Dike intrusions are often accompanied by localized deflation, interpreted as depressurizing magma chambers feeding the dike. In some cases the inferred volume decrease is a factor of 4 or 5 less than ...the volume increase of the dike. Here we explore whether this discrepancy can be explained by compressibility of the magma combined with the fact that cracks are much more compliant than equidimensional magma chambers. If pressure changes are small, the magma compressibility βm is constant, and the dike ends up in hydrostatic equilibrium with an ellipsoidal magma chamber at the same depth, the ratio rV of the volume of the crack to the volume lost by the chamber is rV = 1 + 4μβm/3 > 1, where μ is the host rock rigidity. For gas poor magmas, βm = 0.6–2 · 10−10 Pa−1 and μ = 3–25 GPa, we find 1.2 < rV < 7.7. Large changes in magma compressibility due to gas exsolution increase rV.
Hydrofracturing is a routine industrial technique whose safety depends on fractures remaining confined within the target rock volume. Both observations and theoretical models show that, if the fluid ...volume is larger than a critical value, pockets of fluid can propagate large distances in the Earth's crust in a self‐sustained, uncontrolled manner. Existing models for such critical volumes are unsatisfactory; most are two‐dimensional and depend on poorly constrained parameters (typically the fracture length). Here we derive both analytically and numerically in three‐dimensional scale‐independent critical volumes as a function of only rock and fluid properties. We apply our model to gas, water, and magma injections in laboratory, industrial, and natural settings, showing that our critical volumes are consistent with observations and can be used as conservative estimates. We discuss competing mechanisms promoting fracture arrest, whose quantitative study could help to assess more comprehensively the safety of hydrofracturing operations.
Plain Language Summary
Fractures in rocks can act as channels for fluids. Fracking, or hydrofracturing, involves injection of fluids at high pressure in order to grow fractures within the rock and increase its permeability. Fluid volumes need to be kept below a threshold value: If the fluid volume is larger, then the stresses at the tips of the fluid pocket will be large enough for the fluids to force their way around by fracturing the rock ahead of them. Previous theoretical models for the critical volumes are unsatisfactory as they are two‐dimensional and based on poorly constrained parameters. We derive and test a new three‐dimensional equation that uses only rock and fluid parameters. We find that typical volumes injected in hydrofracturing operations are over the limit we define. We argue they are still mostly safe as additional processes often hinder fracture growth. Further work is needed to comprehensively quantify mechanisms that hinder hydrofracture arrest.
Key Points
We define critical volumes for fractures under the influence of a stress gradients that cause self‐sustaining propagation
We define such critical volumes analytically such that they are independent of scale. These are verified numerically
The equation predicts the correct scale in natural and analog examples but for hydro‐fracturing its too low
Magma is transported in the crust mainly by dike intrusions. In volcanic areas, dikes can ascend toward the free surface and also move by lateral propagation, eventually feeding flank eruptions. ...Understanding dike mechanics is a key to forecasting the expected propagation and associated hazard. Several studies have been conducted on dike mechanisms and propagation; however, a less in‐depth investigated aspect is the relation between measured dike‐induced deformation and the seismicity released during its propagation. We individuated a simple x that can be used as a proxy of the expected mechanical energy released by a propagating dike and is related to its average thickness. For several intrusions around the world (Afar, Japan, and Mount Etna), we correlate such mechanical energy to the seismic moment released by the induced earthquakes. We obtain an empirical law that quantifies the expected seismic energy released before arrest. The proposed approach may be helpful to predict the total seismic moment that will be released by an intrusion and thus to control the energy status during its propagation and the time of dike arrest.
Plain Language Summary
Dike propagation is a dominant mechanism for magma ascent, transport, and eruptions. Besides being an intriguing physical process, it has critical hazard implications. After the magma intrusion starts, it is difficult to predict when and where a specific horizontal dike is going to halt and what its final length will be. In our study, we singled an equation that can be used as a proxy of the expected mechanical energy to be released by the opening dike. We related this expected energy to the seismic moment of several eruptive intrusions around the world (Afar region, Japanese volcanoes, and Mount Etna). The proposed novel approach is helpful to estimate the total seismic moment to be released, therefore allowing potentially predicting when the dike will end its propagation. The approach helps answer one of the fundamental questions raised by civil protection authorities, namely, “how long will the eruptive fissure propagate?”
Key Points
The study investigated the relationship between the deformation induced by dike propagation leading to eruptions and the released seismic energy
We individuated a simple equation that can be used as a proxy of the expected mechanical energy released by a propagating dike that is related to its average thickness
We obtained an empirical law that quantifies the seismic moment released by a dike intrusion, thus providing a tool to control the energy status during its propagation
Abstract
Shallow magmatic reservoirs that produce measurable volcanic surface deformation are often considered as discrete independent systems. However, petrological analyses of erupted products ...suggest that these may be the shallowest expression of extensive, heterogeneous magmatic systems that we show may be interconnected. We analyse time series of satellite-radar-measured displacements at Western Galápagos volcanoes from 2017 to 2022 and revisit historical displacements. We demonstrate that these volcanoes consistently experience correlated displacements during periods of heightened magma supply to the shallow crust. We rule out changes in static stress, shallow hydraulic connections, and data processing and analysis artefacts. We propose that episodic surges of magma into interconnected magmatic systems affect neighbouring volcanoes, simultaneously causing correlations in volcanic uplift and subsidence. While expected to occur globally, such processes are uniquely observable at the dense cluster of Western Galápagos volcanoes, thanks to the high rate of surface displacements and the wealth of geodetic measurements.
Aseismic and seismic slip scaling indicate similar physics governing tremor and earthquake swarms during slow slip events.
Slow slip events (SSEs) represent a slow faulting process leading to ...aseismic strain release often accompanied by seismic tremor or earthquake swarms. The larger SSEs last longer and are often associated with intense and energetic tremor activity, suggesting that aseismic slip controls tremor genesis. A similar pattern has been observed for SSEs that trigger earthquake swarms, although no comparative studies exist on the source parameters of SSEs and tremor or earthquake swarms. We analyze the source scaling of SSEs and associated tremor- or swarm-like seismicity through our newly compiled dataset. We find a correlation between the aseismic and seismic moment release indicating that the shallower SSEs produce larger seismic moment release than deeper SSEs. The scaling may arise from the heterogeneous frictional and rheological properties of faults prone to SSEs and is mainly controlled by temperature. Our results indicate that similar physical phenomena govern tremor and earthquake swarms during SSEs.
By performing buoyancy-driven fracture experiments in brittle gelatin we observe that the ascent velocity of a fracture containing a finite volume of fluid increases when approaching the free ...surface. We theoretically describe this free-surface effect and quantify it by introducing an effective depth-dependent fracture toughness and developing an ascent model on the basis of linear fracture mechanics. We develop a successful inversion approach and resolve the actual and critical fracture length and the ascent velocity far away from the free surface from the observation of the fracture tip migration alone. Other parameters, as the fluid volume included in the fracture and the in situ fracture toughness, can be derived. Applying the model and inversion to the 1998 eruption at Piton de la Fournaise, Reunion Island, reveals estimates of the length and critical length of the feeding magma batch, the magma batch volume and the in situ fracture toughness. It further indicates that the ascent velocity of the magma batch was probably much smaller at greater depths and that the batch might have been initiated several months or years before the eruption.
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