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moment rate functions. Journal of Geophysical Research, 104, 863–894. EARTHQUAKE, FORESHOCKS Bridgman, P. W., 1945. Polymorphic transition and geological phe- nomenon. American Journal of Science, 243A,90–97. Mian Liu Dziewonski, A. M., Chou, A.-T., and Woodhouse, J. H., 1981. Department of Geological Sciences, University of Determination of earthquake source parameters from waveform data for studies of global and regional seismicity. Journal of Missouri, Columbia, MO, USA Geophysical Research, 86, 2825–2852. Ekström, G., 1994. Anomalous earthquakes on volcano ring- Synonyms fault structures. Earth and Planetary Science Letters, 128, Preshocks 707–712. Frohlich, C., and Apperson, K. D., 1992. Earthquake focal mecha- nisms, moment tensors and the consistency of seismic activity Definition near plate boundaries. Tectonics, 11, 279–296. Foreshocks. Smaller earthquakes preceding a large earth- Gilbert, J. F., and Dziewonski, A. M., 1975. An application of quake (the mainshock) in the same ruptured area. normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra. Philosophical Transaction of Royal Society London, 278A, 187–269. Introduction Isacks, B. L., and Molnar, P., 1971. Distribution of stresses in the Earthquakes typically occur in sequences that may include descending lithosphere from a global survey of focal-mechanism foreshocks, the mainshock (the largest event or events), solutions of mantle earthquakes. Reviews of Geophysics and Space Physics, 9, 103–174. and Earthquake, Aftershocks. Earthquake sequences with- Isacks, B. L., Oliver, J., and Sykes, L. R., 1968. Seismology and the out a clear mainshock are called swarms. newglobal tectonics. Journal of Geophysical Research, 73, Foreshocks are the most obvious premonitory phenom- 5855–5899. enon of earthquakes. They are thought to indicate earth- Kagan, Y. Y., 1991. 3-D rotation of double-couple earthquake quake nucleation and hence may have the potential for sources. Geophysical Journal International, 106, 709–716. short-term earthquake prediction (Scholz, 2002). How- Kanamori, H., Ekström, G., Dziewoński, A. M., Barker, J. S., and Sipkin, S. A., 1993. Seismic radiation by magma injection: an ever, proof of the physical link between foreshores and anomalous seismic event near Tori Shima, Japan. Journal of earthquake nucleation is inconclusive, and earthquake Geophysical Research, 98, 6511–6522. prediction using foreshocks has not been reliable. Kawakatsu, H., 1991. Insignificant isotropic components in the The problem begins with their recognition – foreshocks moment tensor of deep earthquakes. Nature, 351,50–53. are earthquakes that are called foreshocks retrospectively, Kirby, S. H., Stein, S., Okal, E. A., and Rubie, D., 1996. Deep earth- when a large event (the mainshock) followed. To be con- quakes and metastable mantle phase transformations in sidered as foreshocks, these events need to occur within subducting oceanic lithosphere. Reviews of Geophysics and Space Physics, 34, 261–306. certain spatial and temporal windows, and these windows Knopoff, L., and Gilbert, J. F., 1959. Radiation from a strike-slip vary in different studies. Foreshocks are typically located earthquake. Bulletin of the Seismological Society of America, within the mainshock’s source area with a dimension 49, 163–178. roughly the length of the fault rupture, which is in the Li, X., Shao, G., and Ji, C., 2009. Rupture process of the Mw = 8.1 order of 100 km for a magnitude 7.0 earthquake. Tempo- Samoa earthquake constrained by joint inverting teleseismic rally, most foreshocks occur a few days to hours before body, surface waves and local strong motion. Eos Transactions, American Geophysical Union, 90, (52), U21D– the mainshock (Jones and Molnar, 1979). In some cases, 03, [abstract]. seismicity increases a few months or years before the Nettles, M., and Ekström, G., 2009. Ice loss and glacial earthquakes mainshock. Some workers consider such increased seis- in Greenland and Antarctica. Eos Transactions, American Geo- micity foreshocks; others do not (Scholz, 2002). physical Union, 90(52), G52B–01 [abstract]. Depending on the choice of these spatial and temporal Okal, E. A., 1996. Radial modes from the great 1994 Bolivian