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| Titel |
Percolating magmas in three dimensions |
| VerfasserIn |
H. Gaonac'h, S. Lovejoy, M. Carrier-Nunes, D. Schertzer, F. Lepine |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 14, no. 6 ; Nr. 14, no. 6 (2007-11-27), S.743-755 |
| Datensatznummer |
250012310
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| Publikation (Nr.) |
 copernicus.org/npg-14-743-2007.pdf |
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| Zusammenfassung |
The classical models of volcanic eruptions assume that they originate as a
consequence of critical stresses or critical strain rates being
exceeded in the magma followed by catastrophic fragmentation. In a recent
paper (Gaonac'h et al., 2003) we proposed an additional
mechanism based on the properties of complex networks of overlapping
bubbles; that extreme multibubble coalescence could lead to catastrophic
changes in the magma rheology at a critical vesicularity. This is possible
because at a critical vesicularity Pc (the percolation threshold),
even in the absence of external stresses the magma fragments. By considering
2-D percolation with the (observed) extreme power law bubble distributions,
we showed numerically that P2c had the apparently realistic value
≈0.7.
The properties of percolating systems are, however,
significantly different in 2-D and 3-D. In this paper, we discuss various new
features relevant to 3-D percolation and compare the model predictions with
empirical data on explosive volcanism. The most important points are a)
bubbles and magma have different 3-D critical percolation points; we show
numerically that with power law bubble distributions that the important magma
percolation threshold P3c,m has the high value ≈0.97±0.01, b)
a generic result of 3-D percolation is that the resulting primary
fragments will have power law distributions with exponent B3f≈1.186±0.002,
near the empirical value (for pumice) ≈1.1±0.1; c) we review the
relevant percolation literature and point out that
the elastic properties may have lower – possibly more realistic – critical
vesicularities relevant to magmas; d) we explore the implications of long
range correlations (power law bubble distributions) and discuss this in
combination with bubble anisotropy; e) we propose a new kind of intermediate
"elliptical" dimensional percolation involving differentially elongated
bubbles and show that it can lead to somewhat lower critical thresholds.
These percolation mechanisms for catastrophically weakening magma would
presumably operate in conjunction with the classical critical stress and
critical strain mechanisms. We conclude that percolation theory provides an
attractive theoretical framework for understanding highly vesicular magma. |
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