Potassium-rich evaporites are economically valuable sedimentary resources frequently associated with salt diapirs, recognized as strategic mineral deposits due to their critical role in fertilizer production and modern agriculture. The Azerbaijan–Zanjan–Hamedan Basin in northwestern Iran hosts numerous evaporite formations, several of which contain potash-bearing sequences. In this study, we investigate the Aji–Chai and Ghareh–Aghaj deposits using subsurface density distributions derived from gravity data inversion. Building on previous studies of salt diapirs in this basin, we introduce several methodological enhancements aimed at improving the geological reliability of density contrast models obtained from mixed \(L_p\) -norm inversions. First, we examine the effectiveness of the depth weighting exponent ( \(\beta\) ), which compensates for the rapid decay of potential fields with depth. We demonstrate that the influence of \(\beta\) depends on the chosen regularization scheme: An exponent that performs well in sparsity-promoting inversion for a single anomalous source may not yield satisfactory results under traditional Tikhonov regularization. Thus, selecting an appropriate depth weighting exponent is critical for accurately reconstructing target geometries in 3D gravity inversion. Second, recognizing the significant influence of the reference model on inversion outcomes, we explore two distinct scenarios: (1) applying equal weights to all smallness and smoothness components and (2) reducing the weight of the smallness term to \(1\%\) of each smoothness term, thereby promoting a more data-driven solution. These strategies are validated using synthetic models representing typical salt dome geometries, including dipping and vertical prisms. By systematically testing a range of depth weighting exponents under both scenarios, we identify optimal configurations for reliable model recovery, which are then applied to field data. The inversion results show that the Aji–Chai salt dome extends approximately 100 m vertically, dips eastward, and shows no clear evidence of structural control on salt emplacement. In contrast, the Ghareh–Aghaj salt dome exhibits a significantly greater vertical extent of approximately 220 m and is situated within a northeast–southwest-trending anticline.