Document Type : Research Article
Author
Department of Geography, Faculty of Humanities, University of Zanjan, Zanjan, Iran
Abstract
The Sefidrood basin in northwestern Iran, situated within the seismically active Alborz–Central Iran tectonic zone, exhibits complex morphotectonic characteristics. This study integrates mathematical-geometric patterns—particularly the Fibonacci sequence and golden ratio—with advanced statistical methods, including gamma distribution, chi-square, and Fisher’s exact test, to analyze the morphotectonic and neotectonic behavior of the basin and its sub-basins. Topographic and structural data were extracted from geological maps and satellite imagery, processed in a GIS environment, and classified into five morphotectonic activity classes using a Fibonacci-based quantitative framework. Results show that 96% of the basin experiences weak to intense morphotectonic activity, while only 4% is affected by neotectonic deformation, primarily along the Qezelozan–Shahrood valley, a zone of active faulting. Gamma distribution analysis confirms a state of dynamic equilibrium, with skewness of 0.7171 and kurtosis of 0.782, indicating a stable, near-symmetric tectonic regime. Chi-square testing reveals structural independence among sub-basins, whereas Fisher analysis demonstrates that all operate within a shared ergodic system. Together, these findings suggest the presence of a negative cybernetic system with exponential memory, progressively adjusting the basin toward base level (Caspian Sea). This hybrid approach highlights how mathematical patterns and statistical modeling can enhance the understanding of tectonic dynamics in complex orogenic regions. The results provide valuable insights for seismic hazard assessment, landscape evolution studies, and regional planning in tectonically sensitive areas.
Introduction
The Sefidrood Basin is one of the key sub-basins in northwestern Iran, characterized by complex tectonic processes. Due to its significant geographical and tectonic position, identifying morphotectonic patterns and determining its long-term equilibrium state are of high importance. In this study, advanced mathematical-geometric Fibonacci patterns and statistical methods—including gamma distribution, chi-square test, and Fisher analysis—were employed. This approach represents the first integrated application of numerical structures in morphotectonic analyses within Iran, distinguishing it from previous studies.
Fibonacci sequences and the golden ratio (ϕ=1.618) have historically been used across various human and natural sciences, including architecture, geology, biology, and systemic modeling. In the Sefidrood Basin, these patterns were applied as quantitative tools for identifying potential zones of tectonic and neotectonic activity, setting this research apart from earlier domestic studies that primarily relied on qualitative assessments.
Material and Methods
This research adopted a hybrid methodological framework combining mathematical-statistical techniques with geomorphological structures to analyze the morphotectonic and neotectonic status of the Sefidrood Basin and its sub-basins. The methodology included several stages:
Data Collection
Essential data were gathered from multiple sources: Topographic maps (DEM), Field geological data, and 350 geospatial and elevation points collected across the basin. These datasets were integrated using ArcGIS software and spatial analysis tools to provide a comprehensive understanding of the area's tectonic characteristics.
Granikagiri Classification Based on Fibonacci Ratios
In this stage, morphotectonic data were classified using the golden ratios of the Fibonacci sequence. These ratios enabled the categorization of tectonic activity intensity into five levels: This classification significantly improved the accuracy of spatial pattern recognition and identification of areas prone to tectonic activity.
Use of Advanced Statistical Techniques
Given the non-normal nature of the dataset (right-skewed distribution), the use of standard normal-based statistical methods would have introduced logical errors. Therefore, advanced non-normal approaches were applied: 1- Gamma Distribution Analysis: Used as the foundation for probabilistic modeling and ergodic structuring of long-term tectonic patterns. 2- Chi-Square Test: Conducted to assess the statistical independence of sub-basins from the main basin. 3- Fisher’s F-Test: Applied to compare variances between the Sefidrood sub-basin and others, revealing structural interdependence despite local independence.
Drawing Probability Density and Cumulative Distribution Curves (PDF & CDF)
Using the gamma distribution, probability density functions (PDFs) and cumulative distribution functions (CDFs) were plotted. These visualizations helped illustrate tectonic patterns and allowed intuitive interpretation of activity distribution.
Spatial Analysis Using GIS
Spatial data were analyzed using ArcGIS Pro, enabling the overlay of multiple thematic layers such as: Fault lines, Tectonic indices, Fibonacci patterns, Gamma curves, and PDF/CDF distributions. This step provided detailed insight into the spatial relationships among tectonic features.
Comparative and Inductive Analyses
The data were analyzed through two complementary approaches: Inductive analysis of two selected sub-basins in detail, and Comparative analysis of other sub-basins summarized in tables. This dual approach enhanced understanding of both commonalities and differences in structural behavior among the sub-basins.
