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Marzocchi W.,Italian National Institute of Geophysics and Volcanology | Zhuang J.,The Institute of Statistical Mathematics of Tokyo
Geophysical Research Letters | Year: 2011

The most used and accepted models for daily forecasts are based on short-term space and time earthquake clustering for occurrence rates and on the Gutenberg-Richter law for the frequency-magnitude. These models have been demonstrated to produce reliable prospective space-time-magnitude forecasts during an aftershock sequence, but their skill in forecasting mainshocks is still under discussion. This paper studies the foreshock statistics of the Italian and Californian seismicity in two ways: i) we compare the foreshock activity observed in real seismic catalogs and in synthetic catalogs derived from a pure Epidemic-Type Aftershock Sequence (ETAS) model; ii) we analyze the triggering capability of earthquakes using different ETAS parameterizations, in order to check whether large events are triggered in the same way as regular earthquakes. The results indicate that the foreshock activity observed in the real catalogs is compatible with what is expected by the ETAS model. Moreover, we find that the empirical foreshock rates have an intrinsic variability due to limited sampling that may explain most of the differences found so far in different seismic catalogs. Copyright © 2011 by the American Geophysical Union.


If aseismic slip occured on a fault or its deeper extension, both seismicity and crustal deformation around the source would be affected. Such anomalies are determined from earthquake occurrence data and geodetic records during the periods leading up to the 2007 March Noto Hanto earthquake of M6.9 and the 2007 July Chuetsu-oki earthquake of M6.8, which successively occurred after the 2004 October Chuetsu earthquake of M6.8 on the Japan Sea coast. Assuming such aseismic slips, seismic zones corresponding to negative and positive increments of the Coulomb failure stress show seismic quiescence and activation, respectively, relative to the rate predicted by the epidemic type aftershock sequence model. These interpretations are further supported by transient crustal movements around the sources preceding the ruptures, for example, the time-series of baseline distances between permanent Global Positioning System stations deviated from their long-term linear trends in a manner that is consistent with the assumed slip. In particular, this paper emphazes on the investigation of the interacting tectonic processes within such a narrow area and a short period, considering the precursory slow slips on the focal faults or their downdip extensions based on the observed anomalies in seismicity and crustal movement. © 2011 The Authors. Geophysical Journal International © 2011 RAS.


Ogata Y.,The Institute of Statistical Mathematics of Tokyo
Earth, Planets and Space | Year: 2011

The space-time version of the epidemic type aftershock sequence (ETAS) model is based on the empirical laws for aftershocks, and constructed with a certain space-time function for earthquake clustering. For more accurate seismic prediction, we modify it to deal with not only anisotropic clustering but also regionally distinct characteristics of seismicity. The former needs a quasi-real-time cluster analysis that identifies the aftershock centroids and correlation coefficient of a cluster distribution. The latter needs the space-time ETAS model with location dependent parameters. Together with the Gutenberg-Richter's magnitude-frequency law with locationdependent b-values, the elaborated model is applied for short-term, intermediate-term and long-term forecasting of baseline seismic activity. Copyright © The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS).


Zhuang J.,The Institute of Statistical Mathematics of Tokyo
Earth, Planets and Space | Year: 2011

This paper gives the technical solutions of implementing the space-time epidemic-type aftershock sequence (ETAS) model for short-term (1-day) earthquake forecasts for the all-Japan region in the Collaboratory for the Study of Earthquake Predictability (CSEP) project in Japan. For illustration, a retrospective forecasting experiment is carried out to forecast the seismicity in the Japan region before and after the Tokachi-Oki earthquake (M 8.0) at 19:50:07 (UTC) on 25 September 2003, in the format of contour images. The optimal model parameters used for the forecasts are estimated by fitting the model to the observation records up to the starting time of the forecasting period, and the probabilities of earthquake occurrences are obtained through simulations. To tackle the difficulty of heavy computations in fitting a complicated point-process to a huge dataset, an "off-line optimization" and "online forecasting" scheme is proposed to keep both the estimates of model parameters and forecasts updated according to the most recent observations. The results show that the forecasts have captured the spatial distribution and temporal evolution of the features of future seismicity. These forecasts are tested against the reference Poisson model that is stationary in time but spatially inhomogeneous. Copyright © The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS).


Iwata T.,The Institute of Statistical Mathematics of Tokyo
Geophysical Journal International | Year: 2013

Earthquake detection capability has been shown to be lower in daytime than nighttime owing to human activity; accordingly, the daily variation in detection capability must be taken into account for the reliable estimation of the completeness magnitude (Mc) of earthquakes. Here, we present estimation results of Mc in which we consider this daily variation in earthquake detection capability. To evaluate such daily variation quantitatively, we introduced a statistical model representing a magnitude-frequency distribution covering the entire magnitude range. Then, the temporal variation in the model parameter, which corresponds to the earthquake detection capability, was estimated by adopting a Bayesian approach with a piecewise linear approximation. This method was applied to the 2006-2010 Japan Meteorological Agency catalogue to estimate the spatial distribution of Mc in and around Japan and to examine the statistical significance of the daily variation. We found significant daily variation in detection capability in 4391 of the 8144 gridpoints examined (i.e. more than 50 per cent) with an interval of 0.1°, which highlights the importance of accounting for this daily variation. The values of Mc we obtained by considering the daily variation were around 2.5 or 3.0 during 2006 and 2010; these values are more conservative than the magnitude threshold suggested by an earlier study. © The Author 2013. Published by Oxford University Press on behalf of The Royal Astronomical Society.


