Guttenberg-Richter law

As the fracture propagates, the elastic energy released due to the micro-fractures occurring within the sample can be measured. This ultrasonic emission due to micro-fracture aftershock relaxation has recently been measured for various laboratory samples. Petri et al (1994) measured the ultrasonic emission amplitude distribution in a large number of stressed solid samples under different experimental conditions. A power law decay for the cumulative energy release distribution n Er) with the released energy amplitude Er was observed in all cases n Er) E (see Fig. 3.21). This is indeed very similar to the Guttenberg-Richter law for the frequency distribution of earthquakes, as discussed briefly in Chapter 1, and will be discussed in detail in the next chapter. 

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. 

In another recent trend of such investigations, one considers the Guttenberg-Richter (power) law to result as a consequence of the criticality of the geometry of the earthquake (fracture) faults of the earth s upper crust, where established power law distributions for the fault geometries occur. One then compares with those for percolation clusters near or at the percolation threshold. One therefore investigates the fracture mechanics of the stressed earth s crust, where such fractal patterns for the fault segments occur near the contact areas of the major plates (Kagan 1982, Barriere and Turcotte 1991, Sahimi 1992). 

The role of disorder, in particular of the fractal structure of the earthquake faults (discussed in Section 4.4), are not clearly understood. As discussed in an earlier chapter (Section 3.8), the dynamics of fracture in disordered solids also indicate similar (Guttenberg-Richter type) power law behaviour in the power spectrum of the ultrasonic emission from such solids, as the fracture propagates. No doubt the understanding of the connections between the dynamics of fracture in disordered solids and the dynamics of earthquakes will become much clearer in the near future, because of the intensive efforts which are being made currently. 

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