Kazuyoshi Z. Nanjo

Rates of aftershock decay and the fractal structure of active fault systems

Abstract Aftershock activity on frequency decay against time is characterized by a power law (the modified Omori formula) of an exponent p, which differs with each aftershock sequence. A theoretical study suggested that p, which is a rate constant of aftershock decay, is related to the fractal dimension of a pre-existing fault system. This has however never been checked. Aftershock activity on size distribution is also characterized by an exponential distribution against magnitude (the Gutenberg—Richter relation) with a slope b. Although p is expected to be related to b, which is related to the partitioning rate of earthquake energy, the relationship has never been established. Here the relation between the p-values and the fractal dimensions of the pre-existing fault systems, and that between the p-values and the b-values are explored, using natural seismicity data and data of the observable fault systems. The p- and b-values were estimated for fifteen aftershock sequences which occurred in Japan. In this paper aftershocks were identified on the basis of a phenomenological definition in the seismicity data. The fractal capacity dimensions D0 are estimated for the pre-existing active fault systems observed on the surface in the aftershock regions. In the present paper the standard box-counting method was adopted to get the D0. Negative correlations between (1) p and D0, and (2) p and b were observed with some scattering. Observation (1) shows that the rate of aftershock decay p decreases systematically with increasing occupancy rate of the pre-existing active fault system D0 and suggests that aftershock decay dynamics is constrained by the pre-existing fracture field. Observation (2) shows that p certainly has a relation with b. Moreover, we offer possible interpretation on these negative correlations and some scatters in both observations: the scatters are interpreted as the scatter of the difference of two fractal dimensions between 3-D fracture construction in the crust and 2-D cross-sectional surface (observed active fault system). Supported by further tests, this paper strongly suggests that the scaling for a natural fracture system is self-affine (with different fractal scalings in different directions) rather than self-similar, which would be a manifestation of regional anisotropy of the fracture system, and that the seismic parameters p and b depend on the 3-D construction of the fracture system in the crust.

Analysis of the Completeness Magnitude and Seismic Network Coverage of Japan

Abstract A reliable estimate of completeness magnitude, M c , above which all earthquakes are considered to be detected by a seismic network, is vital for seismicity-related studies. We show a comprehensive analysis of M c in Japan. We use the catalog maintained by the Japan Meteorological Agency (JMA) and also available information on seismic stations that report to JMA. For computing M c , we adopt a commonly used method based on the Gutenberg–Richter frequency-magnitude law. Presently, M c =1.0 might be typical in the mainland, but to have a complete catalog, one needs to use earthquakes with magnitudes of 1.9 or larger. Comparison with the Southern California Seismic Network (SCSN) suggests that the recent event detectability in the mainland generally shows similar completeness levels to that in the authoritative region of SCSN. We argue that the current M c of Japan is due to the success of network modernization over time. Particularly, we show that the spatiotemporal change of M c closely matches the addition of the Hi-net borehole stations to enhancing seismic-station density; it started in October 1997 in southwestern Japan, continuing to northeastern Japan until 2002. As suggested from this matching, we confirm that M c inversely correlates with station density. Further, we find that irrespective of the network change after 1997, this correlation is unchanged in time, demonstrating that the influence on M c from factors beyond station density does not vary in time. Contrary to Alaska and California (Wiemer and Wyss, 2000), our results do not attribute such factors simply to anthropogenic noise. Because this is due to the borehole stations that reduce ambient noise, we conclude that in Japan the anthropogenic noise has an insignificant effect on M c .

Pattern Informatics and its Application for Optimal Forecasting of Large Earthquakes in Japan

Pattern Informatics (PI) technique can be used to detect precursory seismic activation or quiescence and make an earthquake forecast. Here we apply the PI method for optimal forecasting of large earthquakes in Japan, using the data catalogue maintained by the Japan Meteorological Agency. The PI method is tested to forecast large (magnitude m ≥ 5) earthquakes spanning the time period 1995–2004 in the Kobe region. Visual inspection and statistical testing show that the optimized PI method has forecasting skill, relative to the seismic intensity data often used as a standard null hypothesis. Moreover, we find in a retrospective forecast that the 1995 Kobe earthquake (m = 7.2) falls in a seismically anomalous area. Another approach to test the forecasting algorithm is to create a future potential map for large (m ≥ 5) earthquake events. This is illustrated using the Kobe and Tokyo regions for the forecast period 2000–2009. Based on the resulting Kobe map we point out several forecasted areas: The epicentral area of the 1995 Kobe earthquake, the Wakayama area, the Mie area, and the Aichi area. The Tokyo forecast map was created prior to the occurrence of the Oct. 23, 2004 Niigata earthquake (m = 6.8) and the principal aftershocks with 5.0 ≤ m. We find that these events were close to in a forecasted area on the Tokyo map. The PI technique for regional seismicity observation substantiates an example showing considerable promise as an intermediate-term earthquake forecasting in Japan.

