Morphometric indices are valuable tools for identifying tectonically active areas. The stream length–gradient index (SL) is one of the most important indices for distinguishing active regions. Compared with other morphometric indices, it is highly sensitive to uplift. However, this index is also sensitive to rock resistance along the flow path; therefore, lithology can significantly influence SL values.In this study, we introduce the fractal characteristics of river gradients for the first time and apply them to evaluate active tectonics and investigate the structural setting of northwestern Sahneh. To compare the effects of faulting and rock resistance on these two parameters and to assess their performance in identifying active areas, the lithological units of the region were first classified into five resistance classes. Geographically weighted regression (GWR) was then applied to examine local variations in SL and FD relative to distance from faults to clarify fault-related influences.The obtained fractal dimensions do not exhibit the limitations of the traditional SL index, such as sensitivity to rock strength and grain size. In addition to identifying thrust faults, the method also reveals strike-slip faults that correspond well with mapped faults in the area. The analysis further identifies active structures that are sometimes overlooked by geologists. These structures are likely anti-Riedel faults associated with the MRF. Their proximity to cities such as Kamyaran, Sonqor, Muchesh, and Sattar highlights the need for further investigation of earthquake risk.