Time Variations in the Parameters of Dynamic Systems of Geodeformation Processes

Abstract

The variability of a correlation dimension parameter of geophysical fields is studied in the tectonically active region of the Parkfield segment of the San-Andreas Fault in 1990–2017 based on understanding a deformation process in the lithosphere as the evolution of a complex dynamic system. The time variability of the correlation dimension is estimated from the long time series of the borehole observations of volumetric strains, creep, and seismicity. The $${{d}_{2}}$$ estimate of the volumetric strain field on short time scales (discretization interval $$dt \leqslant 1$$ h) indicates a local character of the behavior of a high-dimensional dynamic system, which is different at the considered observation points. At the same time, the variability of $${{d}_{2}}$$ on the longer observation scales is largely governed by the main common factor—the change in the regime of deformation activity due to the Parkfield earthquake with $$M = 6.0.$$ The dynamic system of fault-slip displacements has a diverse response to the earthquake on longer time scales ( $$dt \geqslant 12$$ h). The seismicity data for the analysis are the cumulative time series of earthquakes’ energies to power 1/3. Based on the model of the time series with the known time density of the event flow, the time behavior of $${{d}_{2}}$$ in a moving window of a variable time scale was compared with the behavior in a window of a constant time scale. The decrease in the correlation dimension of the dynamic system during aftershock activation on shorter scales ( $$dt$$ < 0.5 h) repeats the characteristic behavior of the b-value (the slope of the frequency–magnitude relationship of the earthquakes). The $${{d}_{2}}$$ estimate of the seismic parameter on longer time scales ( $$dt = 24$$ h) shows the growth of the dimension of the dynamic system on the time segment containing the time of the earthquake. This behavior may suggest that the dynamic system vigorously varies on the longer time scales. The results of this work can be used for studying the evolution of the stress–strain state of the geological medium and for developing the approaches, methods, and algorithms of nonlinear dynamics for analyzing the geophysical fields.