Regional variations in the diffusion of triggered seismicity Conor McKernon and Ian G. Main School of GeoSciences, University of Edinburgh, Edinburgh, UK Received 15 August 2004 revised 11 March 2005 accepted 25 March 2005 published 12 May 2005. [1] We determine the spatiotemporal characteristics of interearthquake triggering in the International Seismological Centre catalogue on regional and global scales. We pose a null hypothesis of spatially clustered, temporally random seismicity, and determine a residual pair correlation function for triggered events against this background. We compare results from the eastern Mediterranean, 25 Flinn-Engdahl seismic regions, and the global data set. The null hypothesis cannot be rejected for distances greater than 150 km, providing an upper limit to triggering distances that can be distinguished from temporally uncorrelated seismicity in the stacked data at present. Correlation lengths L and mean distances between triggered events hri are on the order of 10���50 km, but can be as high as 100 km in subduction zones. These values are not strongly affected by magnitude threshold, but are comparable to seismogenic thicknesses, implying a strong thermal control on correlation lengths. The temporal evolution of L and hri is well fitted by a power law, with an exponent H 0.1 �� 0.05. This is much lower than the value H = 0.5 expected for Gaussian diffusion in a homogenous medium. We observe clear regional variations in L, hri and H that appear to depend on tectonic setting. A detectable transition to a more rapid diffusion regime occurs in some cases at times greater than 100���200 days, possibly due to viscoelastic processes in the ductile lower crust. Citation: McKernon, C., and I. G. Main (2005), Regional variations in the diffusion of triggered seismicity, J. Geophys. Res., 110, B05S05, doi:10.1029/2004JB003387. 1. Introduction [2] A triggered earthquake has been defined by Gomberg et al. [1998, p. 24,411] as ������one whose failure time has been advanced by Dt (clock advance) due to a stress perturbation.������ This broad definition includes aftershocks, foreshocks, and induced seismicity, all normally defined at short range (within a few source dimensions) and, more rarely, longer-range triggered events. Importantly, it makes no retrospective judgment on what is a ������main shock,������ since an individual earthquake may trigger subsequent larger events. [3] Earthquake triggering is most evident in the spatial and temporal clustering of events in earthquake catalogues where the background seismicity is low. A high degree of temporal clustering of seismicity, especially in aftershock sequences [Utsu et al., 1995], has long been recognized, but the spatial limits of more generally triggered events are still very much open to debate. One of the main reasons is the need to define an objective and robust ������background������ seismicity that would be expected for a temporally random (stationary) process, to act as a null hypothesis. [4] Several authors have recently solved this problem, providing evidence for long-range triggering in the form of spatial and temporal clustering of seismicity outside the traditional ������aftershock zone.������ Lomnitz [1996] suggested that triggered events were more likely to occur in two regions: (1) within 200 km of a main shock and (2) in an annulus of radii 300���1000 km over a 30 day period. Gasperini and Mulargia [1989] reported an aftershock ������influence region������ of 80���140 km, in a time window of 14���60 days. Evidence for triggering at distances up to 240 km was reported by Parsons [2002], with aftershocks occurring for 7���11 years. Brodsky et al. [2003] proposed that well water level changes could be linked to earthquakes hundreds of kilometers away, suggesting a very long range poroelastic mechanism. In contrast, Melini et al. [2002] found no strong statistical evidence for triggering at distances of several hundred kilometers. [5] The precise mechanisms for triggering remain the subject of debate. One hypothesis is that earthquake trig- gering is caused by static Coulomb stress changes, where optimally orientated faults are brought closer to failure by stress redistribution after the triggering event. This view is supported by a wide literature of individual case studies [King et al., 1994 Stein et al., 1994 Harris et al., 1995 Harris and Simpson, 1998 Toda et al., 1998]. However, the more general effectiveness of Coulomb modeling as a predictive tool for zones of enhanced or reduced seismicity has recently come into question, based on statistical studies of the directional effect of triggering. For example, studies of global seismicity using centroid moment tensor (CMT) data [Kagan and Jackson, 1998 Huc and Main, 2003] demonstrate that shallow aftershocks do not necessarily concentrate preferentially in the dilatational quadrant. In a systematic statistical study of 100 large events, Parsons JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, B05S05, doi:10.1029/2004JB003387, 2005 Copyright 2005 by the American Geophysical Union. 0148-0227/05/2004JB003387$09.00 B05S05 1 of 12

