Renormalization schemes for earthquake prediction

Some recent renormalization schemes for earthquake prediction are considered. These schemes suppose that there is some seismic activity prior to the main earthquake. This activity is characterized by an increase in the regional Benioff strain release. One of the schemes (Bufe & Varnes 1993; Bufe, Nishenko & Varnes 1994) can be reduced to a simple power-law approximation of the regional seismic-activity data, while another 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 based on the use of discrete groups of coordinate dilations and which includes log-periodicity as a particular case, can be useful in the description of the data and can be used in earthquake predictions in the framework of the above hypothesis. In addition, parametric-homogeneity allows us to take into account the fractal features of the process.