Spatial distribution of aftershocks and the fractal structure of active fault systems

—The relationship between the fractal dimensions of aftershock spatial distribution and of pre-existing fracture systems is examined. Fourteen main shocks occurring in Japan were followed by aftershocks, and the aftershocks occurred in swarms around the main shock. Epicentral distributions of the aftershocks exhibit fractal properties, and the fractal dimensions are estimated by using correlation integral. Observable pre-existing active fault systems in the fourteen aftershock regions have fractal structures, and the fractal dimensions are estimated by using the box-counting method. The estimated fractal dimensions derive positive correlation, showing independence from the main-shock magnitude. The correlation shows that aftershock distributions become less clustered with increasing fractal dimensions of the active fault system. That is, the clusters of the aftershocks are constrained under the fractal properties of the pre-existing active fault systems. If the fractal dimension of the active fault system is the upper limit value of the fractal dimension of the actual fracture geometries of rocks, then the clustering aftershocks manifest completely random and unpredictable distribution.

Fractal properties of spatial distributions of aftershocks and active faults

Abstract The relationship between the fractal dimensions of spatial distributions of aftershocks and pre-existing active faults is examined. Fourteen mainshocks taking place in Japan were followed by aftershocks, and the aftershocks occur in swarms around the mainshocks. The epicentral distributions of the aftershocks exhibit fractal properties, and the fractal dimensions are estimated by using the two-point correlation integral. The pre-existing active fault systems observed in the 14 aftershock regions have fractal structures, and the fractal dimensions are estimated by using the box-counting method. A positive correlation between the estimated fractal dimensions is found, and it is independent on the mainshock magnitude. The correlation shows that aftershock distributions become less clustered with increasing the fractal dimensions of active fault systems. Namely, the fractal clusters of aftershocks are put under the constraint of the fractal properties of the pre-existing active fault systems. If the fractal dimension of active fault system is the upper limit value of the fractal dimension of actual rock-fracture geometries, then the spatial clustering of aftershocks shows completely random and unpredictable. The fractal structure of active fault systems is discussed to relate with self-organized criticality in a nonconservative model of earthquakes and “cumulative Benioff strain-release relationship” associating the total sum of the square root of the energy released for sequential fracture events to the time prior to the collapse failure.

CSEP Testing Center and the first results of the earthquake forecast testing experiment in Japan

Major objectives of the Japanese earthquake prediction research program for the period 2009–2013 are to create earthquake forecasting models and begin the prospective testing of these models against recorded seismicity. For this purpose, the Earthquake Research Institute of the University of Tokyo has joined an international partnership to create a Collaboratory for the Study of Earthquake Predictability (CSEP). Here, we describe a new infrastructure for developing and evaluating forecasting models—the CSEP Japan Testing Center—as well as some preliminary testing results. On 1 November 2009, the Testing Center started a prospective and competitive earthquake predictability experiment using the seismically active and well-instrumented region of Japan as a natural laboratory.

Comparison of seismicity declustering methods using a probabilistic measure of clustering

