Does Shear Heating of Pore Fluid Contribute to Earthquake Nucleation?

Earthquake nucleation requires reduction of frictional strength $\tau = \mu (\sigma - p)$ with slip or slip rate, where $\mu, \sigma_n$, and $p$ are the friction coefficient, normal stress, and fluid pressure, respectively. For rate state $\mu$ at fixed $(\sigma - p)$, instabilities can occur when $d \mu_{ss}/dv0$ are linearly stable at all wavelengths to adiabatic perturbations when v is near a plate rate if the wall rock permeability exceeds a critical value that is orders of magnitude less than inferred. Thus shear heating alone cannot then nucleate unstable slip; frictional weakening is required. However, shear heating can produce inertial instability on velocity strengthening faults following strong stress perturbations. On faults with $d \mu_{ss}/dv<0$, shear heating increases pore pressure faster than is dissipated by Darcy flow at slip speeds of order $1$ mm $s^{−1}$. For faults bounding half-spaces with uniform thermal and hydraulic properties, $\mu \dot{p}$ exceeds $\dot{\mu}(\sigma - p)$ during nucleation for slip speeds in excess of $10^{−2}$ to $10^1$ mm $s^{−1}$, depending on parameters chosen. Thus thermal effects are likely to dominate late in the nucleation process, well before seismic waves are radiated, as well as during fast seismic slip. By the time shear heating effects dominate, inertial slip is imminent $(∼10^{−1} s)$, so that time-to-failure calculations baseed on rate state friction are not biased by thermal pressurization.Earth and Planetary SciencesEngineering and Applied Science

On the Integrated Surface Uplift for Dip‐Slip Faults

Interferometric Synthetic Aperture Radar observations often provide maps of vertical displacement that can be integrated to estimate an uplift volume. Relating this measure to source processes requires a model of the deformation. Bignami et al. (2019) argue that the negative uplift volume associated with the 2016 Amatrice–Norcia, central Italy, earthquake sequence requires a coseismic volume collapse of the hanging wall. Using results for dip‐slip dislocations in an elastic half‐space we show that V_(uplift)=(P/4)(1−2ν)sin(2δ) in which P is the seismic potency, ν is the Poisson’s ratio, and δ is the fault dip, consistent with an earlier result of Ward (1986). For reasonable estimates of net potency for the 2016 Amatrice–Norcia sequence, this simple formula yields uplift volume estimates close to that observed. We conclude that the data are completely consistent with elastic dislocation theory and do not require a volume collapse at depth

Deep Learning Forecasts Caldera Collapse Events at Kilauea Volcano

During the three month long eruption of Kilauea 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 - 2.2 days. These failure events offer a unique dataset 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 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

Numerical Modeling of Caldera Formation Using Smoothed Particle Hydrodynamics (SPH)

Calderas are kilometer-scale basins formed when magma is rapidly removed from shallow magma storage zones. Despite extensive previous research, many questions remain about how host rock material properties influence the development of caldera structures. We employ a mesh-free, continuum numerical method, Smoothed Particle Hydrodynamics (SPH) to study caldera formation, with a focus on the role of host rock material properties. SPH provides several advantages over previous numerical approaches (finite element or discrete element methods), naturally accommodating strain localization and large deformations while employing well-known constitutive models. A continuum elastoplastic constitutive model with a simple Drucker–Prager yield condition can explain many observations from analogue sandbox models of caldera development. For this loading configuration, shear band orientation is primarily controlled by the angle of dilation. Evolving shear band orientation, as commonly observed in analogue experiments, requires a constitutive model where frictional strength and dilatancy decrease with strain, approaching a state of zero volumetric strain rate. This constitutive model also explains recorded loads on the down-going trapdoor in analogue experiments. Our results, combined with theoretical scaling arguments, raise questions about the use of analogue models to study caldera formation. Finally, we apply the model to the 2018 caldera collapse at Kīlauea volcano and conclude that the host rock at Kīlauea must exhibit relatively low dilatancy to explain the inferred near-vertical ring faults

