Background and Objective: The Stream Length–Gradient (SL) index is widely used in morphotectonic studies to evaluate the effects of tectonic activity. However, SL values may be influenced not only by tectonic processes but also by other factors, such as lithological variations. In this study, the performance of the fractal characteristic of stream gradient, represented by the FD index, was evaluated for assessing tectonic activity and compared with that of the conventional SL index. The main objective was to evaluate FD's ability to reveal patterns associated with active tectonics and assess its spatial correspondence with seismic events, compared with the SL index.

Materials and Methods: The study area in the Sahneh region of western Iran was divided into 23 drainage basins for analysis. The longest stream in each basin served as the basis for calculations of the Stream Length (SL) index, which was derived from the local channel gradient and its position along cumulative stream length, resulting in one SL value per midpoint. The fractal dimension of the stream gradient (FD) was also calculated at intersections between the stream and contour lines between consecutive midpoints. The calculated values were interpolated into raster surfaces to analyze spatial variations, and contour maps of SL and FD were created. These patterns were compared with known fault locations, regional structural features, and lithological units. To quantitatively evaluate the relationship between the indices and seismic activity, the SL and FD rasters were each classified into 10 classes. The corresponding class value was then extracted for each earthquake epicenter, and the frequency ratio of seismic events was calculated for the different classes. In addition to the frequency-ratio analysis, the values of both indices at earthquake locations were extracted, and descriptive statistical parameters, including the mean, median, standard deviation, and coefficient of variation, were calculated to assess the concentration and dispersion of seismic events across different ranges of SL and FD values.

Results and Discussion: Higher SL values were mainly observed in the vicinity of thrust faults and were, in many cases, associated with lithological units of moderate to high resistance. This pattern suggests that variations in SL may result from the combined effects of tectonic activity and lithological contrasts. In contrast, lower SL values did not show a clear or consistent relationship with specific fault structures or lithological units at the scale of the present analysis. The pattern obtained from the FD index was different. Negative FD values were mainly associated with thrust structures and areas affected by uplift and vertical deformation, whereas positive values showed a stronger association with strike-slip regimes. Thus, in addition to reflecting variations related to the vertical component of deformation, the FD index also demonstrated the ability to detect changes associated with the horizontal and strike-slip components of deformation. These results suggest that fractal analysis of stream-gradient variations can also be useful for identifying potential structures and providing a more detailed assessment of regional deformation patterns. The evaluation of the relationship between the two indices and seismic events also indicated the relative superiority of FD. The highest frequency-ratio values for FD were obtained in classes with high FD values, indicating a considerable concentration of seismic events within these ranges. In contrast, only one SL class had a frequency ratio greater than 2. The descriptive statistical results were also consistent with the findings of the frequency-ratio analysis. The lower dispersion of FD values indicates that seismic events are concentrated within a relatively more uniform and distinct range of FD values, whereas SL values show greater variability at earthquake locations.

Conclusion: The results of this study showed that although the SL index remains a useful tool for identifying topographic variations and investigating the combined effects of tectonics and lithology, the fractal FD index exhibits greater sensitivity to structural controls in the study area. The spatial pattern of FD shows a clearer relationship with the fault mechanism. Furthermore, FD shows a stronger spatial correspondence with seismic events than the SL index. Overall, fractal analysis of stream-gradient variations can be used as a quantitative and complementary approach in morphotectonic studies for identifying tectonically active areas and for investigating the relationships among active structures, drainage-network response, and seismicity.