Inverse modeling for estimating fluid-overpressure distributions and stress intensity factors from an arbitrary open-fracture geometry

Depth of origin of magma in eruptions

“…This equation applies strictly only to the maximum opening. However, many dykes show comparatively smooth flat-elliptical variations in their openings/displacements, in which case the maximum displacement is similar to the average displacement781415. The overpressure in the dyke at the surface is given by15 where p e is the fluid excess pressure in the source magma chamber, ρ r is the average density of the host rock, ρ m is the average density of the magma in the dyke, g is acceleration due to gravity, h is the depth to the source chamber, and σ d is the differential stress (the difference between the vertical stress and the minimum principal horizontal stress) at the surface where the volcanic fissure forms.…”

“…the section on Methods below). The detailed variations in the aperture of a volcanic fissure/thickness of a feeder-dyke can be modelled using Fourier cosine series14 or polynomials15. Commonly, however, the detailed variation in aperture/thickness is not known but rather the opening/thickness at a single site or, at most, a few sites678.…”

“…(1) was initially derived in the context of general fracture mechanics16, and is discussed elsewhere in the context of volcanotectonics15. The equation assumes the internal fluid overpressure in the dyke to be constant, which is generally a good first approximation when there is limited data available as to the exact aperture/thickness variation141533. When the aperture/thickness variation of the fissure/dyke is known, the potential variation in overpressure can be considered1415.…”

Basaltic feeder dykes in rift zones: geometry, emplacement, and effusion rates

“…Here the overpressure (p o ) derives from the term in the brackets, and is partly due to the excess pressure p e in the source magma chamber of the dyke, and partly on the buoyancy term (ρ r − ρ m )g as defined above (note that the term is multiplied by the height or length L to get the proper units). The aperture is thus known to vary with overpressure, and can be modelled in various ways (e.g., Gudmundsson, 1986;Gray, 1992;Kusumoto et al, 2012). Currently, however, there are no available analytical models that allow the coupled changes in overpressure and aperture to be directly related to changes in volumetric flow rates during volcanic eruptions.…”

Aspect ratios and magma overpressures of non‐feeder dikes observed in the Miyake‐jima volcano (Japan), and fracture toughness of its upper part

“…For example, the magnitude of the regional tensile stress field has been estimated from the aspect (length/aperture) ratios of tension fractures in the rift zone of Iceland [Gudmundsson, 1983]. Since equation (1) is very simple and suggests a linear relation between the crack shape and the driving pressure or stress, it has also been applied to estimate the overpressure associated with observed dikes in the field, although more general solutions exist [e.g., Gudmundsson, 2011;Gudmundsson et al, 2012;Kusumoto et al, 2013].…”