earth- windows, a global survey shows that up to 70% of large quake: no evidence of an isotropic component to the source. Geophysical Research Letters, 23, 431–434. earthquakes (M 7) may be preceded by foreshocks Stein, S., and Wysession, M. E., 2003. An Introduction to Seismol- (Jones and Molnar, 1979). While the percentage varies ogy, Earthquakes and Earth Structure. Malden: Blackwell, with different studies and in different regions, it is impor- 498 pp. tant to note that not all earthquakes are preceded by Sykes, L. R., 1967. Mechanisms of earthquakes and nature of foreshocks. faulting on the mid-oceanic ridges. Journal of Geophysical Research, 72, 2131–2153. Vvedenskaya, A. V., 1956. Opredelenie polej smeshchenii pri Characteristics of foreshocks zemletryasenyakh s pomoshchyu teorii dislokatsii. Izv Akad Foreshocks, when they do occur, are typically few in com- Nauk SSSR, Ser Geofiz, 6, 277–284 [in Russian]. parison with aftershocks, sometimes consisting of only Wilson, J. T., 1965. A new class of faults and their bearing on con- – a few or a single event, hence are difficult for quantitative tinental drift. Nature, 207, 343 347. analysis. When considered collectively, they are shown to exhibit a temporal pattern similar to that of aftershocks Cross-references (Jones and Molnar, 1979; Shaw, 1993). Most foreshocks Earthquakes, Source Theory occur within 10 days before the mainshock, and their Earthquake Rupture: Inverse Problem numbers rapidly accelerate till the occurrence of the 200 EARTHQUAKE, FORESHOCKS mainshock. The collective time sequence of foreshocks Can foreshocks be used to predict earthquakes? seems to fit an inverse Omori’s law: As the most obvious precursor of earthquakes, fore- nðtÞ¼atq shocks are thought to be useful for short-term prediction of earthquakes, and successful predictions have been where nðtÞ is the number of foreshocks by time t before the reported in numerous cases. The best example is perhaps origin of the mainshock, and a and q are constants, with q the 1975 Haicheng earthquake (magnitude 7.3) in China, close to 1 (Kagan and Knopoff, 1978; Papazachos, 1975). which was predicted largely based on foreshocks, more Thus, the number of foreshocks tends to increase hyper- than 500 of which were recorded within 4 days before bolically as the time approaches the origin of the the mainshock (Jones et al., 1982). However, a recent mainshock. Some studies suggest that foreshocks may investigation (Wang et al., 2006) has revealed that the have lower b-values (see entry Earthquake, Aftershocks) role of foreshocks in this prediction was more psycholog- relative to other earthquakes (Scholz, 2002). ical than scientific: the jolts and damages from increased It is not clear why some earthquakes have foreshocks seismicity in the preceding months stressed the minds of while others do not. Studies of global and regional earth- earthquake workers and the general public, and the inten- quake catalogs have found that neither the time sified foreshocks in the last day before the mainshock sequences nor the largest magnitude of foreshocks cor- prompted some local officials to order an evacuation. In relate to the magnitude of the mainshock (Jones and other places where official orders were not issued, the Molnar, 1979), suggesting either the size of the increased seismicity caused many residents to evacuate mainshock is independent of the earthquake nucleation voluntarily. process, or foreshocks are not part of earthquake nucle- Aside from the problem that many earthquakes do not ation (Abercrombie and Mori, 1996). The incidence of have foreshocks, short-term earthquake prediction using foreshocks is found to decrease with increasing depth foreshocks is challenging in theory and in practice. For of the mainshock (Abercrombie and Mori, 1996). For foreshocks to be a predictor, they must be an essential part earthquakes in California, more foreshocks are associ- of the physical process leading to the mainshock. ated with strike-slip events than with thrust events Although this physical link between foreshocks and (Abercrombie and Mori, 1996). This is opposite to the mainshock is suggested in the nucleation model, its vali- results from a study of global catalogs by Reasenberg dation in natural