogeneities in the lithosphere. J Geophys Res 90:10,261–10,273, DOI 10.1029/ JB090iB12p10261
Wu RS, 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 128:49–80, DOI 10.1007/BF01772590
Wu RS, Aki K (eds) (1988b) Seismic wave scattering in three-dimensionally heterogeneous earth, Part I. Pure Appl Geophys 128:1–447
Wu RS, Aki K (eds) (1989) Seismic wave scattering in three-dimensionally heterogeneous earth, Part II. Pure Appl Geophys 131:551–739
Wu RS, Aki K (eds) (1990) Seismic wave scattering in three-dimensionally heterogeneous earth, Part III. Pure Appl Geophys 132:1–244
Wu RS, Flatte SM (1990) Transmission fluctuations across an array and heterogeneities in the crust and upper mantle. Pure Appl Geophys 132:175–196, DOI 10.1007/ BF00874362
Wu RS, Toksöz MN (1987) Diffraction tomography and multisource holography applied to seismic imaging. Geophysics 52:11–25, DOI 10.1190/1.1442237
Wu RS, Xu Z, Li XP (1994) Heterogeneity spectrum and scale-anisotropy in the upper crust revealed by the German Continental Deep-Drilling (KTB) holes. Geophys Res Lett 21:911–914, DOI 10.1029/94GL00772
Yamakawa N (1962) Scattering and attenuation of elastic waves. Geophys Mag 31:63–103
Yamamoto M, Sato H (2010) Multiple scattering and mode conversion revealed by an active seismic experiment at Asama volcano, Japan. J Geophys Res 115:B07304, DOI 10.1029/2009JB007109
Yamashita T (1990) Attenuation and dispersion of SH waves due to scattering by randomly distributed cracks. Pure Appl Geophys 132:545–568, DOI 10.1007/BF00876929
Ying CF, Truell R (1956) Scattering of a plane longitudinal wave by a spherical obstacle in an isotropically elastic solid. J Appl Phys 27:1086–1097, DOI 10.1063/1.1722545
Yomogida K, Benites R (1995) Relation between direct wave Q and coda Q: A numerical approach. Geophys J Int 123:471–483, DOI 10.1111/j.1365-246X.1995.tb06866.x
Yoshimoto K (2000) Monte-Carlo simulation of seismogram envelope in scattering media. J Geophys Res 105:6153–6161, DOI 10.1029/1999JB900437
Yoshimoto K, Jin A (2008) Coda Energy Distribution and Attenuation. In: Sato H, Fehler MC (eds) Earth Heterogeneity and Scattering Effects on Seismic Waves, Advances in Geophysics (Series Ed. R. Dmowska), vol 50, Academic Press, New York, Chap. 10, pp 265–300
Yoshimoto K, Sato H, 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 114:165–174, DOI 10.1111/j.1365-246X.1993.tb01476.x
Yoshimoto K, Sato H, 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 104:63–73, DOI 10.1016/S0031-9201(97)00062-9
Yoshimoto K, Sato H, Ohtake M (1997b) Three-component seismogram envelope synthesis in randomly inhomogeneous semi-infinite media based on the single scattering approximation. Phys Earth Planet Inter 104:37–61, DOI 10.1016/S0031-9201(97) 00061-7
Yoshimoto K, Sato H, Iio Y, Ito H, Ohminato T, Ohtake M (1998) Frequency-dependent attenuation of high-frequency P and S waves in the upper crust in western Nagano, Japan. Pure Appl Geophys 153:489–502, DOI 10.1007/s000240050205
Yoshimoto K, Wegler U, Korn M (2006) A volcanic front as a boundary of seismic-attenuation structures in northeastern Honshu, Japan. Bull Seism Soc Am 96(2):637–646, DOI 10.1785/0120050085
Yun S, Lee WS, Lee K, Noh MH (2007) Spatial distribution of coda Q in South Korea. Bull Seism Soc Am 97:1012–1018, DOI 10.1785/0120060097
Zelt CA, Smith RB (1992) Seismic traveltime inversion for 2-D crustal velocity structure. Geophys J Int 108:16–34, DOI 10.1111/j.1365-246X.1992.tb00836.x
Zener C (1948) Elasticity and anelasticity of metals. University of Chicago Press, Chicago
Zeng Y (1993) Theory of scattered P- and S-wave energy in a random isotropic scattering medium. Bull Seism Soc Am 83:1264–1276
Zeng Y (2006) Scattered surface wave energy in the seismic coda. Pure Appl Geophys 163:533–548, DOI 10.1007/s00024-005-0025-7
Zeng Y, Su F, Aki K (1991) Scattering wave energy propagation in a random isotropic scattering medium 1. Theory. J Geophys Res 96:607–619, DOI 10.1029/90JB02012
Zeng Y, Aki K, Teng TL (1993) Mapping of the high-frequency source radiation for the Loma Prieta earthquake, California. J Geophys Res 98:11,981–11,993, DOI 10.1029/ 93JB00346
Zhang H, Thurber C (2003) Double-difference tomography: The method and its application to the Hayward fault, California. Bull Seism Soc Am 93(5):1875, DOI 10.1785/ 0120020190
Zhang H, Thurber C, Bedrosian P (2009) Joint inversion for Vp, Vs, and Vp/Vs at SAFOD, Parkfield, California. Geochem Geophys Geosyst 10(11):Q11,002
Zhao D, Wang Z, Umino N, Hasegawa A (2009) Mapping the mantle wedge and interplate thrust zone of the northeast Japan arc. Tectonophysics 467:89–106, DOI 10.1016/j. tecto.2008.12.01
Zhu T, Chun K, West GF (1991) Geometrical spreading and Q of Pn waves: An investigative study in eastern Canada. Bull Seism Soc Am 81:882–896
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sato, H., Fehler, M.C., Maeda, T. (2012). Introduction. In: Seismic Wave Propagation and Scattering in the Heterogeneous Earth : Second Edition. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23029-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-23029-5_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23028-8
Online ISBN: 978-3-642-23029-5
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)