A cellular automaton for the factor of safety field in landslides modeling

Abstract

[1] Landslide inventories show that the statistical distribution of the area of recorded events is well described by a power law over a range of decades. To understand these distributions, we consider a cellular automaton model based on a dissipative dynamical variable associated to a time and position dependent factor of safety. The model is able to reproduce the complex structure of landslide distribution, as experimentally reported. In particular, we investigate the role of the rate of change of the system dynamical variables, induced by an external drive, on landslide modeling and its implications on hazard assessment. As the rate is increased, the model has a crossover from a critical regime with power-laws to non power-law behaviors. We suggest that the detection of patterns of correlated domains in monitored regions can be crucial to identify the response of the system to perturbations, i.e., for hazard assessment. Citation: Piegari, E., V. Cataudella, R. Di Maio, L. Milano, and M. Nicodemi (2006), A cellular automaton for the factor of safety field in landslides modeling, Geophys. Res. Lett., 33, L01403,

Recurrence time distribution and temporal clustering properties of a cellular automaton modelling landslide events

“…2a, for a small value of ν, p(τ ) exhibits a linear regime in a log-log scale -that means a power-law regime in a linear scale -for recurrence time intervals that enlarge by increasing the threshold q. We note that in the limit of small values of ν, the model resembles the results of the OFC model (Olami et al, 1992), as extensively discussed in previous works (Piegari et al, 2006a(Piegari et al, , 2009a. Thus, in this regime p(τ ) is expected to be characterized by a power-law regime according to SOC-like models proposed for explaining recurrence time statistics of earthquakes and solar flares (Sanchez et al, 2002;Corral, 2004;Pacuzski et al, 2005).…”

“…In other words, we take into account non-conservative (dissipative) cases where the quantity C = nn f nn , which fixes the degree of conservation of the system, is less than 1, contrary to other approaches (Hergarten and Neugebauer, 2000;Hergarten, 2003). The role of the model parameter C has been investigated in previous works, where we found that the shape of the frequencysize probability distribution of landslide events is strongly affected by the values of C (Piegari et al, 2006a), while it is not significantly affected by the values of the coefficients f nn in the range of values that supply power-law distributions (Piegari et al, 2006b). In particular, only if C < 1 do our synthetic frequency-size distributions reproduce those from catalogues (Piegari et al, 2009a), pointing out the relevance of dissipative phenomena to landslide triggering.…”

“…In this paper, we analyse the recurrence time statistics of a cellular automaton (CA) model aimed at reproducing the main features of landslide event statistics by means of some characteristic parameters (Piegari et al, 2006a(Piegari et al, , 2009a.…”

Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes

“…Lübeck (1997) conducted large-scale simulations of a similar Zhang sandpile and obtained exponents slightly higher than 1.2, which can go even higher for large driving rates ν. In a similar model that incorporated non-conservation, Piegari et al (2006) obtained power-law exponents that approach 1.6 in the conservative limit for the same order or magnitude of ν that we used. The higher exponents and the effect of the driving rates are also verified by an equivalent conservative model and actual sand avalanche experiments by Juanico et al (2008), and in other asynchronous updating models (Paguirigan et al, 2015).…”

“…The sandpile model, introduced as a representative system for illustrating self-organized criticality (SOC; Bak et al, 1987), has opened up new avenues for the use of discrete cellular automata (CA) models in capturing the salient features of many systems in nature (Olami et al, 1992;Drossel and Schwabl, 1992;Malamud and Turcotte, 2000;Piegari et al, 2006;Juanico et al, 2008). Seismicity, which is rife with power-law statistical distributions (Saichev and Sornette, 2006), is an interesting test case for such approaches.…”