Curved Crystal Size Distribution Produced by Mixing of Magmas from Multiple Reservoirs

Crystal size distribution (CSD) analysis is a powerful tool for quantitative texture analysis of igneous rocks. Interpretation of CSD data commonly relies on linear relationships between the logarithm of crystal number density and crystal length, which have been used to infer nucleation density, crystal growth rate, and magma residence time. However, many CSDs measured in volcanic rocks deviate from linearity, reflecting the influence of additional magmatic processes. In this study, we quantify the effects of magma mixing on the shape and temporal evolution of CSDs in volcanic systems. We develop steady-state and transient models for CSDs produced by the mixing of crystal-bearing magmas from two or three magma reservoirs and use analytical solutions to identify the key parameters controlling CSD evolution. Our results show that curved CSDs arise naturally during magma mixing when characteristic crystal lengths differ among reservoirs, whereas kinked CSDs form when these differences are large. Concave-downward CSDs may develop when the nucleation density of the resident magma is lower than that of the inflowing magma. The timescale of CSD evolution induced by magma mixing is found to be significantly longer than the magma mixing timescale. Consequently, a family of quasi-linear, curved, subparallel, or crossed CSDs from a set of temporally correlated samples may provide a diagnostic signature of transient magmatic behavior and prolonged magma residence times. The multi-parameter nature of CSD mixing models presents significant challenges for extracting CSD parameters from measured data, particularly due to strong nonlinear trade-offs among model parameters, limited data points in CSD measurement, and measurement uncertainties. Depending on data quality and parameter values, distinguishing different mixing models may be difficult. To address these challenges, we develop a stepwise inversion approach that combines linear piecewise regression with nonlinear least squares method to iteratively refine parameter estimates. Initial applications of the inversion protocol to olivine, plagioclase, clinopyroxene, and magnetite CSDs from Kilauea and Mt. Etna yield promising results, underscoring the importance of high-resolution CSD data, the utility and limitation of multi-reservoir mixing models, and the need for caution in interpreting curved CSDs in volcanic rocks.