EARTHQUAKE, AFTERSHOCKS Definition Introduction Scaling Laws for Aftershocks Causes of Aftershocks
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192 EARTHQUAKE, AFTERSHOCKS Earthquakes, Source Theory law, named for Fusakichi Omori’s observation of the Propagation of Elastic Waves: Fundamentals 1891 Nobi earthquake in Japan (Omori, 1894) and later Seismic Instrumentation modified by Utsu (1961): Surface Waves K nðtÞ¼ ðc þ tÞp EARTHQUAKE, AFTERSHOCKS where nðtÞ is the number of aftershocks by time t after the mainshock; K, p, and c are constants. The value of c is typ- Mian Liu1, Seth Stein2 ically positive close to zero, and p close to 1. Hence, the 1Department of Geological Sciences, University of number of aftershocks drops nearly hyperbolically with Missouri, Columbia, MO, USA time (Figure 1). The values of these constants are obtained 2Department of Earth and Planetary Sciences, by fitting to the data for each aftershock sequence. Northwestern University, Evanston, IL, USA It has been observed that the largest aftershock is usu- ally about 1 magnitude unit smaller than the mainshock, Definition independent of the mainshock magnitude. This is known as Båth’s law (Bath, 1965; Richter, 1958). However, Aftershocks. Smaller earthquakes following a large earth- because the data selection is retrospective and subjective, quake (the mainshock) in the same ruptured area. the size of aftershocks can vary substantially for different earthquake sequences. Introduction Like all earthquakes, the size distribution of aftershocks Earthquakes typically occur in sequences that may include follow the Gutenberg–Richter law (Gutenberg and foreshocks, the mainshock (the largest event or events), Richter, 1954): and aftershocks. Earthquake sequences without a clear mainshock are called swarms. log10NðMÞ¼a À bM Aftershocks generally refer to the smaller earthquakes where NðMÞ is the number of earthquakes of magnitude that follow a mainshock within certain spatial and tempo- M, a and b are constants. This relationship plots as ral windows. However, the criteria for choosing these win- a straight line with slope b, whose value, often referred dows are somewhat arbitrary. Typically, aftershocks are – ’ to as the b-value, is typically in the range of 0.8 1.2. For defined within an area around the mainshock s source b = 1, the number of earthquakes increases by a factor of region (i.e., the ruptured fault segment, which is about 10 for every unit drop. The b-value varies in time and 100 km long for a magnitude 7.0 earthquake). Most after- space even for the same fault. Some studies have shocks occur on the main rupture surface; hence, they are suggested that the b-value can be used as a stress indicator, often used to define the complex geometry of the rupture with lower b-values often associated with higher stresses plane. However, in many cases, especially for earthquakes (Schorlemmer et al., 2005). in subduction zones, the aftershock area increases signifi- cantly following the mainshock (Tajima and Kanamori, Causes of aftershocks 1985). Some aftershocks also occur off the main rupture Because most aftershocks occur on or near the rupture sur- surface. Distant earthquakes triggered by the mainshock’s face, they are thought to result from incomplete rupture seismic waves (see Artificial Water Reservoir Triggered and heterogeneous slip (e.g., Bullen and Bolt, 1947). This Earthquakes) may also be regarded as aftershocks notion is consistent with some case studies that found (Gomberg and Johnson, 2005). Temporally, aftershocks aftershocks concentrated around the perimeter of the rup- are defined as seismicity above the background activity ture zone or around asperities within the rupture zone following a main shock. This definition also leaves room where most of the coseismic slip occurred (Beroza, for ambiguity, as the background seismic activity can be 1991; Scholz, 2002). difficult to define in some places. The main causes of aftershocks are thought to include Aftershocks usually count for less than 5% of the total mainshock-induced changes of frictional properties of seismic energy release of the entire seismic sequence, so the fault zone and stress perturbations. Laboratory experi- they are secondary products (Scholz, 2002). However, ments indicate that frictional properties change with the besides their spatial and temporal relations to the duration of stationary contact and the instantaneous slid- mainshock, aftershocks are fundamentally no different ing velocity (Scholz, 2002). A constitutive relationship from other earthquakes and are recognized as aftershocks based on such results, known as the rate-and-state law only retrospectively (Helmstetter et al., 2003; Utsu, 2002). (Dieterich, 1979; Ruina, 1983), can explain the time- dependent changes of seismic rates that are consistent with Scaling laws