fault zones has not been conclusive. On (1999), who attribute the low rate of foreshocks for the other hand, if foreshocks are fundamentally the same Californian thrust events to their relatively greater as other earthquakes (Felzer et al., 2004), then foreshocks depths. cannot be predictors of mainshocks. In practice, we have yet to find any reliable ways to recognize foreshocks from background seismicity before the occurrence of the Causes of foreshocks mainshock. The causes of foreshocks remain uncertain. Some studies Nonetheless, there must be some symptoms associated link foreshocks to earthquake nucleation (Scholz, 2002). with the stress buildup and physical property changes in Theoretically, fault ruptures only when slip has occurred and around the fault leading to a major rupture, and over a fault patch of some critical radius. Ohnaka (1992) foreshocks are the most obvious symptoms known to has proposed a theoretical model that attributes the gener- us. Further studies of foreshocks will improve our under- ation of foreshock to failure of asperities loaded by accel- standing of the mechanics of earthquakes. A recent study erating premonitory creep. This model predicts numerous of the foreshock sequences on East Pacific Rise trans- features found in foreshocks: their occurrence typically form faults (McGuire et al., 2005) suggests that fore- a few days before the mainshock, their accelerated rates shocks are linked to the mainshock through stress as time approaches that of the mainshock, and their occur- changes driven by aseismic slip transients or some fault rence in the immediate vicinity of the hypocenter of the preparation process, hence potentially can be useful for mainshock. However, not all foreshocks readily fit the short-term earthquake prediction. On the other hand, by nucleation model. Aside from the obvious problem that treating every earthquake as a potential foreshock that many earthquakes do not have foreshocks, the nucleation may be followed by a mainshock, statistical models model has difficulties explaining foreshocks that occur based on the clustering properties of earthquake away from the rupture plane or have significantly different sequences can be developed to assess the real-time prob- focal mechanisms from that of the mainshock (Jones et al., ability of damaging earthquakes, as has been done in 1982). California (Gerstenberger et al., 2005; Jones, 1985; Others think that foreshocks are fundamentally the Reasenberg and Jones, 1989). same as other earthquakes (Felzer et al., 2004; Helmstetter et al., 2003). In this view, foreshocks, the mainshock, and aftershocks are just different names for earthquakes within Summary the same sequence of cascading ruptures triggered by Foreshocks are smaller earthquakes preceding a mainshock. a common mechanism. They are thought to manifest the nucleation of the EARTHQUAKE, LOCATION TECHNIQUES 201 mainshock, hence have the potential for short-term earth- quake prediction. However, not all large earthquakes are EARTHQUAKE, LOCATION TECHNIQUES preceded by foreshocks, and they are difficult to recognize from the background seismicity before the occurrence of Clifford H. Thurber the mainshock. Foreshocks may also be fundamentally Department of Geoscience, University of the same as other earthquakes, if so they cannot be used Wisconsin-Madison, Madison, WI, USA as earthquake predictors. Synonyms Bibliography Hypocenter determination Abercrombie, R. E., and Mori, J., 1996. Occurrence patterns of fore- shocks to large earthquakes in the western United States. Nature, Definition 381, 303–307. Earthquake location. Methods for determining the lati- Dodge, D. A., Beroza, G. C., and Ellsworth, W. L., 1995. Foreshock tude, longitude, depth, and time of origin of a seismic sequence of the 1992 Landers, California, earthquake and its event (earthquake, explosion, etc.) using the arrival times implications for earthquake nucleation. Journal of Geophysical of seismic waves. Research, 100, 9865–9880. Felzer, K. R., Abercrombie, R. E., and Ekström, G., 2004. A common origin for aftershocks, foreshocks, and multi- Introduction plets. Bulletin of the Seismological Society of America, 94, Knowing the location of an earthquake (its latitude, longi- 88–98. tude, depth, and origin time) is an essential starting point Gerstenberger, M. C., Wiemer, S., Jones, L. M., and Reasenberg, P. A., 2005. Real-time forecasts of tomorrow's earthquakes in for the vast majority of quantitative seismological ana- California. Nature, 435, 328–331. lyses. In the context of this article, earthquake location Helmstetter, A., Sornette, D., and Grasso, J.