Spatiotemporal Comparison of Declustered Catalogs of Earthquakes in Turkey

Abstract

In earthquake seismology, an independent earthquake can produce a set of clusters having fore- and/or aftershocks. The main purpose of seismicity declustering is to refine a given earthquake catalog in order to retain independent events. The goal of retention of independent events by only declustering is a crucial benchmark for most of the mainshock-based analysis in seismology. In the present article, we used a re-updated unified earthquake catalog of Turkey and obtained several declustered catalogs applying different declustering methods. To compare the performance of applied declustering methods, each declustered catalog was then examined by simulation envelopes and Monte Carlo tests using some summary statistics for temporal and spatial point patterns. We found that the declustering method of Zhuang et al. (2002) based on the Epidemic Type Aftershock Sequence (ETAS) model, original version, and particularly Grünthal’s variant of the Gardner and Knopoff (1974) method seemed to be most successful in finding and removing clusters in space and time for the earthquake catalog of Turkey examined.

Appendix: Estimation of Spatial Seismicity Rates

For each declustered catalog, the spatial seismicity rate $\lambda (x,y)$ was estimated by applying the variable bandwidth kernel density estimator

$$\hat{\lambda }\left( {x,y} \right) = \frac{1}{T}\mathop \sum \limits_{i = 1}^{N} k\left( {x - x_{i} ,y - y_{i} ;\sigma_{i} } \right)$$

(5)

where

$$k\left( {x,y;\sigma_{i} } \right) = \frac{1}{{2\pi \sigma_{i}^{2} }}{ \exp }\left( { - \frac{{x^{2} + y^{2} }}{{2\sigma_{i}^{2} }}} \right)$$

(6)

is the bivariate Gaussian kernel with standard deviation (bandwidth) $\sigma_{i} = { \hbox{max} }\left( {d_{np} \left( {x_{i} ,y_{i} } \right),\sigma_{ \hbox{min} } } \right)$, $d_{np} \left( {x_{i} ,y_{i} } \right)$ is the $n_{p}$-th nearest distance of the epicenter of the i-th event, and $\sigma_{ \hbox{min} }$ is the minimum bandwidth (Zhuang 2011). We considered $n_{p} = \left[ {{ \log }(N)} \right]$ and let $\sigma_{min}$ be the first quartile of $d_{np} \left( {x_{i} ,y_{i} } \right)$’s. The estimated spatial seismicity rates of the full updated and each declustered catalog are shown in Fig. 11.

Fig. 11

Estimated background seismicity (event per square kilometer) rates of the full updated and declustered catalogs

In the analyses that we made, success is considered obtaining spatially homogeneous background seismicity rates depending on the degree of refinement due to declustering. In practice, there is a lack of clear physical metric measuring of the performance of a declustered catalog, or, in other words, the declustering method, to remove dependent events in the strict sense because, as mentioned above, there has not yet been a consensus on the definitions of the dependent and independent events because the source of the earthquake occurences can still be explained by semi-empirical theories. However, resorting to checking the level of Poissonian behavior of the declustered catalog examined could be used as a semi-empirical tool in statistical seismology, which is the primary motivation of the current article.

The convergence of the Eurasian and Arabian plates creates explicit coercion into the plate boundaries making Turkey one of the most earthquake-prone regions in the world as an emblematic area. The major neotectonic structures of Turkey can be briefly summarized in three components, namely the North Anatolian fault zone (NAFZ), East Anatolian fault zone (EAFZ) and Aegean–Cyprean Arc (AA-CA). For brevity, the following resources (Turkelli et al. 2003; Bozkurt 2001; Sengör et al. 1985; Sengör and Yilmaz 1981; Delph et al. 2015; Barka 1992; Saroglu et al. 1992; Duman and Emre 2013; Tatar et al. 2013; Duman et al. 2016) are recommended for the readers.

As shown in Fig. 11, the background seismicity rate ($\lambda$) distribution is large and identified in the major tectonic elements of Turkish seismicity. The full updated catalog emerged as the weakest catalog, which was not able to reflect the smoothly scattered visible seismicity rates (lambda). Grünthal’s variant of the Gardner and Knopoff (1974) method was the most successful candidate, and the original windows of the Gardner and Knopoff (1974) and stochastic declustering method by Zhuang et al. (2002) were the most successful models. All variations of the Reasenberg (1985) method that we used were not successful since their plots contain a great deal of similarity to the full updated catalog. Although Uhrhammer’s (1986) windowing was not as unsuccessful as Reasenberg’s, it was still not considered successful.

Moreover, it is known that there are intense earthquake occurrences near the specific seismicity zone called the Aegean Arc, and this is even clearly visible to the eye, as shown in Figs. 1 and 11a. When the background seismicity rates are examined, the focus seismicity zones, which could not yet be fully refined by any method, provide examples of the hot spot regions that are so problematic for both understanding earthquake occurrences and managing seismic hazard calculations. In our example, each method can be judged by the refinement capability at hot spot regions like the one apparent in a zone where the island of Crete is located. While all other methods mostly fail, the original and Grünthal variants of the Gardner and Knopoff (1974) and Zhuang et al. (2002) method are the most successful ones in this regard.