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Conference Abstract: Lecture format preferred 


           The Slab Avalanche as a Self-Organized Critical Phenomenon

                                David McClung
                  Professor and NSERC - Canadian Mountain 
                Holidays Chair in Snow and Avalanche Science
                            Department of Geography
                         University of British Columbia
                            Vancouver, B.C. V6T 1Z2

                     Tel: 604-822-9157; FAX: 604-822-6150
                        e-mail: mcclung@geog.ubc.ca

Abstract:

Alpine snow  causing slab avalanches fails in shear as a pressure sensitve, 
dilatant strain-softening material. This behaviour   is similar to soils 
responsible for some landslides, such as over-consolidated clay, and rock 
joints which are responsible for earthquakes. Avalanches, landslides and 
earthquakes undergo a transition in time scales when they occur: rapid 
fractures are preceded by a much longer period of development before failure. 
In this sense,  they represent some characteristics of a critical system. 
During the 1990's, self-organized ciriticality (SOC) as formulated by Per Bak 
and others was explored by countless papers, with perhaps the most quoted 
papers in all the scientific literature.  Avalanche phenomena were used 
initally as the proto-types with a combination of modelling and lab 
experiments. In order to obey  SOC, basically 3 criteria must be satisfied 
for a phenomenon: 1. it must fit the definition of a critical system; 2. size 
scaling for events must be scale invariant; and 3. the arrival frequency must 
be fractal. 

In this paper, I present field data on slab fracture properties and time 
arrival of slab avalanches to explore these 3 criteria for the snow slab. 
The results represent the first time that all three criteria for SOC have 
been examined entirely from field data for avalanche phenomena without 
resorting to  theoretical modelling. The primary results are: 1. the c
lassical definition of a critical system does not fit for slab avalanches; 2. 
slab avalanches are not scale invariant with respect to the fundamental size 
scaling parameter (slab thickness) derived from fracture mechanics. Instead, 
the slab thickness follows a log-normal probability density function; 3. time 
arrival of slab avalanches  in the frequency domain is not fractal as shown 
by calculation of  power spectra. Instead, the frequency dependence appears 
to decay exponenitally  The combined results suggest that if the slab 
avalanche is to be described as a critical system similar to SOC, 
modification of the definitions proposed for SOC is required. The results 
have fundamental implications for definition of critical systems  and 
forecasting for natural events including avalanches, landslides and 
earthquakes.