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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. 

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 There is a growing recognition that subsurface fluid injection can produce not only earthquakes, but also aseismic slip on faults. A major challenge in understanding interactions between injection-related aseismic and seismic slip on faults is identifying aseismic slip on the field scale, given that most monitored fields are only equipped with seismic arrays. We present a modeling workflow for evaluating the possibility of aseismic slip, given observational constraints on the spatial-temporal distribution of microseismicity, injection rate, and wellhead pressure. Our numerical model simultaneously simulates discrete off-fault microseismic events and aseismic slip on a main fault during fluid injection. We apply the workflow to the 2012 Enhanced Geothermal System injection episode at Cooper Basin, Australia, which aimed to stimulate a water-saturated granitic reservoir containing a highly permeable ($$k = 10^{-13} - 10^{-12}$$ $k={10}^{-13}-{10}^{-12}$$$\hbox {m}{^2}$$ $\text{m}{}^2$) fault zone. We find that aseismic slip likely contributed to half of the total moment release. In addition, fault weakening from pore pressure changes, not elastic stress transfer from aseismic slip, induces the majority of observed microseismic events, given the inferred stress state. We derive a theoretical model to better estimate the time-dependent spatial extent of seismicity triggered by increases in pore pressure. To our knowledge, this is the first time injection-induced aseismic slip in a granitic reservoir has been inferred, suggesting that aseismic slip could be widespread across a range of lithologies. 

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. 

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 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.