Snow Avalanche Release, Scale Invariance and Criticallity
Abstract
It is widely recognised that a number of geophysical phenomena as volcanic eruptions, landslides, etc, obey the so-called Gutenberg-Richter relation, first established for the frequency-magnitude statistics of earthquakes, where is the occurence frequency of earthquakes with a magnitude greater than m. This power law behaviour, character- istic of critical phenomena, is usually evidenced in the form of a linear distribution in a double logarithmic plot, in a way similar to the self organised criticality of a sand pile (2). We have shown very recently and for the first time that snow avalanche release exhibited such a behaviour (3). The only reliable parameter we had at that time was the amplitude of the acoustic emission associated with the avalanche release. Since it was not possible to record several events in the same gully, data were taken in sev- eral gullys of the same mountain range. Yet, the data aligned quite well on a unique straight line, with a critical exponent of about 1.6. This observation suggests that the very nature of the release mechanism is independent of the average slope and mor- phology of the gully. In order to understand the origin of this critical behaviour and to further investigate the mechanisms responsible for avalanche release, the avalanche release is studied in the present paper both by discrete elements simulations and cel- lular automata, and compared to further field data. The discrete elements simulations deal with a population of spheres on a slope, experiencing both a gravitational stress, interactions with the substrate, and mutual contact interactions. A gradual increase of the slope or a gradual change in contact forces (accounting for thermal snow mi- crostructure evolution) eventually result in avalanche release. The conditions are ad- justed until the frequency-magnitude of avalanches exhibit a critical behaviour. The cellular automaton is more or less similar to a game of life: a 2-d grid of boxes repre- sents the interface between the substrate and the snow slab, loaded in shear by the slab weight. Each box can be in one of two states labelled 0 and 1, according whether the slab/substrate interface is locally cracked or not. The state of a box can be changed ac- cording whether a given number of neighbours are in a 0 state or in a 1 state. A group of adjacent boxes in the 0 state represents a crack. The automaton is run from vari- ous randomly generated initial populations. Avalanches of various sizes are recorded. The local rules are adjusted until the avalanche frequency- size distribution aligns on a critical line. In both cases, the critical slopes are compared to field data.
1 (1) B. Gutenberg and C.F. Richter, seismicity of the earth and associated phenomenon, 2d edition, Princeton University Press, Princeton (1954) (2) P. Bak, How Nature Works, Springer Verlag (1996) (3) F. Louchet, J. Faillettaz, D. Daudon, N. Bédouin, E. Collet, J. Lhuissier and A-M. Portal XXVI General Assembly of the European Geophysical Society, Nice (F), 25-30 mars 2001 2- Publication:
-
EGS General Assembly Conference Abstracts
- Pub Date:
- 2002
- Bibcode:
- 2002EGSGA..27.2899D