مدل‌سازی مؤلفه‌های مورفومتری دولین‌ها و ارائه شاخص بعد فرکتال در مطالعه گسل‌های مناطق کارستی (مطالعه موردی: مناطق کارستی بین پرآو و شاهو)

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشگاه تهران

چکیده

دولین یکی از لندفرم­های شاخص مناطق کارستی است که در اثر عوامل و فرآیندهای گوناگونی شکل می­گیرد. مطالعه مورفومتریک این عوارض علاوه بر اینکه یک تحلیل کمی از محیط‌های کارستی را فراهم می‌کند، بلکه مقایسه پارامترهای متنوع دولین ها ممکن است منجر به طرح فرضیاتی در مورد نحوه تکامل آن‌ها شود. هدف از این پژوهش تجزیه‌وتحلیل کمّی مؤلفه‌های مورفومتری دولین­ها جهت مدل‌سازی و ارائه شاخص بعد فرکتال گسل­ها برای ارزیابی فعالیت گسل­ها در مناطق کارستی بین پرآو و شاهو است. در این راستا از روش­های ژئومورفومتری، CCLs، شمارش جعبه­ای هاسدورف و تکنیک­های آنالیز رگرسیون استفاده شده است تا امکان تحلیل رگرسیون، مدل­سازی و حل تابع لگاریتمی Number – Size فراهم شود. نتایج آنالیز رگرسیون خطی تک متغیره نشان‌دهنده این است که مؤلفه‌های محیط با قطر بزرگ، قطر کوچک با محیط، قطر بزرگ با مساحت، مساحت با محیط و عمق با مساحت به ترتیب با ضرایب تبیین 93/0، 86/0، 85/0، 83/0 و 668/0 از بیشترین میزان همبستگی معنی‌دار برخوردارند. همچنین حداکثر ارتباط معنی‌داری برای روابط درجه 2 و 3 در سطح معنی‌داری 99/0، بین مؤلفه‌های مساحت و محیط با ضرایب تبیین 940/0 و 945/0 و خطای برآورد 05/0 و  04/0 وجود دارد. نتایج رگرسیون چند متغیره خطی نیز مؤید ارتباط معنی‌دار عمق با پارامترهای شیب، قطر کوچک و مساحت با ضریب تبیین 834/0 و خطای برآورد 85/7 است. تخمین بعد فرکتال در مناطق مورد مطالعه مؤید آن است که منطقه شاهو و پرآو به ترتیب با مقادیر 24/1 و 15/1 دارای بیشینه و کمینه ابعاد فرکتالی گسل‌ها می‌باشند. در واقع ارزیابی میزان فعالیت گسل‌ها به‌وسیله هندسه فرکتال نشان داد که معادله Number – Size و شاخص بعد فرکتال روشی مناسب جهت ارزیابی گسل‌ها در مناطق کارستی می‌باشند.

کلیدواژه‌ها


عنوان مقاله [English]

Modeling dolines morphometric factors and presenting an index of fractal dimension in studying the faults of karstic regions (a case study of the karstic areas between Paraov and Shahoo)

چکیده [English]

Introduction
Karst is a geomorphic and hydrologic system which is created due to the dissolution of soluble stones like lime, dolomite and Gypsum (Ozyurt et al., 2014). The development of a karstic system is dependent upon climactic, lithologic and structural (wrinkle, fault and gap) factors (Ford and Williams, 2013). The most important landforms in the created perspectives include carnic bands, dolines and swallowing gaps. These shapes are usually but not necessarily formed in the areas which suffer from a fracture or a gap (Kovacic & Ravbar, 2013). Nowadays the theory of fractal collections and multifractal measuring is extensively used in describing some natural processing like the activity of faults (Ayunova et al., 2007 & Feder, 1988). In fact the process of fault creation can be investigated through fractal concepts (Mandelbrot 1983 & Sarp 2014). As the behavior of the faults certainly nonlinear (Turcottee, 1990) and the fractal theory is a method for determining and predicting complex dynamic nonlinear behaviors (Yang et al., 2007) this method can be used to examine the behavior of faults (Torcotte, 1997).
 
Materials and instrumentation
Initially the dolines of the target areas were extracted on the basis of DEM10 meter and method CCLs. after extracting these dolines their morphometric factors which consisted of area, perimeter, depth, slope, large diameter and small diameter were calculated in GIS software. Following that the SPSS software was utilized for the descriptive and regressive analysis the morphometric parameters of dolines. To this end single and multivariable variable linear methods were employed and those models which were of more value were presented.
1/100000 geological maps of Kermanshah, Kamiaran, Miyan Rahan and Paweh were used to determine the fault systems of the examined areas and extract their fault maps. Afterwards, since the faults followed a vector shape, the Number-Size equation was selected to calculate the fractal dimension of the faults. In this equation a self-similar exponential relationship exists which is affected by the number factors and the size of spatial quantities. Therefore, based on what was explained, Number-size equation can be explained according to equation 1 (Mehrnia, 2006).
Equation 1): Log (Ns)= a K Log (s)
 In this equation Ns is the number of the phenomena (in this study the number of the faults), S is the size of the network, k is the coefficient of the line slope or the fractal dimension (Mandelbrot, 1983).
 
