Burridge-Knopoff model

Fig. 4.1. Schematic diagram of the Burridge-Knopoff model of earthquakes.

It may be mentioned here that a recent study (Vasconcelos 1996) of a simple noncooperative (one-block) model of stick-slip motion (described by eqn (4.2) with / o = 0 or eqn (4.4) with k = 0) shows discontinuous velocity-dependent transition in the block displacement, for generic velocity-dependent friction forces. Naive generalisation of this observation for the coupled Burridge-Knopoff model would indicate a possible absence of criticality in the model. 

In another, somewhat more realistic automata model, Olami et al. (1992) (see Perez et al 1996 for a recent review) considered the mapping of the two-dimensional Burridge-Knopoff spring-block model into a cellular automata model. In fact, if one considers the two-dimensional geometry of the Burridge-Knopoff model as shown in Fig. 4.10, one can write for the total elastic force Fij on the block at site (i, j), from (4.4),... 

In the following, we give some details of these studies of response to weak pulses in the BTW model, and of weak periodic pulses in the Burridge-Knopoff model. 

Response of the Burridge-Knopoff model to localised periodic pulses... 

We discuss the various dynamical models of earthquake-like failures in Chapter 4. Specifically, the properties of the Burridge-Knopoff stick-slip model (Burridge and Knopoff 1967) and of the self-organised criticality models, the Guttenberg-Richter type power laws, for the frequency distribution of earthquakes in these models are discussed here. 

Burridge-Knopoff stick-slip model of earthquakes 4.2.1 Laboratory simulation model... 

In their original one-dimensional model for the table top laboratory simulation of earthquakes, Burridge and Knopoff (1967) took a chain of eight massive wooden blocks (of mass around 140 grams each) connected by iden-... 

Fig. 4.2. A typical plot of the time variation of the potential energy (Et) of the spring-block model. Each discontinuity (almost vertical fall) in the potential energy correspond to an earthquake with the magnitude given by the energy release Er) corresponding to the fall. A plot of the frequency n Er) versus energy release (Er) on a log-log scale is indicated in the inset (cf. Burridge and Knopoff 1967).

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