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Statistical Seismology Seminars    統計地震学セミナー   Updated on 28 September 2017

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67 NEW!

講演者: Dr. Wu, Stephen (統計数理研究所 モデリング研究系 ・助教) 

日 時: 2017 10 3() 16:30 -17:30

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Review of earthquake early warning from an engineering perspective

 

Abstract: 

After the concept of earthquake early warning (EEW) first appeared in the 1980s, we now have officially working EEW systems around the world, such as, Japan, Taiwan, Mexico, USA, Italy, and so on. The algorithms of EEW have evolved to a large variety, including both on-site, regional and some hybrid methods. The underlying seismic model ranges from simple point-source ground motion prediction equations to sophisticated finite fault prediction models. Recently, researchers have also proposed to develop real-time GPS based EEW and purely data-driven seismic intensity prediction models. Besides the scientific advances, engineering applications of EEW have became another important research topic. In this talk, I will briefly go through all the topics above in a practical implementation point of view, and highlight some important challenge of EEW.

 

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講演者: Dr. () 晶(Wu, Jing (中国科学院地質・地球物理研究所 ・准教授)

日 時: 2017 8 29() 16:00 -17:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Seismicity and Seismic Anisotropy beneath eastern Tibet

 

Abstract: 

Eastern Tibet is one of the most tectonically active areas in Chinese Mainland. Songpan-Ganzi Block, Longmenshan Orogenic Belt, and Sichuan Basin are located in this area from west to east. The uplifting mechanisms of eastern Tibet are hot debated in recent years. In addition,  a series of great earthquakes in eastern Tibet (2008 Wenchuan Mw7.9, 2013 Lushan Mw6.6, and the most recent 2017 Jiuzhaigou Mw6.5) show the urgent need for accurate seismicity detection, as we are still not clear how aftershocks evolve because of the poor station coverage and overlapping of aftershocks.

 

Here, I would like to present our studies in eastern Tibet, including seismic anisotropy and seismicity detection. Crustal anisotropy are inversed according to shear-wave splitting of Pms phase from permanent station, and we observed that tectonic escaping, crustal flow, and crustal shortening may contribute to the tectonic evolution in various sub-areas in eastern Tibet. We also concentrated on the seismicity detection of 2013 Lushan earthquakes, and obtained details of the spatial and temporal aftershock evolution with the help of matched filter technique, suggesting that afterslip is the potential mechanism triggering Lushan aftershocks.

 

In order to understand more about eastern Tibet, we would keep on working in this area by focusing on the SKS, SKKS, PKS (hereafter, XKS phase) splitting and repeating earthquakes, which may reveal geodynamic processes in mantle and fault slip rate respectively.

 

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講演者: Dr. Mak, Sum German Research Centre for Geosciences (GFZ-Potsdam), Germany ・リサーチ・アシスタント(RA)

日 時: 2017 8 29() 17:00 -18:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Empirical Validation of Seismic Hazard Models

 

Abstract: 

Seismic hazard, for applications such as engineering structural design and insurance loss estimation, is represented as a probabilistic forecast. The most common form of seismic hazard representation is in the probability for a certain level of ground motion exceedance. The hazard also varies spatially, forming a hazard map.

 

As the amount of observation accumulates, recently there are more and more attempts to statistically evaluate the performance of probabilistic seismic hazard prediction using ground motion observations. This talk presents the general theory of this type of studies, using the United States Geological Survey National Seismic Hazard Maps as an example.

 

65

講演者: Prof. 正彦 (Liu,Jann-Yenq) (台湾国立中央大学 太空科学研究所 ・教授) 

日 時: 2017 6 13() 16:00 -17:00

場 所: 統計数理研究所 A508セミナー室6

 

Title: Statistical Analyses on seismo-ionospheric disturbances and precursors of the 11 March 2011 M9.0 Tohoku Earthquake

 

Abstract: 

