Multi-method investigation of mass transfer mechanisms in a retrogressive clayey landslide (Harmalière,French Alps)     

Fiolleau  Sylvain  Jongmans  Denis  Bièvre  Gregory  Chambon  Guillaume  Lacroix  Pascal  Helmstetter  Agnès  Wathelet  Marc  Demierre  Michel 《Landslides》2021,18(6):1981-2000

Landslides - The mass transfer mechanisms in landslides are complex to monitor because of their suddenness and spatial coverage. The active clayey Harmalière landslide, located 30 km south of...  相似文献   

Power-law Distributions of Offspring and Generation Numbers in Branching Models of Earthquake Triggering     

A. Saichev  A. Helmstetter  D. Sornette 《Pure and Applied Geophysics》2005,162(6-7):1113-1134

We consider a general stochastic branching process,which is relevant to earthquakes as well as to many other systems, and we study the distributions of the total number of offsprings (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We apply our results to a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model. The ETAS model assumes that each earthquake can trigger other earthquakes (aftershocks). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake (fertility), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime in which the distribution of fertilities is characterized by a power law ~1/¹⁺. For earthquakes we expect such a power-distribution of fertilities with =b/ based on the Gutenberg-Richter magnitude distribution ~ 10^–bm and on the increase ~ 10^–m of the number of aftershocks with the mainshock magnitude m. We derive the asymptotic distributions p_r(r) and p_g(g) of the total number r of offsprings and of the total number g of generations until extinction following a mainshock. In the regime < 2 for which the distribution of fertilities has an infinite variance, we find This should be compared with the distributions obtained for standard branching processes with finite variance. These predictions are checked by numerical simulations. Our results apply directly to the ETAS model whose preferred values =0.8–1 and b=1 puts it in the regime where the distribution of fertilities has an infinite variance. More generally, our results apply to any stochastic branching process with a power-law distribution of offsprings per mother  相似文献