-R., 2003. Mainshocks will be taken to mean determining the initiation point of are aftershocks of conditional foreshocks: how do foreshock sta- fault rupture, that is, the hypocenter. After briefly tracing tistical properties emerge from aftershock laws. Journal of Geo- some of the early history of methods for the quantitative physical Research, 108, 2046. determination of earthquake locations, the focus of discus- Jones, L. M., 1985. Foreshocks and time-dependent earthquake haz- sion turns to modern methods for single-event location ard assessment in southern California. Bulletin of the Seismolog- ical Society of America, 75, 1667–1679. and uncertainty estimation. The final section covers Jones, L. M., and Molnar, P., 1979. Some characteristics of fore- multiple-event location, with an emphasis on the substan- shocks and their possible relationship to earthquake prediction tial to – in some cases – profound improvement in relative and premonitory slip on faults. Journal of Geophysical location accuracy that can be achieved by combining Research, 84, 3596–3608. waveform cross-correlation with relative location Jones, L. M., Wang, B., Xu, S., and Fitch, T. J., 1982. The foreshock techniques. sequence of the February 4, 1975, Haicheng earthquake (M = 7.3). Journal of Geophysical Research, 87, 4575–4584. Kagan, Y. Y., and Knopoff, L., 1978. Statistical study of the occur- Early history rence of shallow earthquakes. Geophysical Journal of the Royal John “Earthquake” Milne devised some of the first quanti- – Astronomical Society, 55,67 86. tatively based methods for earthquake location, known as McGuire, J. J., Boettcher, M. S., and Jordan, T. H., 2005. Foreshock sequences and short-term earthquake predictability on East the methods of circles, hyperbolas, and coordinates (Milne, Pacific Rise transform faults. Nature, 434, 457–461. 1886). For the method of circles, the difference in arrival Ohnaka, M., 1992. Earthquake source nucleation: a physical model time between later observing stations i (i =1,N) and the – for short-term precursors. Tectonophysics, 211, 149 178. first observing station 0, tit0 =dti, is used to construct cir- Papazachos, B. C., 1975. Foreshocks and earthquake prediction. cles of radii V dti, where V is the velocity of “shock” (i.e., Tectonophysics, 28, 213–226. seismic wave) propagation, and the center of the circle Reasenberg, P. A., 1999. Foreshock occurrence before large earth- quakes. Journal of Geophysical Research, 104, 4755–4768. through station 0 that is roughly tangent to all the other cir- Reasenberg, P. A., and Jones, L. M., 1989. Earthquake hazard after cles defines the earthquake epicenter. The scale factor V is a mainshock in California. Science, 243, 1173–1176. determined by trial and error. The commonly taught Scholz, C. H., 2002. The Mechanics of Earthquakes and Faulting. S minus P time location method (Bolt, 2006) is similar in Cambridge/New York: Cambridge University Press, Vol. xxiv. concept. The method of hyperbolas is a variant on the 471 pp. method of circles, whereby differential times between pairs Shaw, B. E., 1993. Generalized Omori law for aftershocks and fore- of stations are used to define hyperbolas of possible loca- shocks from a simple dynamics. Geophysical Research Letters, 20, 907–910. tions, and the intersection of hyperbolas defines the earth- Wang, K., Chen, Q. F., Sun, S., and Wang, A., 2006. Predicting the quake epicenter. The method of coordinates goes a step 1975 Haicheng earthquake. Bulletin of the Seismological Society further by setting up a system of four equations (defined of America, 96, 757–795. in Cartesian coordinates centered on the last-observing sta- tion) relating differential times to “shock” velocity and the Cross-references (x,y,z) coordinates of the earthquake. With four equations Earthquake, Aftershocks and four unknowns, the solution is unique. These methods