Ground-based observations of the GPS TEC (total electron content) and satellite probing of radio occultation (RO) of FORMOSAT-3/COSMIC (F3/C) are employed to study the co-seismic disturbances and precursors of the 11 March 2011 M9.0 Tohoku earthquake.  It is for the first time the tsunami origin observed.  The horizontal propagation of seismo-traveling ionospheric disturbances (STIDs) induced by tsunami and seismic waves of the Tohoku earthquake are observed by the GPS TEC, while the associated vertical propagation is probed by multi ground-based observations and F3/C RO sounding.  The raytracing and beamforming techniques are used to find the propagation and origin of the STIDs triggered by the seismic and tsunami waves.   Meanwhile, z test and the Receiver Operating Characteristic (ROC) curve are employed to find the characteristic of the temporal SIPs (seismo-ionospheric precursor) of the GIM (global ionosphere map) TEC associated with earthquakes in Japan during 1998-2014.  It is found that anomalies appearing 3 days before the Tohoku earthquake well agree with the characteristic, which suggests that the SIPs of the earthquake have been observed.  A global study on the distribution of anomalies shows that the SIPs specifically and continuously occur over the epicenter on 8 March 2011, 3 days prior to the Tohoku earthquake.  Finally, a physical model of the ionosphere is used to reproduce the observed anomalies and find possible causal of the Tohoku SIPs.

 

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講演者: Prof. 長勝(Jiang, Changsheng (中国地震局地球物理研究所 ・研究員(教授相当)

日 時: 2017 3 29() 13:30 -14:30

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Assessment of earthquake monitoring capability and score of seismic station detection capability in China Seismic Network (2008~2015)

 

Abstract: 

In order to scientifically assess the earthquake monitoring capability of China Seismic Network (CSN), we investigated the seismic observation date of CSN with total 1001 stations considered during the period from 2008/10/01 to 2015/09/17. The distribution of seismic detection probability (PE) and the minimum magnitude of completeness (MP) were analyzed by using the method of "Probability-based magnitude of completeness" (PMC). In addition to mapping the seismic monitoring capability for entire CSN, we developed a new method named “seismic monitoring capability scale”, and defined the seismic detection capability scale Dscore to analyze the statistical characters and spatial distribution of the seismic detection capabilities for each national and regional stations, which based on the amplitude contour curves. Additionally, the method of setting the "best objective function" of seismic detection capability was used to simulate the seismic monitoring capability improvement of CSN obtained by improving the conditions of observation.

 

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講演者: Prof. 石(Chen, Shi (中国地震局地球物理研究所・研究員(教授相当)

日 時: 2017 3 29() 14:30 -15:30

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Gravity changes before and after the 2015 Mw 7.8 Gorkha, Nepal and the 2008 Mw 7.9 Wenchuan, China earthquakes

 

Abstract: 

Absolute gravity measurements at four stations in southern Tibet show significant gravity increase from 2011 to 2013, up to ~22 μGals at the Shigatse station. Here we report new measurements at the Shigatse station conducted in 2016, which show that the gravity increase ended after the 2015 Nepal Mw 7.8 earthquake. Similar gravity changes are measured at the Pixian absolute gravimetry station near the epicenter of the 2008 Wenchuan Mw 7.9 earthquake, where 17 absolute gravity measurements have been conducted since 2002, including four pre-earthquake measurements that show ~30 μGals increase from 2002 to 2008. The trend of gravity increase ended after the Wenchuan earthquake. We analyzed the gravity effects from ground vertical motions using data from continuous GPS stations collocated with these absolute gravimetry stations, and surficial and hydrological processes using local hydrological data. We found that these effects are much smaller than the observed gravity increase before the earthquakes, and suggest that the pre-earthquake gravity increase may be caused by strain and mass (fluid) transfer in broad seismic source regions. Further studies are needed to validate such pre-earthquake gravity changes, which however are difficult to be resolved from space-based gravity models.

 

63

講演者: Prof. 周 仕勇 (Zhou, Shiyong) (北京大学 地球空間科学学院 ・教授) 

日 時: 2017 1 18() 16:00 -17:00

場 所: 統計数理研究所 A504セミナー室7

 

Title: Could the abnormal seismicity increase triggered remotely by great earthquakes be used to judge the regional earthquake risk?