Moment Analysis and Statistical Inference
Statistical moments were calculated to characterize the distribution of tectonic activity: First Moment (E(X)): Equivalent to the weighted average of tectonic activity. Second Moment (M2): Reflecting variance and dispersion level. Skewness: Indicating asymmetry in the distribution. Kurtosis: Representing the concentration of data. These analyses enabled accurate description of the statistical structure of the basin and its sub-basins.
Results and Discussion
The findings of this study reveal that the Sefidrood Basin, despite its tectonic complexity, exhibits a highly organized and coherent large-scale structure, identifiable through an integrated application of mathematical-statistical analyses and Fibonacci-based patterning. The morphotectonic assessment of 350 field-based data points, classified using a five-tier framework based on Fibonacci ratios (0.236, 0.382, 0.5, 0.618, 0.764), demonstrates that 96% of the basin area falls within the range of weak to intense morphotectonic activity, while only 4% is classified as neotectonically active. This spatial distribution aligns closely with regional tectonic models involving compressional forces from the Arabia-Eurasia convergence (Radfar et al., 2019), suggesting that the basin is currently in a phase of relative tectonic quiescence.
This dynamic equilibrium can be interpreted through two key mechanisms: first, the basin appears to operate under a negative feedback, memory-dependent exponential cybernetic system that drives it toward long-term stability by dampening abrupt tectonic fluctuations. Second, the scattered and non-uniform distribution of deformation indicates a heterogeneous and nonlinear tectonic regime, where strain is accommodated locally rather than uniformly. These insights have significant implications for regional planning, emphasizing that hazard management should be implemented in a spatially targeted rather than basin-wide manner.
Furthermore, gamma distribution analysis, applied due to the right-skewed nature of the data (skewness = 0.7171, kurtosis = 0.782), revealed a mean of 1.45, second moment of 0.27, and standard deviation of 0.519, all within acceptable bounds for a stable system. The absence of extreme fluctuations and the near-normal distribution pattern confirm that the basin is in a state of dynamic equilibrium, with no signs of imminent morphotectonic instability. This finding is consistent with Khosin & Wang (2022), who emphasize the importance of non-normal probability functions in tectonic analysis.
Statistical evaluation of sub-basins using chi-square and Fisher’s exact tests yielded a critical insight: although all sub-basins showed structural independence from the main basin (chi-square values ranging from 6.2 to 53), they all fell within the 99% confidence interval, indicating a shared underlying pattern. This paradox—local independence within global coherence—suggests that each sub-basin operates within a large-scale ergodic cybernetic framework governed by a common tectonic driver. This phenomenon, previously underexplored in regional studies, resonates with Turner’s (1999) theory on the spatial geometry of Fibonacci sequences in natural systems, highlighting how complex basins can exhibit both localized autonomy and systemic unity.
GIS-based intensity maps further reveal that the highest concentration of morphotectonic activity is located in the northern and central sectors of the basin, particularly along the Qezel Ozan–Shahroud valley and the Manjil Gorge, coinciding with known active fault zones. These areas are identified as high-risk zones for ongoing tectonic deformation. In contrast, the Rudshur sub-basin lies outside the 95% confidence interval, indicating complete statistical independence from the Zanjanrood sub-basin.
Finally, validation results, with a confidence level of 90.85% and a two-tailed error margin below 8.9%, confirm the high accuracy and reliability of the applied methodologies. This study not only advances the novel application of Fibonacci sequences and gamma distribution in morphotectonic analysis, but also provides a new conceptual framework for understanding sub-basin dynamics within a unified tectonic system. These findings can inform water resource management, urban planning, and natural hazard mitigation, particularly landslide and flood risk assessment, in tectonically sensitive regions.
Conclusions
This study introduced an innovative approach to analyzing the tectonic and geomorphological dynamics of the Sefidrood Basin by integrating Fibonacci mathematical patterns and gamma statistical models. Key findings include:
The Sefidrood Basin operates under a dynamic equilibrium state, indicated by low skewness and mesokurtic distribution. Only 4% of the basin shows neotectonic activity, mainly concentrated along the Qezelozan–Shahroud corridor (Manjil Fault). Sub-basins are statistically independent, yet part of a larger ergodic system, suggesting shared long-term tectonic control. Fibonacci ratios and gamma distributions serve as powerful tools for hazard zone identification and structural tectonic modeling. These findings offer a new theoretical framework for understanding tectonic evolution and can guide future research in similar basins across Iran. Additionally, this study introduces multi-scale analysis, artificial intelligence, and spatial modeling as promising methodologies for further investigations in seismically active regions.
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