for aftershocks the Omori’s law (Dieterich, 1994). Stress perturbations A large earthquake is usually followed by many smaller may arise from creep recovery of rocks in the immediate events (aftershocks); their occurrence rate decreases with areas of the fault (Benioff, 1951), viscous relaxation from time, typically following a pattern known as the Omori’s the lower crustal and upper mantle (Lieber and Braslau, EARTHQUAKE, AFTERSHOCKS 193 37°12′ 36°48′ a −122°24′−122°00′−121°36′−121°12′ 7 800 6 600 5 400 4 Magnitude 3 200 2 (shocks/yr) Seismicity rate 0 1980 1985 1990 1995 2000 2005 2010 1980 1985 1990 1995 2000 2005 2010 b Year c Year Earthquake, Aftershocks, Figure 1 (a) Topography and seismicity (circles, size proportional to magnitude) around the epicenter (star) of the 1989 Loma Prieta earthquake (Mw 6.9) on the San Andreas Fault. Green line marks the fault rupture; red lines enclose the spatial window for the aftershocks. (b) Earthquake occurrence between 1980 and 2010 within the spatial window. (c) Plot of seismicity showing the tÀ1 decay of aftershocks. 1965; Stein and Liu, 2009), and pore-elastic effects aftershocks are found to last 50–100 years. Within the (Scholz, 2002). In particular, the changes of the Coulomb stable continental interior, aftershock sequences may last static stress resulted from the mainshock have been shown hundreds of years or even longer (Stein and Liu, 2009). to cause spatial migration of seismicity and trigger earth- Such long aftershock sequences in continental interiors, quakes (Parsons, 2002; Stein, 1999). Other causes may where large earthquakes are infrequent and historic records include dynamic triggering (Gomberg and Johnson, are often incomplete, could bias hazard assessment. 2005) and pore fluid flow (Miller et al., 2004; Nur and Further complication may arise from the fact that earth- Booker, 1972). quakes tend to cluster in time and space, which is best shown in aftershock sequences. Studies of large shallow earthquakes in the world show that these large events often Aftershocks and earthquake hazard occur in pairs or groups (called doublets or multiplets); the Aftershocks can be large and damaging (e.g., Wiemer later events, which could be regarded as aftershocks, can et al., 2002). The durations of aftershock sequences for be bigger than the triggering event (the mainshock) plate-boundary earthquakes are typically around 10 years (Kagan and Jackson, 1999). Such clustering patterns are (Parsons, 2002)(Figure 1). However, aftershock sequences consistent with the emerging view that all earthquakes away from plate-boundary faults tend to last longer. In the can trigger their own earthquakes that in turn trigger more broadly deforming western United States, for example, quakes, and the triggered events may be bigger than the 194 EARTHQUAKE, FOCAL MECHANISM triggering event (Helmstetter et al., 2003; Ogata, 1998). Omori, F., 1894. On the aftershocks of earthquakes. Journal of Because the triggered events (the aftershocks) statistically the College of Science, Imperial University of Tokyo, 7, – follow the Omori’s law, statistical models can be devel- 111 200. Parsons, T., 2002. Global Omori law decay of triggered earth- oped to assess time-dependent probability of future dam- quakes: Large aftershocks outside the classical aftershock zone. aging earthquakes after each event (Gerstenberger et al., Journal of Geophysical Research, 107(B9), 2199, doi:10.1029/ 2005; Jones, 1985; Reasenberg and Jones, 1989). 2001JB000646. Reasenberg, P. A., and Jones, L. M., 1989. Earthquake hazard after a mainshock in California. Science, 243, 1173–1176. Summary Richter, C. F., 1958. Elementary Seismology. San Francisco: W. Aftershocks are smaller earthquakes following the H. Freeman. 768 pp. mainshock. They typically occur on or near the rupture Ruina, A., 1983. Slip instability and state variable friction laws. plane of the mainshock, resulting from changes of stress Journal of Geophysical Research, 88, 10359–10370. and frictional properties of the fault zone caused by the Scholz, C. H., 2002. The Mechanics of Earthquakes and Faulting. Cambridge/New York: Cambridge University Press. 471 pp. mainshock. The duration of aftershock sequences is typi- Schorlemmer, D., Wiemer, S., and Wyss, M., 2005. Variations in cally a few years for earthquakes at plate boundaries, but earthquake-size distribution across different stress regimes. can last much longer within stable continental interiors. Nature, 437, 539–542. Stein, R. S., 1999. The role of stress transfer in earthquake occur- rence. Nature, 402, 605–609. Bibliography Stein, S., and Liu, M., 2009. Long aftershock sequences within con- Bath, M., 1965. Lateral inhomogeneities in the upper mantle. tinents and implications for earthquake hazard assessment. Tectonophysics, 2, 483–514. Nature, 462,87–89. Benioff, H., 1951.