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i i Meyers: Encyclopedia of Complexity and Systems Science — Entry 317 — 2009/3/24 — 14:46 — page 2473 — le-tex Earthquake Magnitude E 2473 (Chairman). Carnegie Institution of Washington Publication, 75. Thurber CH, Kissling E (2000) Advances in travel-time calcula- vol 87 (reprinted 1969) tions for three-dimensional strucutres. In: Thurber CH, Rabi- 53. Rothman DH (1985) Nonlinear inversion, statistical mechanics, nowitz N (eds) Advances in Seismic Event Location. Kluwer, and residual statics estimation. Geophysics 50:2784–2796 Amsterdam 54. Rydelek P, Pujol J (2004) Real-Time Seismic Warning with 76. Uhrhammer RA (1980) Analysis of small seismographic station a Two-Station Subarray. Bull Seism Soc Am 94:1546–1550 networks. Bull Seism Soc Am 70:1369–1379 55. Sambridge M (1998) Exploring multi-dimensional landscapes 77. Um J, Thurber C (1987) A fast algorithm for two-point seismic without a map. Inverse Probl 14:427–440 ray tracing. Bull Seism Soc Am 77:972–986 56. Sambridge M (1999) Geophysical inversion with a Neighbour- 78. van den Berg J, Curtis A, Trampert J (2003) Bayesian, nonlin- hood algorithm, vol I. Searching a parameter space. Geophys ear experimental design applied to simple, geophysical exam- J Int 138:479–494 ples. Geophys J Int 55(2):411–421. Erratum: 2005. Geophys J Int 57. Sambridge M (1999) Geophysical inversion with a neighbour- 161(2):265 hood algorithm, vol II. Appraising the ensemble. Geophys J Int 79. Vidale JE (1988) Finite-difference calculation of travel times. 138:727–746 Bull Seism Soc Am 78:2062–2078 58. Sambridge M (2003) Nonlinear inversion by direct search us- 80. Winterfors E, Curtis A (2007) Survey and experimental design ing the neighbourhood algorithm. In: International Handbook for nonlinear problems. Inverse Problems (submitted) of Earthquake and Engineering Seismology, vol 81B. Academic 81. Wither M, Aster R, Young C (1999) An automated local and Press, Amsterdam, pp 1635–1637 regional seismic event detection and location system using 59. Sambridge M, Drijkoningen G (1992) Genetic algorithms in waveform correlation. Bull Seism Soc Am 8:657–669 seismic waveform inversion. Geophys J Int 109:323–342 82. WithersM,AsterR,YoungC,BeirigerJ,HarrisM,MooreS,Tru- 60. Sambridge M, Gallagher K (1993) Earthquake hypocen- jillo J (1998) A comparison of select trigger algorithms for au- ter location using genetic algorithms. Bull Seism Soc Am tomated global seismic phase and event detection. Bull Seism 83:1467–1491 Soc Am 88:95–106 83. Wittlinger G, Herquel G, Nakache T (1993) Earthquake location 61. Sambridge M, Kennett BLN (1986) A novel method of hypocen- in strongly heterogeneous media. Geophys J Int 115:759–777 tre location. Geophys J R Astron Soc 87:679–697 84. Zhou H (1994) Rapid 3-D hypocentral determination using 62. Sambridge M, Mosegaard K (2002) Monte Carlo Methods In a master station method. J Geophys Res 99:15439–15455 Geophysical Inverse Problems. Rev Geophys 40:1009–1038 63. Satriano C, Lomax A, Zollo A (2007) Optimal, Real-time Earth- quake Location for Early Warning. In: Gasparini P, Gaetano M, Books and Reviews Jochen Z (eds) Earthquake Early Warning Systems. Springer, Gasparini P, Gaetano M, Jochen Z (eds) (2007) Earthquake Early Berlin Warning Systems. Springer, Berlin 64. Satriano C, Lomax A, Zollo A (2007) Real-time evolutionary Lee WHK, Stewart SW (1981) Principles and applications of mi- earthquake location for seismic early warning. Bull Seism Soc croearthquake networks. Academic Press, New York Am 98:1482–1494 Thurber CH, Rabinowitz N (eds) (2000) Advances in Seismic Event 65. Sen M, Stoffa PL (1995) Global optimization methods in geo- Location. Kluwer, Amsterdam physical inversion. Elsevier, Amsterdam, p 281 66. Sethian JA (1999) Level set methods and fast marching meth- ods. Cambridge University Press, Cambridge 67. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423 Earthquake Magnitude 68. Shearer PM (1994) Global seismic event detection using PETER BORMANN,JOACHIM SAUL a matched filter on long-period seismograms. J Geophys Res 99:13,713–13,735 GeoForschungsZentrum Potsdam, Potsdam, Germany 69. Shearer PM (1997) Improving local earthquake locations using the L1 norm and waveform cross correlation: Application to Article Outline the Whittier Narrows, California, aftershock sequence. J Geo- phys Res 102:8269–8283 Glossary 70. Steinberg DM, Rabinowitz N, Shimshoni Y, Mizrachi D (1995) Definition of the Subject Configuring a seismographic network for optimal monitor- Introduction to Common Magnitude Scales: ing of fault lines and multiple sources. Bull Seism Soc Am Potential and Limitations 85:1847–1857 Common Magnitude Estimates 71. 