Identifying a reference frame for calculating mass change during weathering: A review and case study utilizing the C# program assessing element immobility and critical ratio methodology

Abstract The first step in calculating mass changes that occur during the transformation of plutonic rock to saprock involves the determination of a reference frame, i.e., an immobile element whose mass was conserved during the alteration process. Procedures for identifying the statistical properties of immobile elements have been available since 1990, but have not generally been applied. We therefore developed the C# program, Assessing Element Immobility (AEI) that allows for rapid assessment of those elements possessing the statistical properties of immobility. AEI utilizes algorithms that test for equal distributions and unchanging means of ratios, subcompositional independence, and subcompositional invariance. Following discussion of the general mathematical and statistical procedures implemented in AEI, we utilize it in a case study involving three sites in an ~ 30 m thick section of regolith. ZR I is located near the base of the regolith, while ZR II and ZR III are located at depths of ~ 20 m and ~ 5 m respectively. From each site previous workers chemically analyzed a number of samples from saprock and adjacent unweathered corestones. In addition, XRD work showed that from ZR I to ZR II to ZR III biotite was altered to vermiculite, vermiculite + kaolinite, and vermiculite + mixed-layer biotite/vermiculite + kaolinite respectively. At ZR III the most dominant clay mineral is kaolinite. AEI performs a series of tests to assess whether or not a given set of elements possess the statistical properties for immobility. It identified the following elements as a potential reference frame: Al, Na, Fe, Mg, Ti, and P at ZR I; Si, Al, Fe, Mn, Mg, Ti, and P at ZR II; and Mg and Mn at ZR III. However, critical ratio methodology indicated that the precision, as measured by the smallest 95% confidence interval, is greatest for Al2O3corestone/Al2O3saprock and Na2Ocorestone/Na2Osaprock at ZR I, for SiO2corestone/SiO2saprock at ZR II, and for MgOcorestone/MgOsaprock at ZR III. Mass balance results using Al2O3 and Na2O at ZR I were nearly identical, and as a result, only the results derived from Al2O3 are reported here. Using Al2O3, SiO2, and MgO as reference frame elements for ZR I, ZR II, and ZR III respectively revealed the following statistically significant losses of K mass; ~ 14% (+ 9%/− 8%) at ZR I, ~ 28% (+ 11%/− 9%) at ZR II, and ~ 33% (+ 8%/− 7%) at ZR III. In addition, at ZR III, the statistically significant loss of ~ 36% (+ 13%/− 11%) P mass is attributed to the dissolution of apatite, and the small nominal loss of ~ 6% (+ 5%/− 5%) Ca mass may reflect incongruent leaching of plagioclase and/or apatite. In contrast, the small additions of ~ 5% (+ 5%/− 4%) Al, 5% (+ 2%/− 2%) Fe, and 4% (+ 2%/− 2%) Ti mass at ZR III are likely the result of the translocation of kaolinite and kaolinitized biotite particles into the crack system by downward percolating fluids, and the exchange and adsorption of Al, Fe, and Ti ions onto the illuviated clay lining as it evolved over time. Overall, the interplay between eluviation and illuviation at ZR III translates into a statistically significant 5% (+ 3%/− 3%) increase in bulk mass.