[2002] found that only 61% of aftershocks occurred in areas predicted to have increased Coulomb shear stress. [6] The second hypothesis for triggered events (particu- larly at longer range) is dynamic stresses, which decay much more slowly with distance than static ones. A classi- cal example of dynamic triggering is the observation of clearly triggered events in hydrothermal areas, beginning at or shortly after the passage of Raleigh waves propagated from the Landers earthquake [Hill et al., 1993]. The most likely mechanism of triggering in such areas is the dynamic degassing of hydrothermal fluids and associated rapid increase in pore pressure. [7] Whatever the primary mechanism, there is a clear time-dependant component to triggering, variously ascribed to pore fluid pressure changes, rate and state friction, stress corrosion cracking, and viscoelastic relaxation through a ductile lower crust. The relative importance of each is still open to question. For example, Harris and Simpson [1998] found that Coulomb stress calculations can in some cases predict stress shadows (areas of seismicity decrease) ade- quately, but require an explicit time-dependent effect (citing rate- and state-dependent friction) to achieve more accurate models. [8] Additional complexity can be introduced through secondary triggering processes. For example, Felzer et al. [2002, 2003] suggested that the 1999 Mw 7.3 Hector Mine earthquake was triggered by aftershocks of the 1992 Mw 7.1 Landers earthquake. They propose that chains of cascading seismicity like this are part of the reason for the large proportion of observed discrepancies in statistical studies of Coulomb modeling. Although directly triggered aftershocks may be constrained to areas where a main shock increases shear stress, secondary aftershocks (aftershocks of after- shocks) can occur outside this area. Felzer et al. [2004] also suggest that the magnitude of each triggered earthquake may even be entirely independent of the magnitude of the triggering earthquake. [9] Marsan [2003] puts forward a similar argument to Felzer et al. [2002, 2003] that positive triggering (i.e. in areas of calculated Coulomb stress increase) is commonly observed, but seismic quiescence (in calculated ������shadow zones������ of Coulomb stress decrease) is less frequent. He suggests that high spatial variability of stresses caused by a main shock may explain the absence of quiescence (which static Coulomb modeling in a homogeneous medium fails to do). The success of Coulomb modeling depends on several factors, such as accurate data regarding the size and geom- etry of the main shock and aftershocks [Steacy et al., 2004], the accuracy of earthquake data sets in general [Kagan, 2003] and knowledge of the regional crustal structure. Coulomb modeling might also benefit from a continuous reapplication of the modeling process with each aftershock, although this may not be practical in real time with large data sets. Irrespective of the mechanism at work, static stress triggering concepts are now being incorporated into proba- bilistic seismic hazard assessment. This model-dependant approach in turn requires detailed models for fault geometry and Earth structure which may not always be accurate, and which may lead to unwarranted complacency in zones of lowered Coulomb stresses. [10] The work presented here tries instead to quantify properties of earthquake triggering statistically, without recourse to physical modeling of the underlying process. The advantage of such a method is that it requires no a priori assumptions about fault geometry or Earth structure, and hence may be used as a benchmark with which to test different physical hypotheses. As a natural progression of the global study carried out by Huc and Main [2003], we apply the method developed there to regional data sets, to look for spatial variations in the nature and scope of interearthquake triggering. We use a pair correlation tech- nique, examining time and distance separations between epicenters of causally related events. It is applied to raw and time-randomized catalogues, to distinguish formally the triggered signal from the background seismicity. This is analogous to the separation of correlated and uncorrelated seismicity mentioned by Helmstetter et al. [2003]. [11] We initially examine triggering in and around Greece, to test the suitability of the method to smaller, bounded areas rather than the Earth as a whole. We then use Flinn-Engdahl seismic regions as boundaries for regional studies, to minimize subjectivity and also to allow our results to be compared with other work using the same system. This allows regional variations in the extent of triggering and earthquake diffusion to be calculated. Finally we look at the global data set for a range of magnitude thresholds, to compare the work here with that carried out previously on the CMT catalogue, and to examine how the triggering signal varies with magnitude. [12] Carrying this method out for a range of time win- dows after each potential triggering event allows correlation lengths L and mean triggering distances hri to be evaluated. Knowing how these parameters change over time means the temporal evolution of the spatial extent of triggered events can be determined. Analysis of this evolution, which can be fitted to a power law, allows us to calculate parameters that can be used as measure of the rate of diffusion of triggered events. The method can also be applied to determine the conditional probabilities for aftershock occurrence within a given distance and time after an earthquake in a direct way. 2. Method [13] We used data from the International Seismological Centre (ISC) catalogue for the period 1 January 1964 to 31 December 2000. The catalogue was filtered to retain shal- low events only (70 km) with 4.5 mb used as the magnitude threshold of completeness, leaving 91,199 events in the reduced catalogue. The analysis of a potential directional effect in triggering carried out by Huc and Main [2003] could not be repeated, as the ISC catalogue does not routinely report source orientation. [14] To investigate the statistical properties of earthquake triggering, we begin by defining our null hypothesis that earthquakes are spatially clustered but temporally random. We treat each earthquake as a potentially triggering event, and every subsequent event as a potentially triggered event, thus making no a priori exclusions on what may be a triggered event [Marsan et al., 1999 Huc and Main, 2003]. We then compare the original, unaltered data and deliberately time-randomized catalogues. This preserves the spatial clustering present in global seismicity, but allows us to look for any nonrandom temporal components in a clear and reproducible way. B05S05 McKERNON AND MAIN: DIFFUSION OF TRIGGERED SEISMICITY 2 of 12 B05S05