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Norikazu Suzuki

Publications and source records attributed to Norikazu Suzuki.

At least 19 recordsLinked to original sources
arXiv2023

Scaling and memory in seismological phenomena

The concept of memory is of central importance for characterizing complex systems and phenomena. Presence of long-term memories indicates how their dynamics can be less sensitive to initial conditions compared to the chaotic cases. On the other hand, it is empirically known that the Feller-Pareto distribution, which decays as the power law i.e. the scale-invariant nature, frequently appears as a statistical law generated by the dynamics of complex systems. However, it is generally not a simple task to determine if a system obeying such a power law possesses a high degree of complexity with a long-term memory. Here, a new method is proposed for characterization of memory. In particular, a scaling relation to be satisfied by any memoryless dynamics generating the Feller-Pareto power-law distribution is presented. Then, the method is applied to the real data of energies released by a series of earthquakes and acceleration of ground motion due to a strong earthquake. It is shown in this way that the sequence of the released energy in seismicity is memoryless in the event time, whereas that of acceleration is memoryful in the sampling time.

physics.geo-ph↗
arXiv2023

Aftershocks and fluctuating diffusivity

The Omori-Utsu law shows the temporal power-law-like decrease of the frequency of earthquake aftershocks and, interestingly, is found in a variety of complex systems/phenomena exhibiting catastrophes. Now, it may be interpreted as a characteristic response of such systems to large events. Here, hierarchical dynamics with the fast and slow degrees of freedom is studied on the basis of the Fokker-Planck theory for the load-state distribution to formulate the law as a relaxation process, in which diffusion coefficient in the space of the load state is treated as a fluctuating slow variable. The evolution equation reduced from the full Fokker-Planck equation and its Green's function are analyzed for the subdynamics governing the load state as the fast degree of freedom. It is shown that the subsystem has the temporal translational invariance in the logarithmic time, not in the conventional time, and consequently the aging phenomenon appears.

physics.geo-ph↗
arXiv2019

Brain activity vs. seismicity: Scaling and memory

The brain activity and seismicity share a remarkable similarity. The Gutenberg-Richter law describing a power-law relation between the frequency of earthquake occurrence and released energy has its counterpart in the brain activity of a patient with epilepsy, that is, the distribution of fluctuations of the voltage difference measured by electroencephalogram (EEG) also obeys a Gutenberg-Richter-like power law. The similarity in the distributions, however, does not directly tell if the processes underlying these intermittent phenomena are also similar to each other. Here, a new simple method is presented for quantitative evaluation of (non-)Markovianity and is applied to the processes of released energy in seismicity and fluctuation of the voltage difference in EEG data. It is shown that the process in seismicity is almost memoryless, whereas that in EEG has long-term memory.

cond-mat.stat-mech↗
arXiv2017

Subdiffusion of volcanic earthquakes

A comparative study is performed on volcanic seismicities at Icelandic volcano, Eyjafjallajökull, and Mt. Etna in Sicily from the viewpoint of complex systems science, and the discovery of remarkable similarities between them is reported. In these seismicities as point processes, the jump probability distributions of earthquakes (i.e., distributions of the distance between the hypocenters of two successive events) are found to obey the exponential law, whereas the waiting-time distributions (i.e., distributions of inter-occurrence time of two successive events) follow the power law. A careful analysis is made about the finite size effects on the waiting-time distributions, and the previously reported results for Mt. Etna (Abe and Suzuki 2015) are reinterpreted accordingly. It is shown that the growth of the seismic region in time is subdiffusive at both volcanoes. The aging phenomenon is commonly observed in the "event-time-averaged" mean-squared displacements of the hypocenters. A comment is also made on (non-)Markovianity of the processes.

physics.geo-ph↗
arXiv2015

Anomalous diffusion of volcanic earthquakes

Volcanic seismicity at Mt. Etna is studied. It is found that the associated stochastic process exhibits a subdiffusive phenomenon. The jump probability distribution well obeys an exponential law, whereas the waiting-time distribution follows a power law in a wide range. Although these results would seem to suggest that the phenomenon could be described by temporally-fractional kinetic theory based on the viewpoint of continuous-time random walks, the exponent of the power-law waiting-time distribution actually lies outside of the range allowed in the theory. In addition, there exists the aging phenomenon in the event-time averaged mean squared displacement, in contrast to the picture of fractional Brownian motion. Comments are also made on possible relevances of random walks on fractals as well as nonlinear kinetics. Thus, problems of volcanic seismicity are highly challenging for science of complex systems.

