Optimizing Ensemble-Based Inversions for Non-unique Volcanic Systems

In recent years, the advent of ensemble-based methods in volcanology has greatly facilitated the use of numerical models within data assimilation frameworks that had previously been limited, either computationally or mathematically, to simpler analytical models. Because numerical models can simulate stress conditions throughout the model space, recent inversions based on assimilated volcanic deformation data are able to track not only the basic parameters of a magma reservoir, but also how those parameters affect the overall mechanical stability of the system. Although this approach has produced successful forecasts and hind-casts of volcanic eruptions, much work remains to be done in assessing its full capabilities and limitations. In particular, non-uniqueness in how source parameters are reflected in surface deformation can significantly impair the inversion’s ability to resolve the magma system’s true state and, by extension, the likelihood of eruption. While this problem is nearly intractable for deep reservoirs, for which changes in pressure and size are indistinguishable from deformation alone, preliminary synthetic tests at shallower systems have demonstrated a limited ability to resolve the main inflation mechanism. In this study, we investigate how the performance of an Ensemble Kalman Filter (EnKF) data assimilation framework varies under a wider range of experimental conditions than used in these initial investigations. In particular, we test how different mathematical implementations of the filter and how different levels of data availability affect the EnKF’s ability to distinguish inflation drivers and to accurately resolve reservoir parameters. To implement this experiment, two time series of synthetic GPS and InSAR data are generated, one in which deformation is driven by excess pressure and another in which it is driven by lateral expansion of the reservoir. For each filter implementation these datasets are down-sampled and given random noise prior to inversion, and after assimilation the resulting model is compared to the original synthetic conditions. We find that newer deterministic formulations of the EnKF are more accurate and consistent than the original stochastic implementation, although the improvement is relatively small. Moreover, some amount of parameter inflation is required to avoid model collapse, but more sophisticated adaptive inflation schemes do not produce better results than more basic formulations. Finally, we show that while increased data sampling does improve performance, this effect is subject to diminishing returns. In particular, data resolution near the center of inflation is more important than overall range of coverage. As new inversion techniques are developed or adapted from other fields, rigorous testing as demonstrated here will be a key step in being able to interpret future results and develop new forecasting frameworks for volcanic eruptions.