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Measurements of volcano deformation are increasingly routine, but constraining complex magma reservoir geometries via inversions of surface deformation measurements remains challenging. This is partly due to deformation modeling being limited to one of two approaches: computationally efficient semi-analytical elastic solutions for simple magma reservoir geometries (point sources, spheroids, and cracks) and computationally expensive numerical solutions for complex 3D geometries. Here, we introduce a pair of Graph Neural Network (GNN) based elasto-static emulators capable of making fast and reasonably accurate predictions (error upper bound: 15 %) of surface deformation associated with 3D reservoir geometries: a spheroid emulator and a general shape emulator, the latter parameterized with spherical harmonics. The emulators are trained on, and benchmarked against, boundary element (BEM) simulations, providing up to three orders of magnitude speed up compared to BEM methods. Once trained, the emulators can generalize to new reservoir geometries statistically similar to those in the training data set, thus avoiding the need for re-training, a common limitation for existing neural network emulators. We demonstrate the utility of the emulators via Bayesian Markov Chain Monte Carlo inversions of synthetic surface deformation data, showcasing scenarios in which the emulators can, and can not, resolve complex magma reservoir geometries from surface deformation. Our work demonstrates that GNN based emulators have the potential to significantly reduce the computational cost of inverse analyses related to volcano deformation, thereby bringing new insights into the complex geometries of magmatic systems. 

Abstract During the 3 month long eruption of Kı̄lauea volcano, Hawaii in 2018, the pre‐existing summit caldera collapsed in over 60 quasi‐periodic failure events. The last 40 of these events, which generated Mw > 5 very long period (VLP) earthquakes, had inter‐event times between 0.8 and 2.2 days. These failure events offer a unique data set for testing methods for predicting earthquake recurrence based on locally recorded GPS, tilt, and seismicity data. In this work, we train a deep learning graph neural network (GNN) to predict the time‐to‐failure of the caldera collapse events using only a fraction of the data recorded at the start of each cycle. We find that the GNN generalizes to unseen data and can predict the time‐to‐failure to within a few hours using only 0.5 days of data, substantially improving upon a null model based only on inter‐event statistics. Predictions improve with increasing input data length, and are most accurate when using high‐SNR tilt‐meter data. Applying the trained GNN to synthetic data with different magma‐chamber pressure decay times predicts failure at a nearly constant stress threshold, revealing that the GNN is sensing the underling physics of caldera collapse. These findings demonstrate the predictability of caldera collapse sequences under well monitored conditions, and highlight the potential of machine learning methods for forecasting real world catastrophic events with limited training data. 

Predicting the recurrence times of earthquakes and understanding the physical processes that immediately precede them are two outstanding problems in seismology. Although geodetic measurements record elastic strain accumulation, most faults have recurrence intervals longer than available measurements. Foreshocks provide the principal observations of processes before mainshocks, but variability between sequences limits generalizations of pre-failure behaviour. Here we analyse seismicity and deformation data for highly characteristic caldera collapse earthquakes from 2018 Kīlauea Volcano (Hawaii, USA), with a mean recurrence interval of 1.4 days. These events provide a unique test of stress-induced earthquake recurrence and document processes preceding mainshocks with magnitude greater than five. We show that recurrence intervals are well predicted by stress histories inferred from near-field deformation measurements and that cycle-averaged seismicity reveals a critical phase, minutes before mainshocks, where earthquakes grew larger and seismic moment rate surged dramatically. The average moment rate in the final 15 minutes (0.7% of the mean cycle duration) was 4.75 times the background, a highly significant change. We infer that as the average stress increased, ruptures were more likely to overcome geometric barriers and grow larger, leading to characteristic, whole-fault ruptures. These findings imply that stress heterogeneity influences both earthquake nucleation and growth, including on potentially hazardous tectonic faults. 

Abstract All instrumented basaltic caldera collapses have generated M_w > 5 very long period earthquakes. However, previous studies of source dynamics have been limited to lumped models treating the caldera block as rigid, leaving open questions related to how ruptures initiate and propagate around the ring fault, and the seismic expressions of those dynamics. We present the first 3D numerical model capturing the nucleation and propagation of ring fault rupture, the mechanical coupling to the underlying viscoelastic magma, and the associated seismic wavefield. We demonstrate that seismic radiation, neglected in previous models, acts as a damping mechanism reducing coseismic slip by up to half, with effects most pronounced for large magma chamber volume/ring fault radius or highly compliant crust/compressible magma. Viscosity of basaltic magma has negligible effect on collapse dynamics. In contrast, viscosity of silicic magma significantly reduces ring fault slip. We use the model to simulate the 2018 Kı̄lauea caldera collapse. Three stages of collapse, characterized by ring fault rupture initiation and propagation, deceleration of the downward‐moving caldera block and magma column, and post‐collapse resonant oscillations, in addition to chamber pressurization, are identified in simulated and observed (unfiltered) near‐field seismograms. A detailed comparison of simulated and observed displacement waveforms corresponding to collapse earthquakes with hypocenters at various azimuths of the ring fault reveals a complex nucleation phase for earthquakes initiated on the northwest. Our numerical simulation framework will enhance future efforts to reconcile seismic and geodetic observations of caldera collapse with conceptual models of ring fault and magma chamber dynamics. 

