Weibull-distributed dyke thickness reflects probabilistic character of host-rock strength

Abstract

Magmatic sheet intrusions (dykes) constitute the main form of magma transport in the Earth’s crust. The size distribution of dykes is a crucial parameter that controls volcanic surface deformation and eruption rates and is required to realistically model volcano deformation for eruption forecasting. Here we present statistical analyses of 3,676 dyke thickness measurements from different tectonic settings and show that dyke thickness consistently follows the Weibull distribution. Known from materials science, power law-distributed flaws in brittle materials lead to Weibull-distributed failure stress. We therefore propose a dynamic model in which dyke thickness is determined by variable magma pressure that exploits differently sized host-rock weaknesses. The observed dyke thickness distributions are thus site-specific because rock strength, rather than magma viscosity and composition, exerts the dominant control on dyke emplacement. Fundamentally, the strength of geomaterials is scale-dependent and should be approximated by a probability distribution.

Low resistivity zones at contacts of igneous intrusions emplaced in organic‐rich formations and their implications on fluid flow and petroleum systems: A case study in the northern Neuquén Basin, Argentina

“…The thickness histogram exhibits an asymmetric thickness distribution with a peak near ca.18 m and a skewed distribution towards the thicker sills. Such distribution is typical of a Weibull distribution, which has been demonstrated to describe the thickness distribution of igneous dykes (Krumbholz et al, ).…”

Dynamics of dikes versus cone sheets in volcanic systems

“…Field observations in extinct and exhumed volcanic areas worldwide have identified different geometries of sheet intrusions, among which (i) vertical dikes [e.g., Pollard , ; Lister and Kerr , ; Rubin , ; Ancochea et al ., ; Geshi , ; Paquet et al ., ], (ii) inclined cone sheets [ Harker and Clough , ; Bailey , ; Ancochea et al ., ; Burchardt et al ., ], and (iii) horizontal sills [e.g., Kavanagh et al ., ; Burchardt , ; Galland et al ., ] represent the main types (Figure ). It is interesting to notice that although the shapes of these distinct sheet intrusions are rather different, they are found together in the same volcanic systems (Figure ) [ Walker , ; Geshi , ; Paquet et al ., ] and their thicknesses follow the same statistical distribution indicating a related emplacement dynamics [ Krumbholz et al ., ]. The spatial association and the close temporal relations between cone sheets and dikes led Walker [] to propose that they may be fed by a common source [see also Geshi , ].…”

Predictability of properties of a fractured geothermal reservoir: the opportunities and limitations of an outcrop analogue study

“…While (sub)recent microcrack orientations are commonly consistent over large volumes (e.g. Vollbrecht et al 1994;Krumbholz et al 2014a) and therefore predictable, larger fractures have usually a more complex history and thus exhibit more variable systematics. A direct implication is that the strength of the rocks is also scale dependent (Krumbholz et al 2014b).…”