Estimation and uncertainty quantification of magma interaction times using statistical emulation

The evolution of volcanic plumbing systems, which controls the style and size of eruptions, is largely determined by processes at depths that are not observable. Scientists use numerical models to simulate these processes and compare the outputs with data on erupted products to understand the plumbing system and eruption processes. However, our ability to explore the parameter space in order to match petrological and geophysical observations is limited by the computational cost required for such simulations. As an alternative, we present a statistical emulator that can reproduce the numerical results as a function of a set of input parameters. This approach can be used to invert the observed distribution of whole rock chemistry to determine the duration of interaction between magmas preceding an eruption and identify the best matching input parameters. This method intrinsically includes error propagation, thus providing reliable confidence intervals for the relevant parameters of the numerical simulations.