Fault friction is central to understanding earthquakes, yet laboratory rock mechanics experiments are restricted to, at most, meter scale. Questions thus remain as to the applicability of measured frictional properties to faulting in situ. In particular, the slip-weakening distance d c strongly influences precursory slip during earthquake nucleation, but scales with fault roughness and is challenging to extrapolate to nature. The 2018 eruption of Kīlauea volcano, Hawaii, caused 62 repeatable collapse events in which the summit caldera dropped several meters, accompanied by M W 4.7 to 5.4 very long period (VLP) earthquakes. Collapses were exceptionally well recorded by global positioning system (GPS) and tilt instruments and represent unique natural kilometer-scale friction experiments. We model a piston collapsing into a magma reservoir. Pressure at the piston base and shear stress on its margin, governed by rate and state friction, balance its weight. Downward motion of the piston compresses the underlying magma, driving flow to the eruption. Monte Carlo estimation of unknowns validates laboratory friction parameters at the kilometer scale, including the magnitude of steady-state velocity weakening. The absence of accelerating precollapse deformation constrains d c to be ≤ 10 mm, potentially much less. These results support the use of laboratory friction laws and parameters for modeling earthquakes. We identify initial conditions and material and magma-system parameters that lead to episodic caldera collapse, revealing that small differences in eruptive vent elevation can lead to major differences in eruption volume and duration. Most historical basaltic caldera collapses were, at least partly, episodic, implying that the conditions for stick–slip derived here are commonly met in nature. 

Abstract In 2018 Kı̄lauea volcano erupted a decade's worth of basalt, given estimated magma supply rates, triggering caldera collapse. Yet, less than 2.5 years later Kı̄lauea re‐erupted. At the 2018 eruption onset, pressure within the summit reservoir was ∼20 MPa above magmastatic. By the onset of collapse this decreased by ∼17 MPa. Analysis of magma surges at the 2018 fissures, following collapse events, implies excess pressure at the eruption end of only ∼1 MPa. Given the new vent elevation, ∼11–12 MPa pressure increase was required to bring magma to the surface in December 2020. Analysis of Global Positioning System data between 8/2018 and 12/2020 shows there was a 73% probability that this condition was met at the onset of the 2020 eruption. Given a plausible range of possible vent elevations, there was a 40%–88% probability of sufficient pressure to bring magma to the surface 100 days before the eruption. 

ABSTRACT Numerical modeling of earthquake dynamics and derived insight for seismic hazard relies on credible, reproducible model results. The sequences of earthquakes and aseismic slip (SEAS) initiative has set out to facilitate community code comparisons, and verify and advance the next generation of physics-based earthquake models that reproduce all phases of the seismic cycle. With the goal of advancing SEAS models to robustly incorporate physical and geometrical complexities, here we present code comparison results from two new benchmark problems: BP1-FD considers full elastodynamic effects, and BP3-QD considers dipping fault geometries. Seven and eight modeling groups participated in BP1-FD and BP3-QD, respectively, allowing us to explore these physical ingredients across multiple codes and better understand associated numerical considerations. With new comparison metrics, we find that numerical resolution and computational domain size are critical parameters to obtain matching results. Codes for BP1-FD implement different criteria for switching between quasi-static and dynamic solvers, which require tuning to obtain matching results. In BP3-QD, proper remote boundary conditions consistent with specified rigid body translation are required to obtain matching surface displacements. With these numerical and mathematical issues resolved, we obtain excellent quantitative agreements among codes in earthquake interevent times, event moments, and coseismic slip, with reasonable agreements made in peak slip rates and rupture arrival time. We find that including full inertial effects generates events with larger slip rates and rupture speeds compared to the quasi-dynamic counterpart. For BP3-QD, both dip angle and sense of motion (thrust versus normal faulting) alter ground motion on the hanging and foot walls, and influence event patterns, with some sequences exhibiting similar-size characteristic earthquakes, and others exhibiting different-size events. These findings underscore the importance of considering full elastodynamics and nonvertical dip angles in SEAS models, as both influence short- and long-term earthquake behavior and are relevant to seismic hazard. 

Abstract Inflationary deformation and very long period (VLP) earthquakes frequently accompany basaltic caldera collapses, yet current interpretations do not reflect physically consistent mechanisms. We present a lumped parameter model accounting for caldera block/magma momentum change, magma chamber pressurization, and ring fault (assumed vertical) shear stress drop. Pressurization of the underlying magma chamber is represented by a tri‐axial expansion source, and the combined caldera block/magma momentum change by a vertical single force. The model is applied to Kīlauea 2018 caldera collapse events, accurately predicting near field static/dynamic ground motions. In addition to the tri‐axial expansion source, the single force contributes significantly to the VLP waveforms. For an average collapse event with fully developed ring fault, Bayesian inversion constrains ring fault stress drop to ∼0.4 MPa and the pressure increase to ∼1.9 MPa. That the predictions fit both geodetic and seismic observations confirms that the model captures the dominant caldera collapse mechanisms. 

Abstract Dike propagation is an intrinsically multiphase problem, where deformation and fluid flow are intricately coupled in a fracture process. Here we perform the first fully coupled simulations of dike propagation in two dimensions, accounting for depressurization of a circular magma chamber, dynamic fluid flow, fracture formation, and elastic deformation. Despite the complexity of the governing equations, we observe that the lengthening is well explained by a simple model, whereis the dike length,is time, andandare constants. We compare the model to seismic data from eight dikes in Iceland and Ethiopia, and, in spite of the assumption of plane strain, we find good agreement between the data and the model. In addition, we derive an approximate model for the depressurization of the chamber with the dike length. These models may help forecast the growth of lateral dikes and magma chamber depressurization.