[Truncated abstract] Mineralogical and geochemical characteristics were identified for regolith overlying two Australian Au deposits that discriminate mineralized and associated hydrothermally-altered rock from weathered rock that was not hydrothermally-altered. Mineralization was lithologically controlled within a previously unrecognized diorite dyke at the lower Proterozoic mesozonal Groundrush deposit, Tanami region, Northern Territory. Although hydrothermal alteration effects within the dyke were subtle and obliterated by weathering, Ti/Zr ratios clearly discriminated the diorite dyke from visually indistinguishable but generally unmineralized dolerite. In contrast, the Carboniferous Vera Nancy low-sulphidation epithermal Au deposit, located in the Drummond Basin, northeast Queensland, comprises structurally-controlled quartz veins within a relatively chemically homogenous suite of andesitic lavas and subvolcanic intrusions. A zoned hydrothermal alteration system in the hangingwall of the main vein grades from a proximal silica-pyrite alteration zone through an argillic zone into regionally extensive propylitic 'background'. Deep chemical weathering has destroyed the minerals diagnostic of the different alteration zones in bedrock to leave a kaolinitic regolith overlying all alteration zones. However, the silica-pyrite alteration zone is identified in regolith by retention of the anomalous concentrations of Au, As, Sb and Mo present in bedrock, and mineralogical characteristics, determined from X-ray diffraction investigations, discriminated weathered argillic from propylitic alteration zones. ... Metasomatic reactions, including weathering reactions, are typically difficult to specify, as some reactants and products may be removed by fluids, and thus evidence for their involvement is absent from the observed assemblages. In addition, the range of possible reactions even for relatively simple systems is such that identifying the real reaction may be intractable without additional information. Linear algebra provides an approach to this problem. If minerals and aqueous phases are represented as columns in a matrix with elements as rows, any vectors in the null space of this matrix (if it is greater than 0-dimensional) provide coefficients to balance reactions between the phases. The 'Gale' vectors for a set of phase are the row vectors of any basis for this null space. The relationships between phases are clarified through examination of these vectors in d-dimensional Gale vector space, where d is the dimension of the null space. The hyperplane normal to any vector in Gale vector space separates the space into reactant and product half-spaces. The geometric relationships between the Gale phase vectors describe all the possible reactions. Because changes to parameters (e.g. volume, mass, density) can be determined for each possible reaction, Gale analysis can be used to identify reactions consistent with these constraints. Gale analysis of weathering at the Vera deposit indicated that all the possible weathering reactions producing kaolinite, goethite and quartz from illite, pyrite and siderite resulted in minor reductions in volume and mass only, whereas acid-neutral weathering of propylitic rocks exhibited greater mass losses, consistent with observation and geochemical interpretation.