Physics – Geophysics
Scientific paper
Jun 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003georl..30k..13g&link_type=abstract
Geophysical Research Letters, Volume 30, Issue 11, pp. 13-1, CiteID 1559, DOI 10.1029/2002GL016022
Physics
Geophysics
6
Mathematical Geophysics: Nonlinear Dynamics, Volcanology: Eruption Mechanisms, Volcanology: Lava Rheology And Morphology
Scientific paper
Magma under pressure rises in conduits, depressurizes, forms bubbles by the exsolution of gas and - at void fractions (P) typically of the order of 0.7 - can fragment and explode. The study of overlapping geometrical units - percolation theory - predicts that at a critical volume fraction P c the size of the largest simply connected region becomes infinite. We apply percolation theory to overlapping bubbles arguing that this geometric singularity at P c implies a physical singularity in the magma rheology. This would imply that if the magma is under stress, - whether it is ductile or brittle - this rapid development of a network of infinitely long ``bubbles'' triggers fragmentation and explosion. Classical monodisperse (equal size) continuum percolation theory predicts P c = 0.2985 +/- 0.005 which is far from the observed values. However, it has recently been shown that the bubble distribution is a power law associated with a huge range of bubble sizes. Using Monte Carlo percolation simulations, we show that distributions exhibiting the empirical exponents are very efficient at ``packing'' the bubbles, drastically raising P c to the value = 0.70 +/- 0.05. Explosive volcanism is thus explained by singular rheology at P c.
Gaonac'h Helene
Lovejoy Shaun
Schertzer Daniel
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