Abstract Accurately determining the mineralogical composition of rocks is essential for precise assessments of key petrophysical properties like effective porosity, water saturation, clay volume, and permeability. Mineral volume inversion is particularly critical in geological contexts characterized by heterogeneity, such as in the Upper Rhine Graben (URG), where both carbonate and siliciclastic formations are prevalent. The estimation of mineral volumes poses challenges that involve both linear and nonlinear rela…