1. Robust Quantification of Earthquake Clustering: Overcoming the Artifacts of Catalog Errors Ilya Zaliapin Department of Mathematics and Statistics University of Nevada, Reno zal@unr.edu http://www.unr.edu/~zal Yehuda Ben-Zion Department of Earth Sciences University of South California benzion@usc.edu http://earth.usc.edu/~ybz/ Summary We review location and registration errors in an earthquake catalog of southern California and examine effects of these errors on statistical analyses of seismicity. We use the high-quality catalog of Hauksson et al. [2012]. We study how catalog errors affect earthquake cluster identification (Panels 2, 3) and apparent temporal changes of the magnitude-frequency distribution (Panel 4). The cluster analyses refer to our recent methodology for detection and classification of seismic clusters. The novelty of this approach is in systematic uniform analysis of thousands of robustly detected seismic clusters of small-to- medium magnitude events, as opposed to the handful of largest clusters analyzed in most studies. Our previous research [Zaliapin and Ben-Zion, 2013a,b] established the existence of three basic types of earthquake clusters (burst-like, swarm-like, and singles) of small-to-medium magnitude, and demonstrated that the cluster type is closely related to the heat flow and other properties governing the effective viscosity of a region. We also have shown that the observed swarm type clusters are not reproduced well by the ETAS model. In this work we show that The location errors are significantly reduced in the central Southern California due to better quality of seismic network (see also Hauksson et al., 2012) – Panel 2 The location errors significantly affect the distance-to-parent and may distort the analyzes of offspring/aftershock/foreshock spatial distribution and decay – Panel 2 The location errors may lead to incorrect parent-offspring assignment and result in underestimation of earthquake triggering productivity – Panel 3 The combined registration/location errors affect the frequency-magnitude offspring distribution for parents of all magnitudes (not only large ones) and may last for very long times – up to years. This may affect the analyses of spatio-temporal b-value variability. The study is a first step toward a comprehensive analysis of catalog errors and related artifacts of statistical analyses of seismic clustering. 1. Data and Cluster Identification Approach We use the relocated catalog of Hauksson et al. [2012] and analyze 111,981 events with magnitude m ≥ 2; Cluster identification is done according to Zaliapin et al. [2008], Zaliapin and Ben-Zion [2013a]. In particular, we identify the single parent of each event according to the nearest-neighbor earthquake distance (in time-space-magnitude domain) introduced by Baiesi and Paczuski [2004]. The 2D distribution of the time (T) and space (R) components of the nearest-neighbor distance in the observed catalogs is prominently bi-modal (see figure below), with upper mode corresponding to background seismicity and lower mode to the clustered seismicity [Zaliapin et al., 2008, Zaliapin and Ben- Zion, 2011, 2013a]. This bimodality is used to separate the analyzed catalog into sequence of individual clusters (see definitions below). The bimodality of the earthquake nearest-neighbor distances allows one to decompose a seismic catalog into individual clusters (families) as shown below. Large distance Short distance Cluster #3 Cluster #2 Cluster #1 4. Time-Dependent Incompleteness SCEC Annual Meeting September 7-10, 2014 Palm Springs, CA Poster 163 The research is supported by the SCEC, project 14082; the United States Geological Survey Grant G09AP00019; and the National Science Foundation grant DMS-0934871. Background = weak links (as in stationary, inhomogeneous Poisson process) Clustered part = strong links (events are much closer to each other than in the background part) 5. References and acknowledgement The studies that employ this cluster analysis include: Gu et al. [2013]; Mignan [2012]; Zaliapin and Ben-Zion [2011, 2013a,b]. 1.Baiesi, M and M. Paczuski (2004) Scale-free networks of earthquakes and aftershocks. Phys. Rev. E, 69, 066106. 2.Gu, C., M. Baiesi and J. Davidsen (2013) Triggering cascades and statistical properties of aftershocks, J. Geophys. Res., 118(8), 4278-4295. 