No Evidence of Magnitude Clustering in an Aftershock Sequence of Nano- and Picoseismicity Jo ¨rn Davidsen * Complexity Science Group, Department of Physics & Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada Grzegorz Kwiatek and Georg Dresen GeoForschungsZentrum Potsdam, Section 3.2: Geomechanics and Rheology, Telegrafenberg, 14473 Potsdam, Germany (Received 9 August 2011; published 17 January 2012) One of the hallmarks of our current understanding of seismicity as highlighted by the epidemic-type- aftershock sequence model is that the magnitudes of earthquakes are independent of one another and can be considered as randomly drawn from the Gutenberg-Richter distribution. This assumption forms the basis of many approaches for forecasting seismicity rates and hazard assessment. Recently, it has been suggested that the assumption of independent magnitudes is not valid. It was subsequently argued that this conclusion was not supported by the original earthquake data from California. One of the main challenges is the lack of completeness of earthquake catalogs. Here, we study an aftershock sequence of nano- and picoseismicity as observed at the Mponeng mine, for which the issue of incompleteness is much less pronounced. We show that this sequence does not exhibit any significant evidence of magnitude correlations. DOI: 10.1103/PhysRevLett.108.038501 PACS numbers: 91.30.Dk, 02.50.r, 89.75.Da One prominent feature of seismicity is the clustering of earthquakes in space and time. This is evident, for ex- ample, from the observation that the local rate of activity after a large earthquake is much higher than before. Starting with the Omori law [1], there has been a signifi- cant amount of research dedicated to quantify, character- ize, and understand this spatiotemporal clustering (see, for example, Refs. [2–12] and references therein). The scien- tific effort is partly driven by the desire to predict or forecast earthquakes. To this end, the Omori law and other empirical observations including the Gutenberg-Richter (GR) law have been used to formulate stochastic models of seismicity [13–16]. Despite some success forecasting aftershock activity and seismicity rates [17–21], we are, however, far away from reliably predicting the occurrence of large earthquakes ahead of time [22,23], which poten- tially could even be an unreachable goal [24]. Recent evidence for the latter hypothesis comes from attempts to determine the magnitude of an earthquake from seismic signals before the rupture terminates. The current conclusion is that this is not possible [25–29]. Thus, it came as a surprise when it was suggested that statistical correlations exist between the magnitudes of earthquakes [30,31]. If indeed true, it would imply that one could predict the magnitude of a future earthquake based on the magnitudes of previously observed earthquakes. In a subsequent paper, it was argued, however, that the exis- tence of nontrivial correlations was not supported by the original earthquake data from southern California [32]. It was shown, in particular, that catalog incompleteness can lead to the spurious detection of magnitude correla- tions. Almost all earthquake catalogs suffer from this effect—even if one constrains the observation to larger earthquakes—due to the presence of short-term aftershock incompleteness [17,33–36]. It arises mainly because seis- micity directly after a large earthquake can be masked by overlapping arrivals of waves from different events. Thus, it is conceivable that magnitude correlations do exist over short space and time scales but they are typically hidden due to catalog incompleteness. Here, we address exactly this point by studying seismic- ity, for which the influence of catalog incompleteness is minimal. Specifically, we focus on an aftershock se- quence of nano- and picoseismicity—corresponding to earthquakes with moment magnitudes M W in the range [ 4, 0] as discussed in [37]—observed at the Mponeng mine, South Africa, with a magnitude of completeness of M C ¼4:3 [38,39]. We find that there is no significant evidence for magnitude correlations. This is even true if one considers events that are close in space and/or time, which were speculated to exhibit particularly strong mag- nitude correlations. The data we analyze are recorded as part of the JAGUARS (Japanese-German underground acoustic emis- sion research in South Africa) project [40]. The project aimed to close the gap between the laboratory research on rock samples and seismicity measured in situ. For that purpose the high-frequency JAGUARS network was in- stalled at a depth of 3550 m in the Mponeng deep gold mine in South Africa. The network was composed of a 3-component (3C) accelerometer and 8 acoustic emission sensors. The sensors were sensitive in a broad frequency range (50 Hz—200 kHz) and allowed us to record ex- tremely small seismic events (M W between 5:0 and 0:8)[38,41]. The recorded seismicity (except for man- made sources) falls into two major groups: (1) postblasting PRL 108, 038501 (2012) PHYSICAL REVIEW LETTERS week ending 20 JANUARY 2012 0031-9007= 12=108(3)=038501(4) 038501-1 Ó 2012 American Physical Society