We present a new measure of earthquake clustering and explore its use for comparing the performance of three different declustering methods. The advantage of this new clustering measure over existing techniques is that it can be used for non-Poissonian background seismicity and, in particular, to compare the results of declustering algorithms where different background models are used. We use our approach to study inter-event times between successive earthquakes using earthquake catalog data from Japan and southern California. A measure of the extent of clustering is introduced by comparing the inter-event time distributions of the background seismicity to that of the whole observed seismicity. Theoretical aspects of the clustering measure are then discussed with respect to the Poissonian and Weibull models for the background inter-event time distribution. In the case of a Poissonian background, the obtained clustering measure shows a decrease followed by an increase, defining a V-shaped trend, which can be explained by the presence of short- and long-range correlation in the inter-event time series. Three previously proposed declustering methods (i.e., the methods of Gardner and Knopoff, Reasenberg, and Zhuang et al.) are used to obtain an approximation of the residual “background” inter-event time distribution in order to apply our clustering measure to real seismicity. The clustering measure is then estimated for different values of magnitude cutoffs and time periods, taking into account the completeness of each catalog. Plots of the clustering measure are presented as clustering attenuation curves (CACs), showing how the correlation decreases when inter-event times increase. The CACs demonstrate strong clustering at short inter-event time ranges and weak clustering at long time ranges. When the algorithm of Gardner and Knopoff is used, the CACs show strong correlation with a weak background at the short inter-event time ranges. The fit of the CACs using the Poissonian background model is successful at short and intermediate inter-event time ranges, but deviates at long ranges. The observed deviation shows that the residual catalog obtained after declustering remains non-Poissonian at long time ranges. The apparent background fraction can be estimated directly from the CAC fit. The CACs using the algorithms of Reasenberg and Zhuang et al. show a relatively similar behavior, with a time correlation decreasing more rapidly than the CACs of Gardner and Knopoff for shorter time ranges. This study offers a novel approach for the study of different types of clustering produced as a result of various hypotheses used to account for different backgrounds.

Distribution of Earthquake Cluster Sizes in the Western United States and in Japan

Earthquakes occur in clusters, which classically are described as foreshock–mainshock–aftershock sequences or swarms. In this paper, every earthquake in a seismicity catalog is assigned to a cluster if it is separated from at least one other event in the cluster by less than Δ t in time and less than Δ r in space. The minimum cluster size is one earthquake. For catalogs that are complete to small magnitudes, this approach is successful in capturing the full spatial extent of an extensive cluster even for Δ r much smaller than the actual cluster dimension. The declustered catalogs are much closer to Poissonian distribution than the originals. This was applied to seismicity catalogs for Japan, Southern California, and Nevada. Cluster sizes measured by the number of earthquakes in the cluster exhibit an approximate power‐law frequency distribution. An upper bound to cluster durations is proportional to K 0.5, where K is the number of earthquakes in the cluster. This paper demonstrates an analytical approach suitable for selecting values of Δ t and Δ r that are appropriate for the earthquake catalog.

A fiber-bundle model for the continuum deformation of brittle material

The deformation of brittle material is primarily accompanied by micro-cracking and faulting. However, it has often been found that continuum fluid models, usually based on a non-Newtonian viscosity, are applicable. To explain this rheology, we use a fiber-bundle model, which is a model of damage mechanics. In our analyses, yield stress was introduced. Above this stress, we hypothesize that the fibers begin to fail and a failed fiber is replaced by a new fiber. This replacement is analogous to a micro-crack or an earthquake and its iteration is analogous to stick–slip motion. Below the yield stress, we assume that no fiber failure occurs, and the material behaves elastically. We show that deformation above yield stress under a constant strain rate for a sufficient amount of time can be modeled as an equation similar to that used for non-Newtonian viscous flow. We expand our rheological model to treat viscoelasticity and consider a stress relaxation problem. The solution can be used to understand aftershock temporal decay following an earthquake. Our results provide justification for the use of a non-Newtonian viscous flow to model the continuum deformation of brittle materials.

A b map implying the first eastern rupture of the Nankai Trough earthquakes

The Nankai Trough megathrust earthquakes inflicted catastrophic damage on Japanese society and more widely. Most research is aimed at identifying strongly coupled regions that are considered as a major source of future disastrous earthquakes. Here we present a b-value map for the entire Nankai Trough zone. The b value, which represents the rate of occurrence of small earthquakes relative to larger ones, is inversely dependent on differential stresses, and has been used to detect highly stressed areas on fault planes in various tectonic situations. A remarkable finding is that the b value is inversely correlated with the slip-deficit rate (SDR). Moreover, the b value for the areas of high SDR in the eastern part is lower than that in the western part, indicating that differential stress on asperities in the eastern part is higher than that in the western part. This may explain the history of the Nankai Trough earthquakes, in which the eastern part tends to rupture first.Earthquakes generated from the Nankai Trough have caused much devastation over the years. Here, the authors present a b-value map for the Nankai Trough zone, where the Eastern part of the trough has lower b-values than the West, which may help to explain why the Eastern part tends to rupture first.