3.Hauksson, E. and W. Yang, and P.M. Shearer, (2012) Waveform Relocated Earthquake Catalog for Southern California (1981 to 2011). Bull. Seismol. Soc. Am., 102(5), 2239-2244. 4.Mignan, A. (2012) Functional Shape of the Earthquake Frequency-Magnitude Distribution and Completeness Magnitude, J. Geophys. Res., 117, B009347, doi: 10.1029/2012JB009347 5.Zaliapin, I., A. Gabrielov, H. Wong, and V. Keilis-Borok (2008). Clustering analysis of seismicity and aftershock identification, Phys. Rev. Lett., 101. 6.Zaliapin, I. and Y. Ben-Zion (2011). Asymmetric distribution of early aftershocks on large faults in California, Geophys. J. Intl., 185, 1288-1304, doi: 10.1111/j.1365-246X.2011.04995.x. 7.Zaliapin, I. and Y. Ben-Zion (2013a) Earthquake clusters in southern California, I: Identification and stability. J. Geophys. Res., 118, 2847-2864. 8.Zaliapin, I. and Y. Ben-Zion (2013b) Earthquake clusters in southern California, II: Classification and relation to physical properties of the crust. J. Geophys. Res., 118, 2865-2877. 2. Location Errors – Controls, Spatial Distribution, Effect on Distance-to-Parent Both absolute and relative errors depend on (i) no. of “similar events”, (ii) no. of differential times, and (iii) no. of P and S picks used to locate event [see Hauksson et al., 2012 for definitions]. The values of each of the above three characteristics significantly increase in in central Southern California, which results in much lower location errors (see panels on the right) The absolute horizontal errors significantly affect the distance-to-parent (see panels on the left). In particular, the rescaled distance to parent R increases more than two orders of magnitude when the absolute error increases from 100m to over 1 km, or when the relative error increases from 1m to 100m. This effect should be taken into account when studying spatial distribution of offspring/aftershock/foreshocks. For example, the rates of spatial decay are expected to decrease with increasing location error. No. Similar Events No. Differential TimesNo. P & S picks Absolute Error Relative Error Absolute Error Absolute error for events with m < 4 is comparable to their estimated fault length (panel A). This contaminates identification of offspring for those events. Absolute error is comparable (ratio 0.3 – 0.8) to the parent fault length (panel B), which may lead to serious problems with proper parent identification. Absolute error of the offspring of m < 4 parents is comparable to their parent’s fault length (panel C). This contaminates identification of parents for those events. 3. Error Effects on Cluster Identification: Underestimation of Productivity Many offspring (32%) have parents outside of their similar event cluster – hence absolute errors must be considered in cluster analysis (m>2 events analyzed) ABC Offspring identification is corrupted for events with large location errors Parent identification is corrupted for events with large location errors D E Proportion of clustered events – events with close parent (panel D) and events with close offsprings (panel E) – strongly depends on absolute error. This suggests that errors indeed contaminate cluster identification, leading to significant underestimation of the number of clustered events (and offspring productivity) and overestimation of background activity. Direct evidence of productivity underestimation Each event is the catalog is assigned absolute and relative (w.r.t. the other events in the similar event cluster) error [Hauksson et al., 2012]. Here we only consider horizontal errors; the analyses and conclusions for vertical errors are similar (not shown). The joint distribution of absolute and relative errors is shown below – the errors are dependent. (We consider here only horizontal absolute and relative errors. The results for vertical errors are similar and are not reported in this poster.) It is well-known that many small-magnitude events are not registered after a large one. This leads to apparent changes in the b- value illustrated in Panel A for parents with 4 < m < 6. The time-dependence of this incompleteness is shown in Panel B. Interestingly, the effect of incompleteness is also seen for small magnitude parents (Panel C). It seems to last longer, although it has smaller magnitude. The incompleteness may explain apparent b-value changes for background vs. clustered events [Gu et al., 2013] ABC Offspring of parents with magnitude 4 < m < 6 Offspring of parents with magnitude 2 < m < 4