Magma reservoir failure on the terrestrial planets: Assessing the importance of gravitational loading in simple elastic models

Using numerical modeling to explore the origin of intrusion patterns on Fernandina volcano, Galapagos Islands, Ecuador

“…) as well as the elastic properties of basalt (Young's modulus E = 73 GPa, Poisson's ratio ν = 0.25) derive from existing literature [Schultz, 1993;Manghnani and Woollard, 1965], but realistic variations in material properties (i.e., density and elastic moduli) do not affect results substantively [Grosfils, 2007]. The left boundary of the model (r = 0 m) defines the axis of rotation, the outer and lower boundaries can only displace vertically or horizontally, respectively, and the upper boundary is free of displacement constraints (Figure 1).…”

“…While σ φ is obtained directly from the model solution, σ t is calculated using equation 2 of Grosfils [2007] with the appropriate geometry-dependent angle α (Figure 1). Potential intrusion configurations depend on the location and orientation of initial rupture and the stress state within the lithosphere.…”

Analytical models of magma chamber stability: An abridged critical review of key concepts

“…For example, although Gudmundsson (1988) mentions the results obtained by Jeffery (1921), his analysis limits to point out that the magnitude of that stress component can become many times greater than the pressure applied on the walls of the chamber without offering further details. Subsequently, Parfitt et al (1993) attempted to recast Jeffery's original result in terms of variables that bear a more direct association with the volcanic problem, such as depth to and from the top of the chamber and the radius of the hole, but unfortunately, as pointed out by Grosfils (2007) that attempt failed because of a mistranslation in the geometry of the problem. Although the geometric factor obtained by Grosfils (2007) amends the error introduced by Parfitt et al (1993), somewhat paradoxically, the original equation obtained by Jeffery (1921) expressing an angular dependence of the tensile stress around the perimeter of the cross sectional area of the hole has a typographic error on Grosfils' paper (his Eq.…”

“…From a pragmatic point of view, the number of alternative approaches and associated equations aiming to quantify the conditions of magma chamber stability already available on the literature (a general overview, and a list of relevant references, can be found on the recent reviews by Gudmundsson, 2006, andGrosfils, 2007), has resulted in the creation of some problems that are related to the question of singling out the "best" model that needs to be adopted when a particular volcano is under examination. Somewhat paradoxically, selecting the best possible model (whether analytical or numerical) may not be an easy task precisely because there is a variety of treatments that have been employed to solve the same fundamental question, and such variety sometimes makes the correct appreciation of key aspects related to the general problem difficult.…”

Evidence for intrusive activity on Mercury from the first MESSENGER flyby

“…At intermediate scales, such as that of Pantheon Fossae, graben commonly radiate away from volcanic edifices and subsurface magma reservoirs and are formed as the surface manifestation of radial dike emplacement (e.g., Johnson, 1961;Parfitt and Head,1993;Ernst et al,1995). Overpressurized shallow magma reservoirs propagate magma-filled cracks (dikes) radially away from the reservoir (Odé, 1957;Pollard and Muller, 1976;Delaney and Pollard, 1981;Gudmundsson, 1984; but see Grosfils, 2007). In cross section, these dikes appear as elongated blade-like forms (Fig.…”