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Solid earth refers to "the earth beneath our feet" or terra firma, the planet's solid surface and its interior. It excludes the Earth's fluid envelopes, the atmosphere and hydrosphere (but includes the ocean basin), as well as the biosphere and interactions with the Sun. Solid-earth science refers to the corresponding methods of study, a subset of Earth sciences, predominantly geophysics and geology, excluding aeronomy, atmospheric sciences, oceanography, hydrology, and ecology. See also

Ad cœlum
Crust (geology) ** Earth's crust
Geosphere
Land
Landform
Landscape
Lithosphere
Pedosphere
Structure of the Earth
Terrain
Solid Earth (journal)
Journal of Geophysical Research - section B (Solid Earth)

Transition from a radial to a 3D buoyancy-driven hydraulic fracture

Brice Tanguy Alphonse Lecampion, Andreas Möri

Magmatic dikes are a naturally occurring type of fluid-driven fractures (Rivalta et al. 2015) propagating in the lithosphere due to buoyant forces emerging from the density difference between the host material and the injected fluid (more precisely the difference between the gradients of the in-situ minimum stress and the hydrostatic pore-fluid pressure). The form of such buoyant fractures has been extensively studied in the context of magmatic dikes and shows the appearance of a head-tail structure (Rivalta et al. 2015). 2D plane-strain evaluations highlighted the fact that lubrication flow in the tail is driving the growth of the hydrostatic head (Lister & Kerr 1991; Roper & Lister 2005), which has been confirmed by Germanovich et al. (2014) for the 3D finger-like geometry. We investigate the 3D transition of a radial hydraulic fracture emerging from a point source towards a buoyancy-driven fracture, focussing on the case of a constant injection rate in homogeneous conditions (homogeneous material properties and buoyancy contrast). We use scaling arguments to characterize the transition and the late time buoyant behavior of the fracture and validate the findings with the fully coupled planar 3D hydraulic fracture growth solver PyFrac (Zia & Lecampion 2020). Our results confirm a characteristic transition time / length scale from a radial to a buoyant fracture depending on a single dimensionless parameter. The same parameter can be used to predict the fractures overrun (maximum breadth / stabilized breadth). A second, very slow transition takes place between the elongated fracture and the late time fully-developed 3D head-tail structure (similar to the solution of Germanovich et al. (2014)). Our simulations support the appearance of a 3D toughness dominated head structure. They also confirm the importance of the viscous tail as the driving mechanism for the dynamics of such a 3D Weertman’s pulse (form of the head). We quantify how and when the transition from a radial to a buoyant fracture takes place, and it’s implications on the late time behavior. REFERENCES Germanovich, L. N. & Garagash, D. I. & Murdoch, L. & Robinowitz, M. 2014: Gravity-driven hydraulic fractures, AGU Fall meeting Lister, J., R. & Kerr, R. C. 1992: Fluid-mechanical models of crack propagation and their application to magma transport in dykes, Journal of Geophysical research: Solid Earth, 96(B6), 10049-10077 Rivalta, E. & Taisne, B. & Bunger, A. P. & Katz, R. F. 2015: A review of mechanical models of dike propagation: Schools of thought, results and future directions, Tectonophysics, 638, 1-42 18th Swiss Geoscience Meeting, Zurich 2020 Roper, S. M. & Lister, J. R. 2005: Buoyancy-driven crack propagation from an over-pressured source, J. Fluid Mech., 536, 79-98 Zia, H. & Lecampion, B. 2020: PyFrac: A planar 3d hydraulic fracture simulator, Computer Physics Communications, page 107368

2020

Fully-coupled 3D modelling of magmatic dike Propagation – finite pulse release from a point source

