We analyzed the time series of released seismic energy using the procedures devised for dynamic systems and fractals, for determination of dynamic and self-similar (fractal) properties of seismotectonic system. We used one of the best in the world catalog of earthquakes – JMA catalog for Japan (1992–1996 years) in our analysis. This catalog is characterized by the highest quality and accuracy of determinations of all parameters of earthquakes.
Released seismic energy is determined on base of magnitude values. The magnitude is proportional to a log of seismic energy. For each earthquake we recalculated magnitude to energy, and then summed energies for all earthquakes happened within calendar days. As a result we received the time series of daily release of seismic energy for all range of magnitudes, and also for various sub- ranges.
Mathematical expressions of self-similarity are the power laws for various parameters of analyzed time series. The parameters we analyzed are spectral scaling parameter Hurst exponent Hu, fractal dimension D, correlation dimension Dc and embedding dimension m.
We detected that examined time series of seismic energy have fractal properties over the range more than one order on time and frequency. The calculated characteristics of self-similarity of analyzed time series indicate that these series for small and mean magnitudes rank to the flicker-noise class. But time series including the large earthquakes have stochastic properties, close to “white” noise.
As values of , D and Hu were calculated separately in our work, it allow to confirm (within the limits of error) validity of application of the equations received on model Brownian functions, for analysis of fractal properties of natural time series.
Analysis of correlation dimension Dc has allowed detecting a certain degree of determinism in investigated process, however on-ly for mid-range of a band of magnitudes. But for time series including the large earthquakes it is not possible detecting characteristics of a degree of determinism of system. Possible explanation is that magnitudes over the range 4 to 5 are determined with the greatest accuracy, and for other bands this accuracy is less. Also small length of analyzed time series can reduce accuracy of analysis. Other possible explanation is that during large earthquake there is a radical structural readjustment, a bifurcation, of seismotectonic system at which one this system practically “forgets” the previous states. This “memory erasing” destroys determined relations, and our results show it. It gives a direction for the further investigations.
Our analysis of dynamic and fractal properties of time series of released seismic energy show that the seismotectonic system generating earthquakes is determined-chaotic system. Dynamics systems of such types generate both small amplitude variations and significant (one or several orders large) peaks. Meantime value of these peaks and time intervals between them are irregular, and capabilities of prognosis of such systems are restricted or quite absent.