The Sefidrood Basin in northwestern Iran, located within the tectonically active Alborz–Central Iran transition zone, displays considerable structural complexity. This study employs mathematical and geometric patterns, particularly the Fibonacci sequence and the golden ratio, in combination with advanced statistical approaches such as the gamma distribution, the chi-square test, and Fisher’s exact test, to investigate the morphotectonic and neotectonic conditions of the basin and its sub basins. Topographic and structural data were derived from maps and satellite imagery and analyzed using a GIS framework. A quantitative classification system based on Fibonacci ratios was applied to categorize the basin into five classes reflecting varying levels of morphotectonic activity. The results show that 96% of the basin lies within the range of weak to strong morphotectonic activity, whereas 4% is affected by neotectonic processes, primarily concentrated along the Qezelozan–Shahroud valleys, where neotectonic activity is most pronounced. Gamma based analysis confirms dynamic equilibrium with a skewness value of 0.7171 and a kurtosis of 0.782. The chi-square test indicates that the sub-basins behave independently with respect to morphotectonic activity, and Fisher’s exact test demonstrates that all sub-basins operate within a shared ergodic structural framework. The findings indicate the presence of a negative cybernetic system with exponential memory that is adjusting the basin toward its base level in the Caspian Sea.
Introduction
The Sefidrood Basin, a key sub-basin in northwestern Iran, features complex tectonic processes. Given its geographical and tectonic significance, identifying morphotectonic patterns and assessing its long-term equilibrium state are essential. This study adopt a Fibonacci-based geometric patterns and statistical analyses, including gamma distribution, chi-square tests, and Fisher’s exact test, representing Iran’s first integrated application of numerical approaches in morphotectonic analyses and distinguishing this work from prior studies.
Fibonacci sequences and the golden ratio (φ = 1.618) have been employed across disciplines, including architecture, geology, biology, and system modeling. In the Sefidrood Basin, these patterns serve as quantitative tools to identify potential zones of tectonic and neotectonic activity, differentiating this work from earlier qualitative assessments.
Material and Methods
A hybrid framework combines mathematical-statistical techniques with geomorphological analyses to evaluate the morphotectonic and neotectonic status of the Sefidrood Basin and its sub-basins. Key stages:
Data Collection: Topographic maps (DEM), field geological data, and 350 geospatial/elevation points were gathered and integrated in ArcGIS Pro to characterize tectonic features.
Fibonacci-based Classification: Morphotectonic data were categorized using Fibonacci ratios (0.236, 0.382, 0.5, 0.618, 0.764) to define five levels of tectonic activity, enhancing spatial pattern recognition.
Statistical Techniques: To address non-normality (right-skewed data), non-normal methods were employed: (1) Gamma distribution analysis for probabilistic modeling of long-term tectonic patterns; (2) Chi-square tests to assess independence between sub-basins and the main basin; (3) Fisher’s exact test to compare variability where appropriate.
PDF/CDF Plots: Probability density functions and cumulative distribution functions were generated from the gamma distribution to visualize tectonic activity distributions.
GIS-Based Spatial Analysis: Overlay of fault lines, tectonic indices, Fibonacci patterns, gamma curves, and PDF/CDF maps in ArcGIS Pro provided insights into spatial relationships among tectonic features.
Comparative and Inductive Analyses: Two sub-basins were analyzed in detail (inductive approach), with remaining sub-basins summarized in tables (comparative approach) to identify commonalities and differences.
Moment Analysis and Inference: Statistical moments (mean, variance, skewness, and kurtosis) described the distribution of tectonic activity, enabling a robust characterization of the basin’s statistical structure.
Results and Discussion
The Sefidrood Basin shows a highly organized large-scale structure despite tectonic complexity. About 96% of the basin area falls within the weak-to-intense morphotectonic activity range, with 4% neotectonically active, concentrated along the Qezelozan–Shahroud corridor (Manjil Fault). This pattern aligns with regional tectonic models of Arabia–Eurasia convergence, suggesting a phase of relative tectonic quiescence.
Interpretations include a negative-feedback, memory-dependent dynamics driving long-term stability, and a heterogeneous, nonlinear regime with localized deformation. These findings have implications for spatially targeted hazard management.
Gamma-distribution results (skewness 0.7171, kurtosis 0.782; mean 1.45, second moment 0.27, SD 0.519) indicate a stable system with no signs of imminent morphotectonic instability, consistent with non-normal probability approaches highlighted by Khosin & Wang (2022).
Chi-square and Fisher’s exact tests show sub-basins are statistically independent from the main basin (chi-square values 6.2–53; all within 99% CI), suggesting a shared underlying tectonic driver within an ergodic framework.
GIS maps identify the highest activity along the Qezelozan–Shahroud corridor and Manjil Gorge; Rudshur lies outside the 95% CI, indicating independence from Zanjanrood.
Validation results show a confidence level of 90.85% with a two-tailed error margin below 8.9%, supporting the reliability of the methods. The study advances Fibonacci-based and gamma-distribution approaches for morphotectonic analysis and offers a framework for sub-basin dynamics within a unified tectonic system, with implications for water resource management, urban planning, and hazard mitigation.
Conclusion
An innovative approach combining Fibonacci patterns and gamma statistics reveals a dynamic equilibrium in the Sefidrood Basin, with only 4% neotectonic activity concentrated along major fault zones. Sub-basins are statistically independent yet integrated within a larger ergodic system, indicating shared long-term tectonic control. Fibonacci ratios and gamma distributions provide effective tools for hazard-zone identification and tectonic modeling, offering a framework for future research in similar basins and suggesting multi-scale, and spatial modeling methods for seismically active regions.