I have a dataset for river water, rain water and geology (main elements and trace elements). I want to apportion the contribution of geology to water chemistry using for that purpose a model. I was trying to use the Inverse model approach (Tarantola, 2005) but no clear definition is provided in the bibliographic sources (Gaillardet et al, 1999; Millot et al, 2003; Wu et al, 2005, Moon et al, 2007).
Any ideas of how to apportion the river elements into different sources (reservoirs) and derive weathering rates as function of the geology (mainly igneous rocks: andesite and some rhyolites, eventually some carbonates) with the described information?