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J Geophys Res 50:159–170 Bibliography i i i i Meyers: Encyclopedia of Complexity and Systems Science — Entry 317 — 2009/3/24 — 14:46 — page 2474 — le-tex 2474 E Earthquake Magnitude Glossary Fundamental modes The longest period oscillations of the whole Earth with periods of about 20 min Technical terms that are written in the text in italics are (spheroidal mode), 44 min. (toroidal mode) and some explained in the Glossary. 54 min (“rugby” mode), excited by great earthquakes. Corner frequency The frequency fc at which the curve Magnitude A number that characterizes the relative that represents the Fourier amplitude spectrum of earthquake size. It is usually based on measurement a recorded seismic signal abruptly changes its slope of the maximum motion recorded by a seismograph (see Fig. 5). For earthquakes, this frequency is related (sometimes for waves of a particular type and fre- to the fault size, rupture velocity, rupture duration and quency) and corrected for the decay of amplitudes with stress drop at the source. Also the frequency at which epicenter distance and source depth due to geometric the magnification curve of a recording system (e. g., spreading and attenuation during wave propagation. Fig. 3) changes its slope. Several magnitude scales have been defined. Some of Dispersion Frequency-dependence of the wave propaga- them show saturation. In contrast, the moment magni- tion velocity. Whereas seismic body-waves show virtu- tude (Mw), based on the concept of seismic moment,is ally no dispersion, it is pronounced for seismic surface uniformly applicable to all earthquake sizes but is more waves. It causes a significant stretching of the length of difficult to compute than the other types, similarly the the surface-wave record and the rather late arrival of its energy magnitude, Me, which is based on direct calcu- largest amplitudes (Airy phases) from which the sur- lation of the seismic energy Es from broadband seismic face-wave magnitude MS and the mantle magnitude records. Mm, respectively, are determined. Saturation (of magnitudes) Underestimation of magni- Earthquake size A frequently used, but not uniquely de- tude when the duration of the earthquake rupture sig- fined term. It may be related – more or less directly – to nificantly exceeds the seismic wave period at which the either the geometric-kinematic size of an earthquake magnitude is measured. The shorter this period, the in terms of area and slip of the fault or to the seismic earlier respective magnitudes will saturate (see relation energy radiated from a seismic source and its poten- (13) and Figs. 4 and 5). tial to cause damage and casualty (moment or energy Seismic energy Elastic energy Es (in joule) generated by, magnitude). and radiated from, a seismic source in the form of seis- Earthquake source In general terms, the whole area or mic waves. The amount of Es is generally much smaller volume of an earthquake rupture where seismic body than the energy associated with the non-elastic defor- waves are generated and radiated outwards. More mation in the seismic source (see seismic moment Mo). specifically, one speaks either of the source mecha- The ratio Es/Mo D (/2) D a/,i.e.,theseismic nism or the source location. The latter is commonly energy released per unit of Mo, varies for earthquakes given as earthquake hypocenter (i. e. the location at in a very wide range between some 106 and 103,de- thesourcedepthh from where the seismic rup- pending on the geologic-tectonic environment, type of ture, collapse or explosion begins) or as the point source mechanism and related stress drop or ap- on the Earth’s surface vertically above the hypocen- parent stress a. ter, called the epicenter. Earthquakes at h < 70 km Seismic moment Mo A special measure of earthquake are shallow, those at larger depth either intermediate size. The moment tensor of a shear rupture (see earth- (up to h D 300 km) or deep earthquakes (h D 300– quake source) has two non-zero eigenvalues of the 700 km). The determination of the geographical coor- amount Mo D DF¯ a with -shear modulus of the dinates latitude ',longitude,andfocaldepthh,is ruptured medium, D¯ -average source dislocation and the prime task of seismic source location. However, Fa-area of the ruptured fault plane. Mo is called the for extended seismic sources, fault ruptures of great scalar seismic moment. It has the dimension of New- earthquakes in particular, the hypocenter is generally ton meter (Nm) and describes the total non-elastic not the location of largest fault slip and/or seismic (i. e., ruptural and plastic) deformation in the seismic moment/energy release and the epicenter is then also source volume.
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