Articulo 3C.indd EARTH SCIENCES RESEARCH JOURNAL SEISmOLOgy Earth Sci. Res. SJ. Vol. 16, No. 2 (December, 2012): 103 - 108 Introduction Since fractal description was developed for the geometry of natu- ral objects (mandelbrot B.B., 1982), it has been recognised that many complex space-time phenomena, such as seismicity, may be described and interpreted in terms of fractal distributions with power-law scaling (e.g. Hirata T., 1989; Öncel A.O. et al., 1995; Caneva A., Smirnov V., 2004; Öncel A.O., Wilson T.H., 2007; Roy S. et al., 2011). However, studies of possible correlation between seismicity and fault distribution are lim- ited. Applying seismic hazard assessment to fractal association between seismotectonic variables requires distinguishing normal and anomalous correlations between such data sets’ fractal attributes. Since the statisti- cal behaviour of seismicity may potentially represent sensitive short-term predictors of major earthquakes, this study’s main aim was to find an em- pirical relationship between seismic b-values and the fractal distribution of epicentres for Turkish earthquakes. Data regarding earthquakes and tectonic zoning Several earthquake catalogues are available for Turkey from both national and international sources. Earthquakes occurring between 1970 and 2006 were taken from Öztürk’s catalogue of instrumental data Statistical correlation between b-value and fractal dimension regarding Turkish epicentre distribution Serkan Öztürk gümüşhane University. Turkey. E-mail: serkanozturk@gumushane.edu.tr ABSTRACT This study was aimed at analysing the relationship between seismic b-value and fractal dimension Dc- value for Turkish epicentres. The earthquake catalogue consisting of 99,737 instrumentally-registered Turkish events was analysed for the period between 1970 and 2011; Turkey was divided into 55 tec- tonic zones for making a detailed comparison. The b-values were calculated by the maximum likelihood method and the Dc-values were obtained with 95% confidence limits by linear regression. The results showed that higher Dc-values were associated with lower b-values and this could have been an indication of relatively high stress intensity and stronger epicentre clustering in these regions. Orthogonal regression was used to estimate a suitable statistical correlation between two seismotec- tonic parameters; the Dc = 2.44 - 0.30*b relationship was obtained with a strong negative correlation (r = -0.82) between b-value and Dc-value for Turkish earthquake distribution. This seemed to agree with other regional results obtained for different parts of Turkey and the rest of the world. RESUmEN Este estudio tuvo como objetivo analizar la relación entre el valor b y la dimensión del valor fractal Dc para los epicentros de Turquia. El catálogo sísmico que consiste en 99.737 eventos registrados instru- mentalmente fue analizado para el período comprendido entre 1970 y 2011; Turquía se dividió en 55 zonas tectónicas para hacer una comparación detallada. Los valores de b se calcularon por el método de máxima verosimilitud y la Dc-valores se obtuvieron con límites de confianza del 95% mediante regresión lineal. Los resultados mostraron que el aumento del valor fractal Dc se asocia con menores valores b y esto podría haber sido un indicador de intensidad de tensiones relativamente altas y una más fuerte agrupación de epicentro en estas regiones. Se utilizó una regresión ortogonal para estimar la correlación estadística adecuada entre dos pará- metros sismotectónicos la relación de la dimensión fractal Dc = 2,44 a 0,30*b, se obtuvo con una fuerte correlación negativa (r = -0,82) entre valores b y valores fractales Dc para la distribución de terremotos en Turquía. Esto parece estar de acuerdo con otros resultados regionales obtenidos para las diferentes partes de Turquía y el resto del mundo. Palabras claves: Terremoto de Turquía, dimensión fractal, valor-b, correlación. Keywords: Turkish earthquake, fractal dimension, b-value, correlation. Record manuscript received: 13/02/2012 Accepted for publications: 06/05/2012 Serkan Öztürk104 (2009), including duration magnitude (M D ) for 73,530 earthquakes oc- curring in Turkey between 1970 and 2006; Öztürk used empirical rela- tionships to compile a homogenous and complete earthquake catalogue (1970 to 2006). The Bogazici University’s Kandilli Observatory and Research Institute (KOERI) catalogue was also used for 2006 to 2011; KOERI usually gives local magnitudes (M L ) for local earthquakes having missing M D . If an M D was unknown in the KOERI catalogue for 2006 to 2011, then M D were calculated using the relationships given in Öztürk (2009). 