Bounding the Moment Deficit Rate on Crustal Faults using Geodetic Data: Methods

The geodetically derived interseismic moment deficit rate (MDR) provides a first-order constraint on earthquake potential and can play an important role in seismic hazard assessment, but quantifying uncertainty in MDR is a challenging problem that has not been fully addressed. We establish criteria for reliable MDR estimators, evaluate existing methods for determining the probability density of MDR, and propose and evaluate new methods. Geodetic measurements moderately far from the fault provide tighter constraints on MDR than those nearby. Previously used methods can fail catastrophically under predictable circumstances. The bootstrap method works well with strong data constraints on MDR, but can be strongly biased when network geometry is poor. We propose two new methods: the Constrained Optimization Bounding Estimator (COBE) assumes uniform priors on slip rate (from geologic information) and MDR, and can be shown through synthetic tests to be a useful, albeit conservative estimator; the Constrained Optimization Bounding Linear Estimator (COBLE) is the corresponding linear estimator with Gaussian priors rather than point-wise bounds on slip rates. COBE matches COBLE with strong data constraints on MDR. We compare results from COBE and COBLE to previously published results for the interseismic MDR at Parkfield, on the San Andreas Fault, and find similar results; thus, the apparent discrepancy between MDR and the total moment release (seismic and afterslip) in the 2004 Parkfield earthquake remains

Community Code Verification Exercise for Simulating Sequences of Earthquakes and Aseismic Slip (SEAS)

Numerical simulations of sequences of earthquakes and aseismic slip (SEAS) have made great progress over past decades to address important questions in earthquake physics. However, significant challenges in SEAS modeling remain in resolving multiscale interactions between earthquake nucleation, dynamic rupture, and aseismic slip, and understanding physical factors controlling observables such as seismicity and ground deformation. The increasing complexity of SEAS modeling calls for extensive efforts to verify codes and advance these simulations with rigor, reproducibility, and broadened impact. In 2018, we initiated a community code‐verification exercise for SEAS simulations, supported by the Southern California Earthquake Center. Here, we report the findings from our first two benchmark problems (BP1 and BP2), designed to verify different computational methods in solving a mathematically well‐defined, basic faulting problem. We consider a 2D antiplane problem, with a 1D planar vertical strike‐slip fault obeying rate‐and‐state friction, embedded in a 2D homogeneous, linear elastic half‐space. Sequences of quasi‐dynamic earthquakes with periodic occurrences (BP1) or bimodal sizes (BP2) and their interactions with aseismic slip are simulated. The comparison of results from 11 groups using different numerical methods show excellent agreements in long‐term and coseismic fault behavior. In BP1, we found that truncated domain boundaries influence interseismic stressing, earthquake recurrence, and coseismic rupture, and that model agreement is only achieved with sufficiently large domain sizes. In BP2, we found that complexity of fault behavior depends on how well physical length scales related to spontaneous nucleation and rupture propagation are resolved. Poor numerical resolution can result in artificial complexity, impacting simulation results that are of potential interest for characterizing seismic hazard such as earthquake size distributions, moment release, and recurrence times. These results inform the development of more advanced SEAS models, contributing to our further understanding of earthquake system dynamics

Health-related quality of life as a predictor of pediatric healthcare costs: A two-year prospective cohort analysis

BACKGROUND: The objective of this study was to test the primary hypothesis that parent proxy-report of pediatric health-related quality of life (HRQL) would prospectively predict pediatric healthcare costs over a two-year period. The exploratory hypothesis tested anticipated that a relatively small group of children would account for a disproportionately large percent of healthcare costs. METHODS: 317 children (157 girls) ages 2 to 18 years, members of a managed care health plan with prospective payment participated in a two-year prospective longitudinal study. At Time 1, parents reported child HRQL using the Pediatric Quality of Life Inventory™ (PedsQL™ 4.0) Generic Core Scales, and chronic health condition status. Costs, based on health plan utilization claims and encounters, were derived for 6, 12, and 24 months. RESULTS: In multiple linear regression equations, Time 1 parent proxy-reported HRQL prospectively accounted for significant variance in healthcare costs at 6, 12, and 24 months. Adjusted regression models that included both HRQL scores and chronic health condition status accounted for 10.1%, 14.4%, and 21.2% of the variance in healthcare costs at 6, 12, and 24 months. Parent proxy-reported HRQL and chronic health condition status together defined a 'high risk' group, constituting 8.7% of the sample and accounting for 37.4%, 59.2%, and 62% of healthcare costs at 6, 12, and 24 months. The high risk group's per member per month healthcare costs were, on average, 12 times that of other enrollees' at 24 months. CONCLUSIONS: While these findings should be further tested in a larger sample, our data suggest that parent proxy-reported HRQL can be used to prospectively predict healthcare costs. When combined with chronic health condition status, parent proxy-reported HRQL can identify an at risk group of children as candidates for proactive care coordination

Logarithmic Growth of Dikes From a Depressurizing Magma Chamber

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 a(t) = c₁ log(1 + t/c₂), where is the dike length, is time, and c₁ and c₂ are 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

Graph Neural Network based elastic deformation emulators for magmatic reservoirs of complex geometries

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