The classical models of volcanic eruptions assume that they originate in the magma as a consequence of critical stresses or critical strain rates being exceeded followed by catastrophic fragmentation of the magma. 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 called the percolation threshold, even in the absence of external stresses the magma fragments. By considering 2D percolation with the (observed) extreme power law bubble distributions, we showed numerically that P2c had the apparently realistic value of 0.7. However, the properties of percolating systems are significantly different in 2D and 3D. We will 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 3D critical percolation points, b) a generic result of 3D percolation is that the resulting primary fragments will have power law distributions with exponent B3f of 1.186±0.002. We will review the relevant percolation literature and point out that the elastic properties may have lower - possibly more realistic - critical vesicularities relevant to magmas. We will then explore the implication of long-range correlations and discuss this in combination with bubble anisotropy.
AGU Fall Meeting Abstracts
- Pub Date:
- December 2007
- 4475 Scaling: spatial and temporal (1872;
- 8414 Eruption mechanisms and flow emplacement