Nonlinear analysis of magnitude and interevent time interval sequences for earthquakes of the Caucasian region

Abstract

Abstract. It is well known that lithospheric seismic processes are characterized by self-similarity or scale invariance in terms of earthquake-size, time, space and space-time distributions, although precise details of underlying dynamics are not clear. In this study we apply nonlinear dynamics theory tools, such as a correlation dimension, "surrogate" data analysis and positive Lyapunov exponent calculation, to investigate dynamical characteristics of seismicity in the Caucasian region. Interevent time intervals and magnitude sequences are considered for different area and magnitude windows. We find significant evidence of a low dimensional nonlinear structure of earthquake time distribution, obtained by consideration of time interval sequences between all events encountered, above some threshold magnitude, in the original catalogue. However nonlinear structure is absent in artificially generated sequences of time intervals between independent events as well as time intervals between aftershocks. It seems that this kind of filtration of the original catalogue destroys the existing temporal structure of considered lithospheric processes. Unlike artificial inter-aftershock time interval sequences, obtained by removing independent events from the original series, the time interval sequence between the Racha earthquake aftershocks reveals clear evidence of nonlinear structure. Earthquake magnitude dynamics. for all considered regions and magnitude windows, reveal high dimensional nonlinearity.

Identification of Complex Processes Based on Analysis of Phase Space Structures

“…waiting time series in central Asia is in good agreement with the above results on low dimensional dynamical structure of earthquake temporal distribution for other seismoactive regions Matcharashvili and Javakhishvili, 2000). On the other hand Fig.…”

“…According to our results as well as to the reports of other authors (Korvin, 1992;Smirnov, 1995) the fractal dimension for the distribution of inter earthquake distances is low (d 2 < 2). Most interesting is that the waiting time interval distribution reveals an obviously low dimensional nonlinear structure (d 2 of the order of 1.6-2.5 and positive λ max of the order of 0.2-0.7), although it can not be recognized as a deterministic chaos (Matcharashvili and Javakhishvili, 2000)(see Fig. 1).…”

“…Dynamics of seismic processes is viewed as extremely complicated, so that the level of "turbulence" of the lithosphere exceeds that of the atmosphere (Kagan, 1994;Kagan, 1997). During more than one hundred years of instrumental observations several important characteristics of spatial, temporal and energetic distributions of earthquakes have been revealed (C.H., 1990;Turcotte, 1992;KeilisBorok, 1994;Matcharashvili and Javakhishvili, 2000;Rundle and Klein, 2000). Nevertheless the character of dynamics of seismic processes remains the subject of intense discussions because it is directly related to the problem of earthquake prediction.…”

“…The above conclusion about the increase of regularity in an earthquake's temporal distribution after beginning of experiments (external influence on seismic process) is confirmed also by results of RQA; namely RR(t) = 9.6, DET (t) = 3.9 before experiments, RR(t) = 25, DET (t) = 18 during and RR(t) = 3, DET = 1.5 after experiments. It was shown in our previous research that small earthquakes play a very important role in the general dynamics of earthquake temporal distribution (Matcharashvili and Javakhishvili, 2000). This is why we also have carried out the analysis of time series containing all data available from the entire catalogue of waiting time sequences, including small earthquakes that are below the magnitude threshold.…”

“…In spite of this, it is clear that natural systems and/or processes are complex due to their nonlinearity, an intrinsic property of the underlying laws conditioning absence of strict determinism of the universe. The presence of this property is revealed in the specificity of systems' temporal behavior and spatial structures, what we name as complex (Kantz and Schreiber, 1997;Matcharashvili and Javakhishvili, 2000). In order to avoid misunderstanding caused by tradition, associating the term nonlinearity exceptionally with dynamics, it should be stressed that at present the terms nonlinearity and complexity commonly are regarded as synonyms.…”