ارزیابی و مقایسه کارایی روش‌های کمی فرکتال و آنتروپی در تحلیل وضعیت لرزه خیزی زاگرس شمال غرب

زمین‌لرزه‌ها حاصل گسلش و پویایی زمین‌ساختی هر ناحیه هستند و نسبت به بزرگا، فضا و زمان توزیع فرکتالی دارند. در این تحقیق پارامترهای لرزه‌خیزی bvalue و fd به عنوان رویکرد کمی فرکتالی در تحلیل لرزه‌خیزی زاگرس شمال غرب بکار رفته است. پارامتر b با توزیع فراوانیبزرگای گوتنبرگریشتر و پارامتر fd به روش مربع‌شمار محاسبه و همچنین با استفاده از 30 خوشه تمرکز زمین‌لرزه‌ و عوامل مهم، پهنه‌های لرزه‌خیز با روش آنتروپی مشخص شدند. کاهش bvalue رخداد زمین‌لرزه‌های با فراوانی کم و بزرگای بالا و افزایش fd عدم خوشه بندی و توزیع یکنواخت زمین‌لرزه‌ها را نشان می دهد. همبستگی منفی این دو موید زمین‌ساخت فعال است. نتایج نشان می‌دهند که افزایش fd با کاهش bvalue (همبستگی منفی 60 درصد) همراه است. منطقه a (غرب کرمانشاه) ، بالاترین میزان (fd (1/02 و پایین‌ترین میزان b (0/78) را داراست که به معنی توزیع بالای تنش در منطقه (و شاهد آن زمین‌لرزه اخیر کرمانشاه با بزرگای 7/3) است. منطقه e (محل اتصال گسل‌های جبهه ‌کوهستان و بالارود)، مشابه a است اما زمین‌لرزه‌های آن بزرگای کمتری دارند (5 و 6 ریشتر). منطقه f (محل پیوند گسل‌های اصلی و جبهه کوهستان زاگرس)، با وجود تراکم بالای گسل و زمین‌لرزه، نقطه مقابل a است که بیانگر رها شدن تنش در قالب زمین‌لرزه‌هایی کوچک است. منطقه c (حاشیه غربی با کمترین تمرکز گسل و فراوانی زمین‌لرزه)، مشابه f است. مناطق d و b (مجاور گسل‌‌های معکوس و رورانده زاگرس، شرایطی زمین‌ساختی متوسطی دارند. نتایج مدل آنتروپی نتایج fd را تایید می‌کند و رابطه معکوسی با مقادیر b دارد.

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

IntroductionThe 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 frequencymagnitude distribution of earthquakes by using FD and bvalue parameters, respectively. Here bvalue is the main factor in GutenbergRichter 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 boxcounting 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 faultedfolded 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). Material and methodsData 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)= abm, 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 frequencymagnitude (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).Result and discussionEstimated bvalue indicates approximately reciprocal values compared with FD values. Decrease in bvalue 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 numbersize 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).ConclusionAreas with high FD value and low bvalue 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 bvalue (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 bvalue as B and the changes of Entropy max values are same as FD values.