Findings and discussion
The results of the single variable linear regression shows that the relationships between perimeter with major diameter, area with perimeter, depth with area, minor diameter with perimeter and area with major diameter were statistically significant and the correlation coefficients were 0/93, 0.837, 0/668, 0/860, and 0/850. Moreover, the most degree of significant correlation for second and third degree equations was observed between perimeter and large diameter with correlation coefficients of 0/932 and 0/942 and the estimated error of 0/297 in the area has a possibility of error which is smaller than 0/01. The results of multiple regressions also revealed that the most significant correlation of the depth is with area, slope, and minor diameter with a correlation coefficient of 0/834 and estimated error of 7/85. The estimation of the fractal dimension in the investigated areas shows that Shahoo and Paraov areas have the maximum and minimum fractal fault dimensions which are 1/24 and 1/15 respectively.
 
Conclusion
This study was an attempt to analyze the dolines which exist between Shahoo and Paraov areas using quantitative geomorphology, statistic methods and fractal geometry. The existence of a high correlation between most of the morphometric factors of dolines indicates that that these landforms can be modelled with a high degree of accuracy provided that exact and sufficient data is existent. The employment of fractal geometry and Number-Size equation also showed that by estimating the fractal dimension through the above method the activity of the faults their relative effect on the solution of the soluble stones can be determined. As a matter of fact this method can be utilized as a new index in studying the faults of the karstic areas.

کلیدواژه‌ها [English]