Brice Tanguy Alphonse Lecampion, Andreas Möri, Haseeb Zia

Magmatic dikes are a naturally occurring type of fluid-driven fractures [1] propagating in the lithosphere driven by buoyancy (more precisely by the difference between the in-situ minimum horizontal stress gradient and the magma weight). Fully-coupled modelling of these 3D fractures is very challenging and most contributions until today have been restricted to 2D plane-strain. These 2D investigations have highlighted the importance of the head-tail structure, notably the fact that lubrication flow in the tail is driving the growth of the hydrostatic head [2, 3]. We investigate the 3D development of a buoyant dike from a point source, focusing on the case of a finite volume release under homogeneous conditions (homogeneous material properties and buoyancy contrast). We use the fully coupled planar 3D hydraulic fracture growth solver PyFrac based on the implicit level set algorithm [4]. This configuration shows an early time behaviour heavily dominated by the effects of the pulse release. The initially radial hydraulic fracture transitions toward a large time buoyant dike solution. At large time our simulations tends to the finger-like/constant breadth solution [5] albeit extremely slowly. Our results confirm the 3D toughness dominated head structure and the importance of the viscous tail as the driving mechanism for the dynamics of such a 3D Weertman’s pulse (form of the head). Depending on the initial phase of the pulse release, we observe an overshoot of the dike breadth when it is initially strongly dominated by viscous dissipation. Using a scaling analysis, we characterize the transition from the early time radial finite pulse fracture to the late dike constant breadth solution. Our simulations show, that the time when the buoyant force takes its full dominance is crucial and governs the existence (or not) of an overshoot. Mainly we show that the overshoot depends on a transitional time/lengthscale. A detailed understanding of the fracture propagation after the end of the finite volume release (yet without buoyancy) is key to quantify this lengthscale. We thus present scalings and semi-analytical solutions for this case and discuss its relevance for the transition toward a buoyancy driven dike propagation. [1] E. Rivalta, B. Taisne, A.P. Bunger, and R.F. Katz. Tectonophysics, 638:1–42, 2015. [2] J. R. Lister and R. C. Kerr. J. Geohpys. Res. Solid Earth, 96(B6):10049–10077, 1991. [3] S. M. Roper and J. R. Lister. J. Fluid Mech., 536:79–98, 2005. [4] A. P. Peirce and E. Detournay. Comput. Methods in Appl. Mech. Eng., 197(33-40):2858–2885, 2008. [5] L.N. Germanovich, D. I. Garagash, Murdoch, L., and Robinowitz M. AGU Fall meeting, 2014.

2020

Effect of Fluid Viscosity on Earthquake Nucleation

Chiara Cornelio, Marie Estelle Solange Violay

Injection of fluids in geo-reservoirs can reduce the effective stresses at depth, lubricating the nearby faults, promoting slip and, potentially, earthquakes. High-viscous fluids are often used during hydraulic fracturing and production phases in geo-reservoirs. Here, we performed dedicated experiments to study the influence of fluid viscosity on earthquake nucleation. We performed frictional sliding experiments at 30 and 50 effective normal stresses and fluids viscosity ranging from 1 to 1,226 mPa s and modeled them with a rate-and-state friction law. In the presence of fluid, the state variable is defined as the ability of the fluid to flow. Our results showed that static friction slightly decreases with increasing viscosity, the dynamic friction is governed by the dimensionless Sommerfeld number (S = 6 eta VL/(sigma'H-n(2))). Moreover, we observed that the (a - b) parameters of the rate-and-state friction law decrease with increasing viscosity down to (a - b) < 0, possibly promoting unstable slip and earthquake nucleation. Plain Language Summary In the last 30 years, the exponential worldwide increase of human-induced seismicity has become an important issue in solid earth sciences. Most of the induced seismicity is due to engineering operations in deep geo-reservoirs for hydrocarbon production, CO2 storage, wastewater disposal, and the exploitation of geothermal resources. While the reactivation of faults at the origin of this seismicity has been extensively studied, the influence of fluid properties including its viscosity has been overlooked, even if the viscosity of injected fluids spans from that of water to that of honey. In this study, we discuss the influence of fluid viscosity on the nucleation of earthquakes in fluid-permeated experimental faults and on induced earthquakes. Our experimental observations suggest that the viscosity of the fluid does not influence the fault strength. Instead, the viscosity of the fluid controls the behavior of the fault from stable to unstable sliding.

2020

Fully-coupled 3D modelling of magmatic dike Propagation – finite pulse release from a point source

Brice Tanguy Alphonse Lecampion, Andreas Möri, Haseeb Zia

2020

Transition from a radial to a 3D buoyancy-driven hydraulic fracture

Brice Tanguy Alphonse Lecampion, Andreas Möri

2020

Effect of Fluid Viscosity on Earthquake Nucleation

Chiara Cornelio, Marie Estelle Solange Violay

2020