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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.

Ensemble based data assimilation approaches, such as the Ensemble Kalman Filter (EnKF), have been widely and successfully implemented to combine observations with dynamic models to investigate the evolution of a system’s state. Such inversions are powerful tools for providing forecasts as well as “hindcasting” events such as volcanic eruptions to investigate source parameters and triggering mechanisms. In this study, a high performance computing (HPC) adaptation of the EnKF is used to assimilate ground deformation observations from interferometric synthetic-aperture radar (InSAR) into high-fidelity, multiphysics finite element models to evaluate the prolonged unrest and June 26, 2018 eruption of Sierra Negra volcano, Galápagos. The stability of the Sierra Negra magma system is evaluated at each time step by estimating variations in reservoir overpressure, Mohr-Coulomb failure in the host rock, and tensile stress and failure along the reservoir boundary. The deformation of Sierra Negra is tracked over a decade, during which almost 5 meters of surface uplift has been recorded. The EnKF reveals that the evolution of the stress state in the host rock surrounding the Sierra Negra magma reservoir likely controlled the timing of the eruption. While increases in magma reservoir overpressure remained modest (< 10 MPa) throughout the data assimilation time period, significant Mohr-Coulomb failure is indicated in the lead up to the eruption coincident with increased seismicity along both trapdoor faults within Sierra Negra’s caldera and along the caldera’s ring faults. During the final stages of pre-eruptive unrest, the EnKF models indicate limited tensile failure, with no tensile failure along the northern portion of the magma system where the eruption commenced. Most strikingly, model calculations of significant through-going Mohr-Coulomb failure correspond in space and time with a Mw 5.4 earthquake recorded in the hours preceding the 2018 eruption. Subsequent stress modeling implicates the Mw 5.4 earthquake along the southern intra-caldera trapdoor fault as the potential catalyst for tensile failure and dike initiation along the reservoir to the north. In conclusion, the volcano EnKF approach successfully tracked the evolving stability of Sierra Negra, indicating great potential for future forecasting efforts.