Zhuang J.,The Institute of Statistical Mathematics of Tokyo
Geophysical Journal International | Year: 2010

This paper presents a new method, namely the gambling score, for scoring the performance earthquake forecasts or predictions. Unlike most other scoring procedures that require a regular scheme of forecast and treat each earthquake equally, regardless their magnitude, this new scoring method compensates the risk that the forecaster has taken. Starting with a certain number of reputation points, once a forecaster makes a prediction or forecast, he is assumed to have betted some points of his reputation. The reference model, which plays the role of the house, determines how many reputation points the forecaster can gain if he succeeds, according to a fair rule, and also takes away the reputation points betted by the forecaster if he loses. This method is also extended to the continuous case of point process models, where the reputation points betted by the forecaster become a continuous mass on the space-time-magnitude range of interest. We also calculate the upper bound of the gambling score when the true model is a renewal process, the stress release model or the ETAS model and when the reference model is the Poisson model. © 2010 The Authors Journal compilation © 2010 RAS.


Ogata Y.,The Institute of Statistical Mathematics of Tokyo
Geophysical Journal International | Year: 2010

For a number of aftershock sequences in and around Japan, we examine detrended space-time coordinates after fitting the Omori-Utsu occurrence rate to each aftershock sequence. The case studies in conjunction with the fault locations and orientations of the main shocks and focal large aftershocks indicate that the region of deficit and surplus in the aftershock activity well corresponds to the decreased and increased region of Coulomb failure stress, respectively, caused by various aseismic slips. We illustrate the relation between the transient stress changes and the anomalous aftershock activity in a local subregion by six scenarios derived from the rate and state dependent friction law of Dietrich. © 2010 The Author Journal compilation © 2010 RAS.


Miyasato Y.,The Institute of Statistical Mathematics of Tokyo
Proceedings of the IEEE Conference on Decision and Control | Year: 2010

Design methods of adaptive H∞ formation control of multi-agent systems composed of Euler-Lagrange systems are presented in this paper. The proposed control schemes are derived as solutions of certain H ∞ control problems, where estimation errors of tuning parameters and error terms in potential functions are regarded as external disturbances to the process. It is shown that the resulting control systems are robust to uncertain system parameters and that the desirable formations are achieved asymptotically via adaptation schemes. ©2010 IEEE.


Someya H.,The Institute of Statistical Mathematics of Tokyo
IEEE Transactions on Evolutionary Computation | Year: 2011

This paper investigates the evolutionary dynamics of steady-state real-valued evolutionary algorithms (RVEAs) with more-than-one-element replacement theoretically, whereas most theoretical studies of RVEAs have considered single-or all-element replacement. The subject RVEAs are of interest because they appear in various fashions, such as real-coded genetic algorithms (RCGAs) and island RVEAs. The analysis is conducted to deepen the understanding of how RVEA components and their parameters influence the phenotypic diversity in the parental pool. First, the diversity evolution is modeled mathematically and then a constraint of diversity control is derived from this model. The control method is demonstrated and the accuracy of the theoretical predictions is evaluated through experiments. The shortest convergence time is estimated. The analysis requires few assumptions about either the variation operators or selection schemes, and therefore is applicable to various RVEAs. As such an application in RCGAs, the influence on the diversity evolution of offspring-population size, parental-pool size, crossover-operator parameter, and selection-pressure parameters of two selection mechanisms is quantified. The computational efficiency, search stability, and selection-pressure controllability are then evaluated. The analysis results are discussed from a practical point of view in parameter settings for preventing premature convergence. © 2006 IEEE.


Fushiki T.,The Institute of Statistical Mathematics of Tokyo
Statistics and Computing | Year: 2011

Estimation of prediction accuracy is important when our aim is prediction. The training error is an easy estimate of prediction error, but it has a downward bias. On the other hand, K-fold cross-validation has an upward bias. The upward bias may be negligible in leave-one-out cross-validation, but it sometimes cannot be neglected in 5-fold or 10-fold cross-validation, which are favored from a computational standpoint. Since the training error has a downward bias and K-fold cross-validation has an upward bias, there will be an appropriate estimate in a family that connects the two estimates. In this paper, we investigate two families that connect the training error and K-fold cross-validation. © 2009 Springer Science+Business Media, LLC.

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