Mikhail Shnirman

On a small-scale roughness of the core^mantle boundary

Abstract The roughness of the core–mantle boundary, on the scale of centimeters to tens of meters, is modelled using a cellular automata method. Square cells, of the size of grains of the mantle material, on a 2-D grid, can be in one of three states corresponding to mantle silicate or oxide, core fluid saturated in light element and unsaturated core fluid. The dynamical process of evolution is defined as a stationary stochastic process without memory. Transitions of doublets of cells from one state to another are governed by parameters representing the rates of physical processes: dissolution and crystallization at the CMB and diffusion of the light element in the core fluid. With reasonable values of the parameters, the boundary roughens on the scale of grains, and a boundary layer of saturated fluid, of a few tens of centimeters thick, soon appears at the interface. An undulation with dominant wavelength of the order of a few tens of meters eventually appears. An interaction of the roughness of the CMB with the fluid flow in the core is considered as possible.

Scaling laws in blocks dynamics and dynamic self-organized criticality

Abstract A hierarchical model of blocks moving in two orthogonal directions is suggested. Temporal evolution of the system is studied with the use of the kinetic equation. The behaviour of the model is essentially dynamic self-organized criticality. It is shown that the model exhibits the general properties of seismicity—the seismic cycle, the foreshock and aftershock activity, the Omori law for temporal decrease of aftershock activity, and the Gutenberg-Richter law.

Hierarchical model of seismicity: scaling and predictability

Abstract One considers the problem of the prediction of strong events in a hierarchical model of blocks moving in two directions. The model exhibits a linear magnitude-frequency relationship with variations in time of the local slope, a behavior which is referred to as dynamic self-organized criticality. An algorithm of prediction is based on this variation of the local slope of the magnitude-frequency relationship. A wide range of predictability is observed when varying the parameters of the model. The relationship between the predictability of synthetic catalogs and some of the parameters of the model is investigated.

Mixed hierarchical model of seismicity: scaling and prediction

Abstract We consider a hierarchical system which is a mixture of elements of different strength. We investigate the scaling properties of this system, varying the proportion in which the elements are mixed. Four kinds of behavior are possible in the system: stability, catastrophe, unstable and stable scale invariance. The heterogeneity of the mixture in the former two cases leads to a linear form of the magnitude–frequency relation with different slopes. Stable scale invariance is specified by a unit slope of the magnitude–frequency relation, it is associated with the self-organized criticality (SOC) and may be realized only if the heterogeneity is high enough. Predictability of strong events for all kinds of system behavior is discussed. It is shown that variations of the slope and form of the magnitude–frequency relation predict the increasing probability of strong events. The role of the total activity variations in the prediction of strong events is described for the SOC case.

Temporal variation of predictability in a hierarchical model of dynamical self-organized criticality

Abstract A hierarchical model reproducing the dynamical self-organized criticality, previously described in Blanter et al. [Blanter, E.M., Shnirman, M.G., Le Mouel, J.-L., 1988. Hierarchical model of seismicity: scaling and predictability. Phys. Earth Planet. Inter. 103 (1998), 135–150] is considered. We investigate the predictability of strong events in a synthetic earthquake sequence generated by this model. We apply a simple prediction algorithm based on variations of the average magnitude in a sliding time window. Though parameters of the model are fixed, the quality of prediction and the optimal threshold of alarm declaration have strong temporal variations. We show that temporal variation of the predictions quality is larger when the energy rate is lower. Possible applications for real seismicity are briefly discussed.