physics.geo-ph↗
arXiv2014

Universal clustering structure and C~0.85 scaling in complex earthquake networks

Earthquake network captures the complexity of seismicity in a peculiar manner. Given a seismic data, the procedure of constructing an earthquake network proposed in [S. Abe, N, Suzuki, Europhys. Lett. 65 (2004) 581] contains as a single parameter the size of the cells, into which a geographical region under consideration is divided. Then, the characteristics of the network depend on the cell size, in general. Here, the dependency of the clustering coefficient, C, of network on the cell size is studied. Remarkably, C of the earthquake networks constructed from the seismic data taken from California, Japan and Iran well coincide for each value of the rescaled dimensionless cell size. It is found that the networks in California and Japan are three-dimensional, whereas the one in Iran is rather two-dimensional. In addition, the values of C of all these three networks monotonically converge to C~0.85 as the dimensionless cell size becomes larger than a common value, highlighting a universal aspect of the concept of earthquake network. An implication of the result to understanding the physics of seismicity is discussed.

physics.geo-ph↗
arXiv2012

Dynamical evolution of the community structure of complex earthquake network

Earthquake network is known to be complex in the sense that it is scale-free, small-world, hierarchically organized and assortatively mixed. Here, the time evolution of earthquake network is analyzed around main shocks in the context of the community structure. It is found that the maximum of the modularity measure quantifying existence of communities exhibits a peculiar behavior: its maximum value stays at a large value before a main shock, suddenly drops to a small value at the main shock, and then increases to relax to a large value again relatively slowly. Thus, a main shock absorbs and merges communities to create a larger community, showing how a main shock can be characterized in the complex-network representation of seismicity.

physics.geo-ph↗
arXiv2012

Universal law for waiting internal time in seismicity and its implication to earthquake network

In their paper (Europhys. Lett., 71 (2005) 1036), Carbone, Sorriso-Valvo, Harabaglia and Guerra showed that "unified scaling law" for conventional waiting times of earthquakes claimed by Bak et al. (Phys. Rev. Lett., 88 (2002) 178501) is actually not universal. Here, instead of the conventional time, the concept of the internal time termed the event time is considered for seismicity. It is shown that, in contrast to the conventional waiting time, the waiting event time obeys a power law. This implies the existence of temporal long-range correlations in terms of the event time with no sharp decay of the crossover type. The discovered power-law waiting event-time distribution turns out to be universal in the sense that it takes the same form for seismicities in California, Japan and Iran. In particular, the parameters contained in the distribution take the common values in all these geographical regions. An implication of this result to the procedure of constructing earthquake networks is discussed.

physics.geo-ph↗
arXiv2012

Aftershocks in Modern Perspectives: Complex Earthquake Network, Aging, and Non-Markovianity

The phenomenon of aftershocks is studied in view of science of complexity. In particular, three different concepts are examined: (i) the complex-network representation of seismicity, (ii) the event-event correlations, and (iii) the effects of long-range memory. Regarding (i), it is shown the clustering coefficient of the complex earthquake network exhibits a peculiar behavior at and after main shocks. Regarding (ii), it is found that aftershocks experience aging, and the associated scaling holds. And regarding (iii), the scaling relation to be satisfied by a class of singular Markovian processes is violated, implying the existence of the long-range memory in processes of aftershocks.

physics.geo-ph↗
arXiv2011

Finite data-size scaling of clustering in earthquake networks

Earthquake network is known to be of the small-world type. The values of the network characteristics, however, depend not only on the cell size (i.e., the scale of coarse graining needed for constructing the network) but also on the size of a seismic data set. Here, discovery of a scaling law for the clustering coefficient in terms of the data size, which is refereed to here as finite data-size scaling, is reported. Its universality is shown to be supported by the detailed analysis of the data taken from California, Japan and Iran. Effects of setting threshold of magnitude are also discussed.

