A document by Taiyi Wang. Click on the document to view its contents.

From August 2018 to May 2019, Kīlauea’s summit exhibited unique, simultaneous, inflation and deflation, apparent in both GPS time series and cumulative InSAR displacement maps. This deformation pattern provides clear evidence that the Halema‘uma‘u (HMM) and South Caldera (SC) reservoirs are distinct. Post-collapse inflation of the East Rift Zone (ERZ), as captured by InSAR, indicates concurrent magma transfer from the summit reservoirs to the ERZ. We present a physics-based model that couples pressure-driven flow between these magma reservoirs to simulate time dependent summit deformation. We take a two-step approach to quantitatively constrain Kīlauea’s magmatic plumbing system. First, we jointly invert the InSAR displacement maps and GPS offsets for the location and geometry of the summit reservoirs, approximated as spheroidal chambers. We find that HMM reservoir has an aspect ratio of ~1.8 (prolate) and a depth of ~2.2 km (below surface). The SC reservoir has an aspect ratio of ~0.14 (oblate) and a depth of ~3.6 km. Second, we utilize the flux model to invert GPS time series from 8 summit stations. Results favor a shallow HMM-ERZ pathway an order of magnitude more hydraulically conductive than the deep SC-ERZ pathway. Further analysis shows that the HMM-ERZ pathway is required to explain the deformation time series. Given high-quality geodetic data, such an approach promises to quantify the connectivity of magmatic pathways between reservoirs in other similar volcanic systems.

Magma chamber volume is critical for volcano monitoring and forecasting. Standard geodetic methods cannot constrain the total volume, only the change in volume. Here, we show that stress perturbations associated with trapdoor faulting allow bounds to be placed on the total chamber volume at Sierra Negra volcano, in the Galapagos. The deformation response of the magma chamber to faulting depends on both the absolute chamber volume and the compressibility of the magma. Bubble-free magma provides the lower limit on compressibility, thus an upper bound on the chamber volume of 13.6 to 20.6 km3, depending on fault dip. We estimate an upper limit on compressibility using a conduit model relating volatile content to lava fountain height, which is compared with observations from the 2005 eruption, constrained by volatile content of olivine melt inclusions. This yields a lower bound on chamber volume of 0.5 times the upper bound.

We employ near-field GPS data to determine the subsurface geometry of a collapsing caldera during the 2018 Kilauea eruption. Collapse occurred in 62 discrete events with “inflationary’ deformation external to the collapse similar to previous basaltic collapses. We employ GPS data from the collapsing block, and constraints on the magma chamber geometry from inversion of deflation prior to collapse. This provides an unparalleled opportunity to constrain the collapse geometry. Employing an axisymmetric finite element model, the co-collapse displacements are best explained by piston-like subsidence along a steep (~85 degree) normal ring-fault that may steepen with depth. Magma compressibility is 2-15 x 10 Pa, indicating bubble volume fractions from 1 to 7 % (lower if fault steepens with depth). Magma pressure increases during collapses are 1-3 MPa, depending on compressibility. A point source in a half-space fits the data well, but provides a biased representation of the source depth and process.

In 2018 Kilauea volcano erupted a decade’s worth of basalt, given estimated magma supply rates, triggering caldera collapse. Yet, less than 2.5 years later Kilauea erupted again. At the 2018 eruption onset, the pressure within the shallow summit reservoir was ~20 MPa above magmastatic as implied by the elevation of the primary vent. By the onset of collapse this decreased by ~ 17 MPa \citep{anderson2019}. Analysis of magma surges observed following collapse events implies that excess pressure at the eruption end was only ~ 1MPa. Given the elevation difference between the 2018 and 2020 vents, we estimate ~ 11.5 MPa pressure increase was required to bring magma to the surface in December 2020. Analysis of GPS data between 8/2018 and 12/2020 shows there were even odds this condition was met 9 months before the 2020 eruption, and 73% probability on the day of the eruption.

With the increasing quantity and quality of data collected at volcanoes, there is growing potential to incorporate all the data into analyses of the magmatic system. Physics-based models provide a natural and meaningful way to bring together real-time monitoring data and laboratory analyses of eruption products, at the same time improving our understanding of volcanic processes. We develop a framework for joint inversions of diverse time series data using the physics-based model for dome-forming eruptions from \citeA{Wong2019}. Applying this method to the 2004-2008 eruption at Mount St. Helens, we estimate essential system parameters including chamber geometry, pressure, volatile content and material properties, from extruded volume, ground deformation and carbon dioxide emissions time series. The model parameter space is first sampled using the neighborhood search algorithm, then the resulting ensemble of models is resampled to generate posterior probability density functions on the parameters \cite{Sambridge1999_Search, Sambridge1999_Appraise}. We find models that fit all three datasets well. Posterior PDFs suggest an elongate chamber with aspect ratio less than 0.55, located at $9.0-17.2$ km depth. Since the model calculates pressure change during the eruption, we can constrain chamber volume to $64-256$ km$^3$. Volume loss in the chamber is $20-66$ million m$^3$. At the top of the chamber, total (dissolved and exsolved) water contents are $4.99-6.44$ wt\% and total carbon dioxide contents are $1560-3891$ ppm, giving a porosity of 5.3-16.6\% depending on the conduit length. Compared to previous inversions using a steady-state conduit model, we obtain a lower magma permeability scale, radius and friction coefficient.

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 shear stress drop. The effect of pressurizing a spheroidal chamber is represented as a tri-axial expansion source, and the combined caldera block/magma momentum change as 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 ~1.7 MPa. That the predictions fit both geodetic and seismic observations confirms that the model captures the dominant caldera collapse mechanisms.

An outstanding question for induced seismicity is whether the volume of injected fluid and/or the spatial extent of the resulting pore pressure and stress perturbations limit rupture size. We simulate ruptures with and without injection-induced pore pressure perturbations, using 2-D dynamic rupture simulations on rough faults. Ruptures are not necessarily limited by pressure perturbations when 1) background shear stress is above a critical value, or 2) pore pressure is high. Both conditions depend on fault roughness. Stress heterogeneity from fault roughness primarily determines where ruptures stop; pore pressure has a secondary effect. Ruptures may be limited by fluid volume or pressure extent when background stress and fault roughness are low, and the maximum pore pressure perturbation is less than 10% of the background effective normal stress. Future work should combine our methodology with simulation of the loading, injection, and nucleation phases to improve understanding of injection-induced ruptures.