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Assessing volcanic hazard in regions of distributed volcanism is challenging because of the uncertain location of future vents. A statistical-mechanical strategy to forecast such locations was recently proposed: here, we further develop and test it with analog models. We stress a gelatin block laterally and with surface excavations, and observe air-filled crack trajectories. We use the observed surface arrivals to sample the distributions of parameters describing the stress state of the gelatin block, combining deterministic crack trajectory simulations with a Monte Carlo approach. While the individual stress parameters remain unconstrained, we effectively retrieve their ratio and successfully forecast the arrival points of subsequent cracks.
Fluids in the Earth's crust can move by creating and flowing through fractures, in a process called `hydraulic fracturing’. The tip-line of such fluid-filled fractures grows at locations where stress is larger than the strength of the rock. Where the tip stress vanishes, the fracture closes and the fluid-front retreats. If stress gradients exist on the fracture's walls, induced by fluid/rock density contrasts or topographic stresses, this results in an asymmetric shape and growth of the fracture, allowing for the contained batch of fluid to propagate through the crust.
The state-of-the-art analytical and numerical methods to simulate fluid-filled fracture propagation are two-dimensional (2D). In this work I extend these to three dimensions (3D). In my analytical method, I approximate the propagating 3D fracture as a penny-shaped crack that is influenced by both an internal pressure and stress gradients. In addition, I develop a numerical method to model propagation where curved fractures can be simulated as a mesh of triangular dislocations, with the displacement of faces computed using the displacement discontinuity method. I devise a rapid technique to approximate stress intensity and use this to calculate the advance of the tip-line. My 3D models can be applied to arbitrary stresses, topographic and crack shapes, whilst retaining short computation times.
I cross-validate my analytical and numerical methods and apply them to various natural and man-made settings, to gain additional insights into the movements of hydraulic fractures such as magmatic dikes and fluid injections in rock. In particular, I calculate the `volumetric tipping point’, which once exceeded allows a fluid-filled fracture to propagate in a `self-sustaining’ manner. I discuss implications this has for hydro-fracturing in industrial operations. I also present two studies combining physical models that define fluid-filled fracture trajectories and Bayesian statistical techniques. In these studies I show that the stress history of the volcanic edifice defines the location of eruptive vents at volcanoes. Retrieval of the ratio between topographic to remote stresses allows for forecasting of probable future vent locations. Finally, I address the mechanics of 3D propagating dykes and sills in volcanic regions. I focus on Sierra Negra volcano in the Gal\'apagos islands, where in 2018, a large sill propagated with an extremely curved trajectory. Using a 3D analysis, I find that shallow horizontal intrusions are highly sensitive to topographic and buoyancy stress gradients, as well as the effects of the free surface.
On October 9, 2014, a Mw 7.1-6.7 seismic doublet occurred at the Juan Fernandez microplate, close to the triple junction with Pacific and Nazca plates. The Mw 7.1 earthquake is the largest earthquake ever to have been recorded in the region. Its thrust focal mechanism is also unusual for the region, although the northern part of the microplate is expected to undergo compression. The region is remote and seismological data is limited to a seismic station at similar to 600 km distance on Easter Island and teleseismic observations for the largest events. We use a combination of advanced seismological techniques to overcome the lack of local data and resolve earthquake source parameters for the doublet and its aftershock sequence, being able to reconstruct the chronology of the sequence and the geometry of affected fault segments. Our results depict a complex seismic sequence characterized by the interplay of thrust and strike-slip earthquakes along different structures, including a second, reversed strike slip-thrust seismic doublet in November 2014. Seismicity occurred within the microplate and only in the late part of the sequence migrated northward, towards the microplate boundary. The first largest doublet, whose rupture kinematic is well explained by stress changes imparted by the first subevent on the second one, may have activated unmapped E-W and NE-SW faults or an internal curved pseudofault, attributed to the longterm rotation of the microplate. Few large, thrust earthquakes are observed within the sequence, taking place in the vicinity of mapped compressional ridges. We suggest that compressional stresses in the northern part of the microplate and at its boundary are partially accommodated aseismically. However, the occasional occurrence of large, impulsive thrust earthquakes, with a considerable tsunamigenic potential, poses a relevant hazard for islands in the South Pacific region.