Journal of Spatial Analysis

---

Flood as a natural disaster follows certain erratic patterns which was made confounding factor. Flood risk is variable and complex that depends on very phenomena such as rainfall, runoff concentration and high exposure of the flooding downstream areas.

    This are changes over time and from regions due to natural conditions, human activities, and damage culture of the community at risk. Occurrence of chaos at flood risk changes the trend of predictable processes. In the other words, although flood is a disaster, the occurred irregularities in its patterns can reveal its complicated nature. Flood pattern irregularities are the incident evidence of chaos in the system which can be studied by fractal geometry. The occurred events in spatial variability of floods in the last 50 years show they can be occur as unusual urban flood in Tehran.

    Tehran city may experiences the difference life and property damages because the high varieties in the socio-economic and the life quality level in regions, also structural varieties in the city fabric??. Ignoring the natural factors in spatial planning, overrun and destruction of natural morphology as a result of urban activities and subsequently disturbing urban drainage system lead to unpredictable and destructive floods in Tehran.

    The Tehran precipitation layer was prepared based on 27 weather stations data in the period of 10 years (1998-2009) and Kriging model with a Gaussian function. The runoff is calculated by Soil Conservation Service Curve Number (SCS-CN) and precipitation layer. The flood hazard potential map has been created by 8 variables and Analytic Hierarchy Process (AHP). This map as an index to define the said complexity was prepared in 5 categories of risk by combination of Tehran metropolis flood hazard and vulnerability maps. Then it was divided into hydrological basins and 12 basins were selected randomly. The Perimeter-Area Fractal and Number-Area Model were used to study the chaos and turbulence in the Tehran’s flood pattern.

     Explanation of locational changes of risk between the basins needs to calculate the weighted average risk and the independent variables in 12 basins that obtained by zonal statistics. Based on these average values the factor analysis used to determine the Varifactors or main components of the variability in flood risk between the basins. Finally, fractal geometry models (perimeter-area and cumulative number-area) were used to demonstrate the chaos of the flood risk value in 5 categories of risk.

    In this research the Tehran flood zoning map was calculated at 5 hazard categories. The fractal of sample basins had increased by increasing in the level of hazard map. Generally, the higher DAP values from 1 represented increasing in the chaos or irregularities of Tehran floodhazard. The obtained DAP from very low to very high risk levels are 1.206, 1.216, 1.23, 1.263 and 1.293 respectively. The increasing of DA indicated that turbulence hazard increases based on Perimeter-Area fractal model, thus, with the increase in hazard the DAP and DP values were greater. Also, the results of Number-Area Model showed turbulence floods in the five classes of hazard. The area cumulative number of risk levels are 0.74, 0.79, 0.85, 0.86 and 0.88 respectively; this trend showed the less size of flood risk polygons from very low to very high risk levels. In the other words, by increasing the risk level the polygons gets smaller and indicates the increase the flood risk chaos.

    The occurrence pattern of natural phenomena and even natural hazards have a regularity type in normally condition; if this regularity disrupts for any reason, irregularities or chaos happens. In present study, the results of fractal analysis in sample basins presented the chaos pattern in Tehran floods. Also the heavy rainfall can be predicted in Tehran but the prediction of the flooding distribution was not provided. According to the recorded floods in Tehran the flooding begins always in the northern valleys of Tehran, like Darband, Kan or Golabdareh basins,  are not similar to damage pattern. As a result, despite several studies and projects which have been implemented about flood phenomenon in Tehran, this is unpredictable and uncontrollable in the city.

---

 
Evaluation and comparison of the accuracy of fault and seismic data in fractal analysis of northwest Zagros tectonic
Introduction
Complexity of natural processes especially tectonic processes that shape landscapes cannot be evaluated by classic geometry. In comparison with integer dimension of Euclidean space, fractal geometry can analyze features with non-integer dimension (Turcotte, 1977:121). Fractal behavior in such features shows self-similarity that this component is independent of the accuracy of investigation (Baas, 2002, 311). In fact, fractal dimension, is scale-invariant (Phillips, 2002, 144). Spatial variations of fractal parameters are an important factor in studying the tectonic state of regions. By determining the fractal dimension of Linear structures such as faults, it is possible to compare their geometry disorder (Suk moon et al, 1996:5). This parameter affects seismic behavior of fault because earthquake is an event related to faulting (Bachmanov, et al, 2012: 221) and Their concentration in an area indicates tectonic activity. In this research we performed fractal analysis using box counting method on fault and seismic data of northwest of Zagros about different scales of fault and different time periods of earthquake epicenters of two organizations with various detail to find and examine their fractal behavior by fractal dimension.
Methods
Data in this research can be divided to three clusters: 1. Fault lines of two scales of geology maps (1:100000 and 1:250000), 2. Earthquake epicenters of two periods of times prepared by two organizations (20 century data of Institute of Geophysics and 1900-2020 data of International Institute of Earthquake Engineering and Seismology) and 3. The second cluster with exert of Magnitude of completeness of earthquakes that show the minimum magnitude above which the data in the earthquake catalog is complete. Fractal analysis applied on these data by box counting method. To achieve this goal firstly, under study area divided to 6 boxes that contain main fault trends horizontally and vertically (A: folded Zagros in west of Kermanshah, B: faulted Zagros around Kermansha and east of kermansha, C: folded Zagros near mountain front fault, D: An area between faulted and folded Zagros near Khoramabad, E: Area around Balarud fault and F: An area between Balarud and mountain front fault to faulted Zagros). To calculate fractal dimension of fault lines and 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 epicenter or fault) are used to calculate FD (total fractal dimension) value (Schuller et al, 2001: 3). Relation between reciprocal of side length (quantity of size) and number of boxes containing point and linear features (quantity of Number) was drawn Logarithmically as a linear regression in Excel that shows fractal dimension.
Result and discussion
Larger values of fractal dimension indicate greater geometric disorder (Sukmono et al., 1996: 5). Analysis of faults of two scales represent that faults geometry is fractal and the amount of FD for scale of 1:100000 compared with scale of 1:250,000 is larger but their result approximately is same. The FD values for both scales are locate between 1 and 2 that expresses development of the fractal community of faults has a linear trend. On the other hand, for earthquakes, increase in FD values shows that earthquakes are not clustered and are distributed homogeneously (Oncel & Wilson, 2002: 339) along a line in understudy area. Calculated number-size values for faults and earthquakes represent both partial and popular FD changes. Based on partial FD, two populations can be classified: (a) Background with FD larger than popular FD; (b) Threshold with FD lower than popular FD.
Conclusion
Fractal analysis of faults of two scales of geology maps reveals that the order of active areas with high FD values in both scales are same but due to different details of faults in geology maps of geology survey and oil company, in scale of 1:100000 area labeled B and in scales of 1:250000 area labeled A is the most tectonically active region, however, area labeled E in both scales has lowest value. The order of active areas based on FD values for earthquake epicenters of 1900-2021 data of geophysics institute do not support other results because area labeled C with low density of faults and earthquake epicenters is in the first order and area labeled A is on the contrary of it. However, FD results of 20 century earthquake epicenters with exert of magnitude of completeness are reliable and higher magnitude of earthquakes spatially recent Ezgeleh earthquake in area labeled A is its evidence.
Keywords: Fractal, Tectonic, Northwest Zagros, Fault, Earthquake