Forecasting Multiphase Magma Failure at the Laboratory Scale Using Acoustic Emission Data

Magmas fracture under high shear stresses, producing radiating elastic waves. At the volcano scale, eruption is often preceded by accelerating seismicity, while at the laboratory scales, sample failure appears to be preceded by similarly accelerating Acoustic Emission (AE). In both cases, empirical relationships between the acceleration and the time of the singular final event have offered tantalizing possibilities for forecast of eruptions and material failure. We explore the success of these tools in the laboratory by briefly reviewing datasets that have been presented previously and comparing the range of errors on forecast times with the range of errors associated with attempts to retrospectively forecast eruptions. We demonstrate that the heterogeneity of a system is crucial to making accurate forecasts on the sample scale, such that homogeneous systems are inherently unpredictable. We then analyse the effect of having an incomplete data sequence, as might be the case for real-time forecasting scenarios. We find that for heterogeneous systems, there is a critical proportion of the sequence that needs to have occurred before a forecast time converges on relatively low errors. As might be expected, the final portion of the sequence is the most important, while uncertainty on the start of the sequence is less important. Finally, we explore the simplest method for scaling the laboratory results to the volcano scenario.