RENORMALIZATION SCHEMES FOR EARTHQUAKE PREDICTION

Some recent renormalization schemes for earthquake prediction are cons idered. These schemes suppose that there is some seismic activity prio r to the main earthquake. This activity is characterized by an increas e in the regional Benioff strain release. One of the schemes (Bufe & V arnes 1993; Bufe, Nishenko & Varnes 1994) can be reduced to a simple p ower-law approximation of the regional seismic-activity data, while an other scheme (Sornette & Sammis 1995; Saleur, Sammis & Sornette 1996a) can be reduced to the log-periodic approximation. I argue that a new concept of parametric-homogeneity (Borodich 1994; 1995b), which is bas ed on the use of discrete groups of coordinate dilations and which inc ludes log-periodicity as a particular case, can be useful in the descr iption of the data and can be used in earthquake predictions in the fr amework of the above hypothesis. In addition, parametric-homogeneity a llows us to take into account the fractal features of the process.