  • dolines
  • morphometry
  • regression analysis
  • Fractal dimension
  • Number-Size equation
  • ثروتی، محمدرضا، رستمی، مژگان، نصرتی، کاظم، احمدی، محمود، (1393)، شناخت عوامل مؤثر بر پراکنش و رخداد فروچاله ها در منطقه گازرونی کرمانشاه با استفاده از رگرسیون لجستیک، جغرافیا و توسعه، شماره 36، صص 194-181.
  • رضایی مقدم، محمدحسین، محمدرضا، قدری، (1390)، تحلیل‌های کمی دولین ها در زمین‌های کارستی (مطالعه موردی، منطقه تخت سلیمان)، جغرافیا و برنامه‌ریزی، شماره 35، صص 135-113.
  • مهرنیا، سید رضا، (1386)، بررسی پتانسیل لرزه‌خیزی گسل شمال قزوین با استفاده از روش سنجش فرکتالی نشانگرهای مغناطیسی، اولین همایش پیش نشانگرهای زلزله.
  • مهرنیا، سید رضا، (1386)، تعاملات فرکتالی در تعامل با سامانه های اطلاعات مکانی (مطالعه موردی: گسل‌های شمال غرب ایران)، همایش ژئوماتیک.
  • قربانی، محمد صدیق، محمودی، فرج‌الله، یمانی، مجتبی، مقیمی، ابراهیم، (1389)، نقش تغییرات اقلیمی کواترنر در تحول ژئومورفولوژیکی فروچاله های کارستی (مطالعه موردی: ناهمواری شاهو، غرب ایران)، پژوهش‌های جغرافیای طبیعی، شماره 74، صص 16-1.
  • Argentieri, A., Carluccio, R., Cecchini, F., Chiappini, M., Ciotoli, G., De Ritis, R., Margottini, S. (2015). Early stage sinkhole formation in the Acque Albule basin of central Italy from geophysical and geochemical observations. Engineering Geology, 191, 36–47.
  • Attikos, C., & Doumpos, M. (2009). Faster estimation of the correlation fractal dimension using box-counting. In Informatics, 2009. BCI’09. Fourth Balkan Conference in (pp. 93–95). IEEE.
  • Ayunova, O. D., Kalush, Y. A., & Loginov, V. M. (2007). Relationship of the seismic activity of the Tuvinian and adjacent Mongolian areas with the fractal dimensionality of a fault system. Russian Geology and Geophysics, 48(7), 593–597.
  • Basso, A., Bruno, E., Parise, M., & Pepe, M. (2012). Morphometric analysis of sinkholes in a karst coastal area. In Geophysical research abstracts (Vol. 14, p. 4066).
  • Bondesan, A., Meneghel, M., & Sauro, U. (1992). Morphometric analysis of dolines. International Journal of Speleology, 21(1), 1.
  • Bruno, E., Calcaterra, D., & Parise, M. (2008). Development and morphometry of sinkholes in coastal plains of Apulia, southern Italy. Preliminary sinkhole susceptibility assessment. Engineering Geology, 99(3–4), 198–209.
  • Cvijić, J. (1893). Das Karstphänomen: Versuch einer morphologischen Monographie. Hölzel.
  • Ennes-Silva, R. A., Bezerra, F. H. R., Nogueira, F. C. C., Balsamo, F., Klimchouk, A., Cazarin, C. L., & Auler, A. S. (2015). Superposed folding and associated fracturing influence hypogene karst development in Neoproterozoic carbonates, São Francisco Craton, Brazil. Tectonophysics, 5, 1–62.
  • Ezersky, M., & Frumkin, A. (2013). Fault—Dissolution front relations and the Dead Sea sinkhole problem. Geomorphology, 201, 35–44.
  • Feder, J. (1988). Fractals, 1988. Plenum Press, New York.
  • Feng, T., Chen, H., Polyakov, V. O., Wang, K., Zhang, X., & Zhang, W. (2016). Soil erosion rates in two karst peak-cluster depression basins of northwest Guangxi, China: Comparison of the RUSLE model with 137 Cs measurements. Geomorphology, 253, 217–224.
  • Ford, D., & Williams, P. D. (2013). Karst hydrogeology and geomorphology. John Wiley & Sons.
  • Gutiérrez, F., Parise, M., De Waele, J., & Jourde, H. (2014). A review on natural and human-induced geohazards and impacts in karst. Earth-Science Reviews, 138, 61–88.
  • Kovačič, G., & Ravbar, N. (2013). Analysis of human induced changes in a karst landscape—the filling of dolines in the Kras plateau, Slovenia. Science of the Total Environment, 447, 143–151.
  • Lace, M. J., & Mylroie, J. E. (2013). Coastal karst landforms. Springer.
  • Liang, F., & Du, Y. (2013). An automated method to extract typical karst landform entities from contour lines on topographic maps. Proceedings of Geomorphometry, 46–49.
  • Liang, F., Du, Y., Ge, Y., & Li, C. (2014). A quantitative morphometric comparison of cockpit and doline karst landforms. Journal of Geographical Sciences, 24(6), 1069–1082.
  • Liu, D., Li, T., & Fu, Q. (2010). Fractal dimension estimation of groundwater depth series of well irrigation area in Sanjiang Plain based on continuous wavelet transform. In Natural Computation (ICNC), 2010 Sixth International Conference on (Vol. 8, pp. 3988–3992). IEEE.
  • Mandelbrot, B. B. (1983). The Fractal Geometry of Nature. Henry Holt and Company.
  • Ozdemir, A. (2015a). Investigation of sinkholes spatial distribution using the weights of evidence method and GIS in the vicinity of Karapinar (Konya, Turkey). Geomorphology.
  • Ozdemir, A. (2015b). Sinkhole Susceptibility Mapping Using a Frequency Ratio Method and GIS Technology Near Karapınar, Konya-Turkey. Procedia Earth and Planetary Science, 15, 502–506.
  • Ozyurt, N. N., Lutz, H. O., Hunjak, T., Mance, D., & Roller-Lutz, Z. (2014). Characterization of the Gacka River basin karst aquifer (Croatia): Hydrochemistry, stable isotopes and tritium-based mean residence times. Science of The Total Environment, 487, 245–254.
  • Parise, M., De Waele, J., & Gutierrez, F. (2009). Current perspectives on the environmental impacts and hazards in karst. Environmental Geology, 58(2), 235–237.
  • Perrin, J., Cartannaz, C., Noury, G., & Vanoudheusden, E. (2015). A multicriteria approach to karst subsidence hazard mapping supported by weights-of-evidence analysis. Engineering Geology, 197, 296–305.
  • Sarp, G. (2014). Evolution of neotectonic activity of East Anatolian Fault System (EAFS) in Bingöl pull-apart basin, based on fractal dimension and morphometric indices. Journal of Asian Earth Sciences, 88, 168–177.
  • Theilen-Willige, B., Malek, H. A., Charif, A., El Bchari, F., & Chaïbi, M. (2014). Remote Sensing and GIS Contribution to the Investigation of Karst Landscapes in NW-Morocco. Geosciences, 4(2), 50–72.
  • Turcotte, D. L. (1990). Implications of chaos, scale-invariance, and fractal statistics in geology. Palaeogeography, Palaeoclimatology, Palaeoecology, 89(3), 301–308.
  • Turcotte, D. L. (1997). Fractals and chaos in geology and geophysics. Cambridge university press.
  • Waltham, T., Bell, F. G., & Culshaw, M. (2007). Sinkholes and subsidence: karst and cavernous rocks in engineering and construction. Springer Science & Business Media.
  • Yang, J., Zhang, Y., & Zhu, Y. (2007). Intelligent fault diagnosis of rolling element bearing based on SVMs and fractal dimension. Mechanical Systems and Signal Processing, 21(5), 2012–2024.
  • Zhang, X., Shang, K., Cen, Y., Shuai, T., & Sun, Y. (2014). Estimating ecological indicators of karst rocky desertification by linear spectral unmixing method. International Journal of Applied Earth Observation and Geoinformation, 31, 86–94.
  • Zhong, L., & Xu, G. (2008). Application Actuality of Fractal Theory in Turbulence and Sediment Studies [J]. Journal of Chongqing Jiaotong University (Natural Science), 5, 34.