Evaluation and comparison of the efficiency of quantitative fractal and Entropy methods in analysis of northwest Zagros seismicity

The purpose of present study is seismicity analysis of Lorestan folded arc and its adjacent thrust belt using quantitative methods. To reach this aim we performed analysis of seismicity using quantitative methods to find possible vertical and horizontal changes in seismic activity across the main Zagros faults of the northwestern part of Zagros. Firstly, we used fractal geometry and frequency-magnitude distribution of earthquakes by using FD and b-value parameters, respectively. Here b-value is the main factor in Gutenberg-Richter empirical relation which indicates the exponential distribution of earthquake magnitudes (Godano et al, 2014; 1765). This parameter also is known as fractal dimension (Mirabedini & aghatabay,2015: 60). FD is fractal dimension of earthquake epicenters distribution which has been calculated by box-counting method (Turcotte 1997). On the other hand Entropy model has been applied to specify potential of seismicity by using effective factors and 30 points of earthquake concentration. The study area in northwestern part of Zagros was divided to the simply folded arc of Lorestan and faulted-folded belt of high Zagros. Several main faults pass through the area from NW to SE and divide its main morphotectonic units as High, folded and foredeep parts of Zagros (Berberian, 1995: 193).

Data in this research can be divided to two part: parameters of earthquakes (magnitude, depth, location of epicenter) and linear data of faults and anticline/syncline axes. These data have been changed into new layers by GIS software extensions (density of epicenter and depth of earthquakes, density of faults and anticline/syncline axes, distance of fault and epicenter of earthquakes, interpolation of epicenter of earthquakes) to be applied in Entropy model, in other hand frequency of magnitude clusters and surface distribution of earthquakes are main data in Gutenberg–Richter relation and Fractal methods respectively. Numerical results of mentioned methods have been calculated and drawn in excel software. Gutenberg–Richter relation (Gutenberg & Richter 1944) is defined as Log N(m)= a-bm, where N is the cumulative number of earthquakes with magnitude larger or equal to m, a is a constant (seismicity level) and b is the slope of frequency-magnitude (size distribution) (Godano, 2014). To calculate fractal dimension of distribution of earthquake epicenters, box counting method suggested by Turcotte (1997) were applied by using Hausdorff dimension, which in two quantity of size (side length of grids) and number (number of grid boxes containing earthquake) are used to calculate FD value (Schuller et al, 2001: 3). In the other section, earthquake epicenters are divided to several clusters with different magnitude, then kernel density of each cluster was applied and subsequently, the maximum concentration of each magnitude cluster was determined as a point layer. Followingly, by overlaying these point layer with effective layers in seismicity analysis, their characteristics was extracted. Finally, an Entropy matrix was calculated and using experts rating and computing the layer’s weight, seismic zones were identified (Zonggi, et al, 2010).

Estimated b-value indicates approximately reciprocal values compared with FD values. Decrease in b-value reveals that stress level and probability of large magnitude earthquakes occurrence is quite high and increase in FD shows that earthquakes are not clustered and are distributed homogeneously along a line in understudy area. Calculated number-size values for earthquakes represent both partial and popular FD changes. Based on partial FD, three populations can be classified: (a) Background with FD larger than popular FD; (b) Threshold with FD lower than 0.7: and (c) Anomaly with FD more than two. Based on popular FD, distribution of earthquakes is linear and transition to chaos phase is not predicted. Comparison between maximum values of Entropy zoning and FD values for each box indicates that these two values show 93% correlation (regardless of the C box values due to incompatibility with value of other boxes).

Areas with high FD value and low b-value are more tectonically active. The box labeled A which represent western parts of Kermanshah in folded Zagros, has the highest FD value (1.02) and lowest b-value (0.78). The box labeled F in southern east part is in contrast with it (highest b value:1.02 and one of the lowest FD value: 0.89) in understudy areas. E (Balarud fault) and D (High and folded Zagros) parts have almost the same FD and b values. FD and b values in B (high Zagros) are equal and less than the aforementioned areas. C (that contains a part of mountain front fault) has the lowest value of FD and same b-value as B and the changes of Entropy max values are same as FD values.