physics.geo-ph↗
arXiv2010

Scale-free and small-world properties of earthquake network in Chile

The properties of earthquake networks have been studied so far mainly for the seismic data sets taken from California, Japan and Iran, and features common in these regions have been reported in the literature. Here, an earthquake network is constructed and analyzed for the Chilean data to examine if the scale-free and small-world properties of the earthquake networks constructed in the other geographical regions can also be found in seismicity in Chile. It is shown that the result is affirmative: in all the regions both the exponent "gamma" of the power-law connectivity distribution and the clustering coefficient C take the universal invariant values "gamma ~1" and "C~0.85", respectively, as the cell size becomes larger than a certain value, which is the scale of coarse graining needed for constructing earthquake network. An interpretation for this remarkable result is presented based on physical considerations.

physics.geo-ph↗
arXiv2010

Universal and nonuniversal distant regional correlations in seismicity: Random-matrix approach

Distant regional cross correlations are analyzed for seismicity in Japan by making use of the theory of random matrices as the null hypothesis. The empirical correlation matrix is shown to strongly deviate from the random matrix of the Wishart type. Accordingly, nonuniversal (i.e., nonrandom) correlations are identified and are represented by the networks on the map of Japan. The effect of setting threshold for magnitude is also examined, and it is found that the threshodling alters the results only slightly.

physics.geo-ph↗
arXiv2009

Determination of the scale of coarse graining in earthquake network

In a recent paper [S. Abe and N. Suzuki, Europhys. Lett., 65 (2004) 581], the concept of earthquake network has been introduced in order to describe complexity of seismicity. There, the cell size, which is the scale of coarse graining needed for constructing an earthquake network, has remained as a free parameter. Here, a method is presented for determining it based on the scaling behavior of the network. Quite remarkably, both the exponent of the power-law connectivity distribution and the clustering coefficient are found to approach the respective universal values and remain invariant as the cell size becomes larger than a certain value, $l_*$, which depends on the number of events contained in the analysis, in general. This $l_*$ fixes the scale of coarse graining. Universality of the result is demonstrated for all of the networks constructed from the data independently taken from California, Japan and Iran.

physics.geo-ph↗
arXiv2008

Violation of the scaling relation and non-Markovian nature of earthquake aftershocks

The statistical properties of earthquake aftershocks are studied. The scaling relation for the exponents of the Omori law and the power-law calm time distribution (i.e., the interoccurrence time distribution), which is valid if a sequence of aftershocks is a singular Markovian process, is carefully examined. Data analysis shows significant violation of the scaling relation, implying the non-Markovian nature of aftershocks.

physics.geo-ph↗
arXiv2008

Scaling relation for earthquake networks

The scaling relation derived by Dorogovtsev, Goltsev, Mendes and Samukhin [Phys. Rev. E, 68 (2003) 046109] states that the exponents of the power-law connectivity distribution, gamma, and the power-law eigenvalue distribution of the adjacency matrix, delta, of a locally treelike scale-free network satisfy 2*gamma - delta = 1 in the mean field approximation. Here, it is shown that this relation holds well for the reduced simple earthquake networks (without tadpole-loops and multiple edges) constructed from the seismic data taken from California and Japan. The result is interpreted from the viewpoint of the hierarchical organization of the earthquake networks.

physics.geo-ph↗
arXiv2006

Dynamical evolution of clustering in complex network of earthquakes

The network approach plays a distinguished role in contemporary science of complex systems/phenomena. Such an approach has been introduced into seismology in a recent work [S. Abe and N. Suzuki, Europhys. Lett. 65, 581 (2004)]. Here, we discuss the dynamical property of the earthquake network constructed in California and report the discovery that the values of the clustering coefficient remain stationary before main shocks, suddenly jump up at the main shocks, and then slowly decay following a power law to become stationary again. Thus, the network approach is found to characterize main shocks in a peculiar manner.

physics.geo-ph↗
arXiv2006

Complex earthquake networks: Hierarchical organization and assortative mixing

To characterize the dynamical features of seismicity as a complex phenomenon, the seismic data is mapped to a growing random graph, which is a small-world scale-free network. Here, hierarchical and mixing properties of such a network are studied. The clustering coefficient is found to exhibit asymptotic power-law decay with respect to connectivity, showing hierarchical organization. This structure is supported by not only main shocks but also small shocks, and may have its origin in the combined effect of vertex fitness and deactivation by stress release at faults. The nearest-neighbor average connectivity and the Pearson correlation coefficient are also calculated. It is found that the earthquake network has assortative mixing. This is a main difference of the earthquake network from the Internet with disassortative mixing. Physical implications of these results are discussed.

cond-mat.dis-nn↗