Complexity of seismic process; measuring and applications — A review

Recent methods of analysis of so called disordered systems show that many objects and processes that earlier were considered as completely random reveal clear evidence of having some ordered structure in both time and space. These new methods (fractals, percolation, nonlinear dynamics and complexity theories) allow visualization and quantitative assessment of the level of complexity (orderliness) of these structures, using both theoretical models and experimental data. We consider sequentially some aspects of structural and evolutionary complexity of dynamics of seismic process and the technique of measuring this property.It is shown that the physical properties of geophysical medium are not always self-consistent and manifest fractal behavior on selected spatial and temporal scales. Mechanical percolation theory can be used for modeling geometry of fracture process. Namely, we consider fractal and connectivity aspects of delayed failure, including energy emission during fracturing. Special attention is paid to relating the intensity of geophysical anomalies to the strain in the framework of the pressure-induced anomalous strain-sensitivity (percolation) model, which explains naturally the observed heterogeneity of response of a geophysical media to the strain variation.Different methods of measuring the dynamic complexity of seismological time series are applied to magnitude and waiting time sequences of Caucasian earthquakes. The fractal (correlation) dimension d₂ of the latter is high (larger than 8), but the former one has as low dimension as 1.6–2.5, which makes waiting time sequences a promising tool for revealing precursory changes.The same nonlinear technique allow detecting significant changes in the seismic regime during external electromagnetic forcing by MHD pulses; similar tests on the laboratory scale show the possibility of triggering/controlling stick-slip process by relatively weak electromagnetic or mechanical forcing.Lastly, the predictive potential of complexity analysis of seismological time series is considered. For example, percolation model predicts the increase of the number of large events and the scatter of magnitudes of events, decrease of the magnitude-frequency relation slope and appearance of multifractality at approaching the final rupture.It seems that seismology can benefit from using the new techniques to cope with the complexity of earthquake machine; for example, the measures of complexity can be characteristic for a given region and change before strong earthquake.