Spatial Fractal Evolutions and Hierarchies for Microearthquakes in Central Greece

Abstract

Statistical characteristics of seismicity represented by microearthquakes are examined for three regions in central Greece, in particular the fractal correlation dimension, D 2 , and traditional b values are examined in tandem as a function of time by using the moving window technique. The Patras region contains the complicated tectonics, extending to damaging historical earthquakes of the western Corinth Gulf and the Rio Graben, yielding D 2 values between 0.40 and 1.20 with b between 0.94 and 1.27: unusually, the temporal evolution between D 2 and b generates a positive correlation, although the variation is mostly in D 2 . When the whole evolution is divided into two stages then the positive correlations are even stronger than for the whole evolution. The views of Henderson and others might suggest a highly fractured, fluid-filled zone. The Pavliani region, with no known acti6e fault, and the Volos region, containing the through-going Nea Ankhialos fault, yield D 2 values 0.33 to 0.79 with b 0.92 to 1.30 and D 2 0.82 to 1.56 with b 1.02 to 1.37, respectively. Temporal evolution between D 2 and b provides a typical negative correlation in both regions. Examination of gross seismicity (time window embracing the whole data set) in each region produces D 2 values for the Patras and Volos regions that are both larger than that for Pavliani; there are no obvious differences amongst the b values. This accords with the knowledge that Patras and Volos are in regions with very active seismotectonic features which generate repeated strong earthquakes exceeding 6 M s . D 2 for both regions is fairly close to 1, the topological dimension of a line, consistent with seismicities on leading active fault zones or through-going faults. These values highlight the ability for microearthquakes to illuminate the character of their parent tectonic province. Resolution and hierarchy in these data from Greece are compared with these aspects elsewhere (Japan, Turkey, South America, USA) in the sense that their banding with respect to examined magnitude, areal extent and duration of observation period for respective data sets is examined in relation to the earthquake potential of the parent seismotectonic province. Evolutions are then categorised as being macroscopic, transitional or microscopic in character.

Earthquake Source Zones in Northeast India: Seismic Tomography, Fractal Dimension and b Value Mapping

“…In the practical calculation, the fractal dimension analysis is based on a power law and is turned into a linear law after logarithmic transformation. Therefore, sufficient data points are the key for a reliable estimate of fractal dimension based on the ensuing linear regression (XU and BURTON, 1999). SMITH (1988) suggested the minimum number of points or events required for a reliable calculation of a correlation dimension as:…”

Seismicity pattern of the Betic Cordillera (Southern Spain) derived from the fractal properties of earthquakes and faults

“…The regional stress field can be nicely identified as follows: 1 NE-SW tension in Ubrique; 2 WNW-ESE compression in Malaga that might be related to the arc-shaped distribution of intermediate earthquakes existing south of this city; 3 ENE-WSW tension (and other secondary NNW-SSE depicting a radial pattern) in Granada; 4 N-S compression in Alicante. Xu and Burton (1999) reported that the coexistence of two different stress fields in a same region (central Greece), interacting with variable seismicity, could explain the relatively low intensity of the stresses (high b-value). This phenomenon may have happened in zone 2 (dominated by extension) with a less stress accumulation, making it more heterogeneous than zone 1 (dominated by compression) that is subjected to local stresses of similar direction.…”

“…According to Utsu (1965), when the number of events used for the estimation exceeds 50, the maximum likelihood method gives a stable estimation of the b-value. Xu and Burton (1999) proposed a minimum of 42 earthquakes for the calculation of the dimension with the Grassberger-Procaccia algorithm, and Bhattacharya and Kayal (2003) reduced this number to 20 earthquakes inside each sample. More recently, Singh et al (2008,2009) have considered a minimum of 50 earthquakes for the calculation of the b-value and the fractal dimension.…”

Magma intrusion as a driving mechanism for the seismic clustering following the 9 May 1989 earthquake swarms at the Canary Islands

“…The fractal approach has introduced a new statistical tool to quantify the scale invariant distribution of seismicity and, with that, the properties of randomness and clusterization. Time variations of the spatial fractal dimension of seismic events have been found for different areas in the world allowing a quantitative characterisation over time of scale invariant failure processes acting in seismogenic volumes/fault zones (Lomnitz-Adler 1992, De Rubeis et al 1993, Öncel et al 1996, Tosi 1998, Xu and Burton 1999, Gospodinov et al 2012). The method often preferred for calculating the fractal dimension D on timespatial earthquake sequences is the correlation integral method (Grassberger and Procaccia 1983).…”

“…The method often preferred for calculating the fractal dimension D on timespatial earthquake sequences is the correlation integral method (Grassberger and Procaccia 1983). Its simplicity and reliability with respect to the box counting algorithm has been widely discussed (among others, by Henderson et al 1992, De Rubeis et al 1993, Öncel et al 1996, Tosi 1998, Xu and Burton 1999.…”