26,207 earthquakes in and around Turkey were thus selected for the aforementioned period. This earthquake catalogue was homogeneous for M D and contained 99,737 earthquakes occurring between 1970 and 2011. many authors have suggested tectonic zoning as a widely-used meth- odology for evaluating the hazard of an earthquake occurring (e.g. Erdik m. et al., 1999; Jiménez m. et al., 2001; Bayrak y. et al., 2009). The pres- ent study’s new seismic source zones for Turkey and its adjacent areas were based on tectonic zoning studies by Erdik (1999) and Bayrak (2009), the existing tectonic structure and earthquake epicentre distribution (Figure 1). Turkey was divided into 55 different zones, as shown in Figure 1. New smaller zones were selected to compare such tectonic zoning in detail, in the same regions. Figure 1 shows Turkey’s active tectonics and many de- tails regarding Turkey’s tectonic structure can be found in Şaroğlu (1992), mcClusky (2000) and Bozkurt (2001). The numbers of earthquakes oc- curring in each zone were sufficient for analysis; Table 1 shows the seismic zones in this study (numbered 1 to 55) with their tectonic environments. Earthquakes’ frequency-magnitude distribution (seismic b-value) Earthquakes’ magnitude distribution (Md) is usually parameterised using gutenberg-Richter’s (g-R) power law relationship (gutenberg B., Richter C.F., 1944); such frequency-magnitude relationship has been found to be applicable (in simplified form) as follows: log 10 N(M) = a – bM (1) where N(M) is the cumulative number of events having a magni- tude greater than M, b describes the slope of the size distribution of events and a is proportional to the productivity of a volume, or the seis- micity rate. The b-value is one of the most important statistical parameters for describing the size scaling properties of seismicity; b-values change Figure 1. Tectonic areas and active fault systems in Turkey. Tectonic structures have been modified from Şaroğlu F. et al., (1992) and Bozkurt E. (2001). roughly in the range of 0.3 to 2.0, depending on the different regions. However, average regional scale estimates of b-value are usually equal to 1 (Frohlich C., Davis S., 1993). many factors can cause perturbation of average b-value (b~1.0); regions having lower b-values are probably regions subjected to higher applied shear stress after the main shock, whereas regions having higher b-values are areas which have experienced slip. High b-values are reported from areas having increased geological complexity, indicating the importance of multi-fracture areas; a low b- value is thus related to a low degree of heterogeneity of cracked medium, large stress and strain, high deformation speed and large faults (Bayrak y., Öztürk S., 2004). many methods can be used for calculating any region’s b-value but the maximum likelihood method is the most robust and widely-accepted method for estimating b-values (Aki K., 1965): b = 2.303 /(M — – M min + 0.005) (2) where M — is average magnitude value and M min is minimum mag- nitude value. 0.05 in equation (2) is a correction constant. If b=1 and M min=1 is used, Maverage=3.25 will be obtained. However, this is an ex- treme Mmin value. Mmin=1 did not occur in previous Turkish earthquake catalogues; Mmin in Turkish earthquake catalogues was around 3.0 until the beginning of the 2000s. many stations have been built in Turkey, especially after two destructive earthquakes in 1999, minimum earth- quake magnitude now being seen to be around 1.5 (average value may sometimes be higher than 3.25 which is not high value for Turkish earth- quakes). The standard deviation of seismic b-value (95% confidence limit) may be determined using the equation suggested by Aki (1965) as  1.96b / √n, where n is the number of earthquakes used to make the estimate. This would yield ±0.1–0.2 confidence limits regarding b-value for a typical sample consisting of n=100 earthquakes. Such sample con- sisting of n=100 events represents a specific calculation. The number of earthquakes in this study was 97,737; Table 1 shows that sometimes 110 earthquakes were used (in region 13) or 10,328 earthquakes on other oc- casions (in region 34). This value for n=100 earthquakes is thus a typical sample for the aforementioned calculation. Fractal dimension (correlation dimension, Dc) of epicentres’ spatial distribution Earthquake distribution spatial patterns and temporal patterns of oc- currence were demonstrated to be fractal using a two-point correlation dimension (Dc). Analysing correlation dimension is a powerful tool for quantifying a geometrical object’s self-similarity. grassberger and Procac- cia (1983) defined Dc and correlation sum C(r) as follows: Dc = lim[logC(r)/logr] (3) r  0 C(r) = 2NR