LETTERS PUBLISHED ONLINE: 27 MARCH 2011 | DOI: 10.1038/NGEO1110 Absence of remotely triggered large earthquakes beyond the mainshock region Tom Parsons 1 * and Aaron A. Velasco 2 Large earthquakes are known to trigger earthquakes elsewhere. Damaging large aftershocks occur close to the mainshock and microearthquakes are triggered by passing seismic waves at significant distances from the mainshock 1–6 . It is unclear, however, whether bigger, more damaging earth- quakes are routinely triggered at distances far from the mainshock, heightening the global seismic hazard after every large earthquake. Here we assemble a catalogue of all possible earthquakes greater than M 5 that might have been triggered by every M 7 or larger mainshock during the past 30 years. We compare the timing of earthquakes greater than M 5 with the temporal and spatial passage of surface waves generated by large earthquakes using a complete worldwide catalogue. Whereas small earthquakes are triggered immediately during the passage of surface waves at all spatial ranges, we find no significant temporal association between surface-wave arrivals and larger earthquakes. We observe a significant increase in the rate of seismic activity at distances confined to within two to three rupture lengths of the mainshock. Thus, we conclude that the regional hazard of larger earthquakes is increased after a mainshock, but the global hazard is not. Surface waves are usually the largest-amplitude arrivals on a seismogram, and they produce transient strain as they travel within Earth’s crustal waveguide. Large (M ≥ 7) earthquakes are known to trigger earthquakes 1–6 and other phenomena, such as non-volcanic tremor 7–11 , at remote distances. Although remote earthquake triggering is seen in all tectonic settings 12 , the mechanism of triggered earthquake failure remains unsolved. Thus far, the remotely triggered earthquakes we have associated with the onset of passing seismic waves have been small-magnitude (M < 5) events. However, what if each large mainshock raises the global rate of other large earthquakes? Should there be a worldwide alarm period of heightened earthquake probability? We turn to the 30-yr global catalogue to search for high-magnitude (M > 5) triggered earthquakes at all offsets following large (M ≥ 7), shallow (Z ≤ 50 km) earthquakes to see whether there are significant rate increases. Our global earthquake catalogue is compiled from the Advanced National Seismic System and Global Seismograph Network. We find the minimum magnitude of completeness to range between coda magnitude (M c ) = 4.7 and M c = 5.1, depending on the methods applied (Supplementary Fig. S1). We thus investigate M > 5 events throughout this study, which we define as earthquakes with catalogue listings of M ≥ 5.1. As will be shown, we conducted tests with M c ≥ 5.5 and M c ≥ 6.0 without substantive change in result. We identify links among large earthquakes by calculating earthquake density (number km -2 ) for 5 < M < 7 events in concentric radii measured from 205 M ≥ 7 global earthquakes (1979–2009). We calculate earthquake density to normalize results 1 US Geological Survey, MS-999, 345 Middlefield Rd, Menlo Park, California 94025, USA, 2 Department of Geological Sciences, University of Texas at EI Paso, EI Paso, Texas 79968-0555, USA. *e-mail:tparsons@usgs.gov. calculated over the larger areas caused by increasing radii. We isolate the largest events (M ≥ 7) for study as triggering mainshocks, leaving 25,222 potentially triggered 5 < M < 7 events. We compute relative origin times and ranges of every 5 < M < 7 catalogue event to each of the 205 M ≥ 7 mainshocks. We then calculate before and after 5 < M < 7 earthquake density (number km -2 ) in bins ranging from 20 to 200 km width, and over 100 time intervals ranging from 30 s to 1 day (Fig. 1; see Methods). We determine the significance of observed rate changes by establishing the global background rate of 5 < M < 7 earthquakes over the time and distance ranges used in the study. The question we want to answer in establishing significance is, what are the mean and confidence bounds on the expected steady-state density of 5 < M < 7 earthquakes as a function of distance from the M ≥ 7 triggering event locations used in the study? This allows us to recognize anomalous rate changes at any distance range. For example, if we know the mean background rate in a given window of time as a function of distance from sources, we can compare it with the observed rate versus distance. Wherever or whenever the observed density is significantly higher than background, then we suspect triggering is happening. We examine many periods at random times throughout the 30-year catalogue to establish mean rates and confidence bounds (see Methods). We search for triggered earthquakes that lie within and after time intervals containing surface-wave arrivals (Fig. 2), but find no sig- nificant 5 < M < 7 earthquake rate increase coincident with surface- wave arrivals at any distance range on Earth in the past 30 years. This result is surprising because past studies 12 , using just 15 mainshocks and spatially limited detection, identified ∼1,500 M ≤ 3 events that occurred within 15 min of the first surface-wave arrivals. Extrapo- lating with the Gutenberg–Richter relation between magnitude and frequency (log N = a - bM , where N is the number of earthquakes and a and b are constants defining intercept and linear slope), we expect a minimum of ∼70 M > 5.0 and ∼25 M > 6.0 trig- gered earthquakes to have occurred above background rates within 15 min of surface-wave arrivals after 205 mainshocks over 30 yr. We calculate the Gutenberg–Richter relation using the number of triggered detections for 15 large (M > 7.0) earthquakes 12 . If we assume that all of the detections recorded in the first 15 min were triggered events (∼1,500) with maximum magnitude M ≤ 3.0 and a b value of 1.0, we expect at least five M > 5.0 and two M > 6.0 triggered earthquakes should have occurred. If we assume M < 2.0 for all triggered events, the number of triggered earthquakes decreases to approximately two for M > 5.0 and 0.2 for M > 6.0 in 14 years previously studied 12 . In our case, we analyse data from a 30-year span, indicating that we should at minimum expect 4–10 M > 5.0 triggered events and 0–2 M > 6.0 triggered events. This is a lower bound estimate, because it is based only on 15 M > 7.0 earthquakes, and detections were spatially limited to events very 312 NATURE GEOSCIENCE | VOL 4 | MAY 2011 | www.nature.com/naturegeoscience © 2011 Macmillan Publishers Limited. All rights reserved.