 

Abstract: 

We study the possible dynamic triggering effect in Northern China, including Tangshan area, when the Japan Tohoku M_w 9.0 earthquake happened at March 11th, 2011(In short, Japan Tohoku earthquake). We use Time-Space Epidemic Type Aftershock Sequence Model (Time-Space ETAS model) as the seismicity statistic model in this research, using Stochastic Declustering method and Gauss Kernel function to get Time-Space background seismicity variation image on the target area. Thus this research may find out whether the area with large co-seismic displacement would have sudden abnormal seismicity increase. As a result, the Japan Tohoku earthquake has little effect on the total and background seismicity of Tangshan area, which means that the seismic structure of Tangshan area is fundamentally stable. However, when we did research on the possible dynamic triggering effect in Southwestern China,  we found that seismicity on some place in Sichuan and Yunnan has sudden abnormally increased almost at the same time when 2004 Sumatra M_w 9.2 earthquake (In short, 2004 Sumatra earthquake) happened. That is the statistic phenomenon which shows the existence of co-seismic dynamic triggering. This research helps to find out the exact position of the high abnormal seismicity area in its time image. Besides, this time image can also help to detect whether this high “abnormal” seismicity in the picture is really abnormal or is triggered by certain large earthquake or not.

 

62

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講演者: Dr. Helmstetter, Agnès Institut des Sciences de la Terre, France Research fellow(上席研究員) 

日 時: 2016 10 26() 15:00 -16:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Repeating icequakes

 

Abstract: 

We have detected repeating icequakes on three different sites : an alpine glacier (Argentière, massif du Mont-Blanc, France), near the base of the western margin of the Greenland Ice Sheet, and on a rock-glacier (Gugla, Valais, Switzerland). Repeating icequakes are events with very similar waveforms, located at the base of a glacier, with quasi-periodic recurrence times of the order of minutes or hours, and progressive changes in magnitude. The activity of each cluster is intermittent. Burst-like episodes can last for a few hours or months, and then disappear. In greenland, temporal changes of inter-event times and magnitudes are correlated with temperature, because surface meltwater yields an increase in basal water pressure and in glacier flow velocity. But each cluster reacts differently to temperature changes, probably because the connectivity to the subglacial drainage system is different for each asperity. In contrast, we observed no correlation between temperature and repeating icequakes at Glacier d'Argentière and at Gugla rock Glacier. However, we observed bursts of repeating icequakes at Gugla triggered by snow falls. We suggest that the snow weight may have induced a transition between aseismic slip and unstable stick-slip. In addition to repeating basal icequakes, we also detected swarms of icequakes induced by crevasse opening, probably promoted by melt-water flow. These swarms of icequakes have very different statistical distributions in time, space and magnitude compared with repeating icequakes. Their recurrence times are power law distributed, their magnitudes obey the Gutenberg-Richter law, and the size of each cluster is several tens of meters. These different patterns may help to identify the triggering mechanisms of earthquake swarms, and to discriminate between fluid flow and aseismic slip.

 

-2

講演者: Dr. Harte, David GNS Science, New Zealand Statistical Seismologist and Hazard Modeller(上席研究員)

日 時: 2016 10 26() 16:00 -17:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Determining the Uncertainty in Earthquake Forecasts

 

Abstract: 

Forecasts based on a self-exciting model, like ETAS, are often produced by simulation. From these simulations, an empirical probability distribution can be derived for a forecast in a specified space-time-magnitude volume.

 

We will show that the forecast distribution can be characterised by probability generating functions. This shows how deeply complex the dependency structure is in such a model. While of theoretical interest, they remain intractable to me in a practical sense.

 

We then consider whether the forecast distribution can be approximated, using less computation than that required for simulation, by a "standard " multi-parameter probability distribution. The multiple parameters gives us the ability to at least fit a distribution with comparable mean and variance to that of the forecast distribution. One of the main questions is how to determine the forecast mean, and then given the mean, the variance.

 

61

講演者: Dr. Helmstetter, Agnès Institut des Sciences de la Terre, France Research fellow(上席研究員)

日 時: 2016 10 11() 16:00 -17:00

場 所: 統計数理研究所 A504セミナー室7

 

Title: Adaptive smoothing of seismicity in time, space and magnitude for long-term and short-term earthquake forecasts

 

Abstract: 

We present new methods for long-term and short-term earthquake forecasting that employ space, time, and magnitude kernels to smooth seismicity. These forecasts are applied to Californian and Japan seismicity and compared with other models. Our models are purely statistical and rely on very few assumptions about seismicity. In particular, we do not use Omori-Utsu law. The magnitude distribution is either assumed to follow  the Gutenberg-Richter law or is estimated non-parametrically with kernels. We employ adaptive kernels of variable bandwidths to estimate seismicity in space, time, and magnitude bins. For long-term forecasts, the long-term rate in each spatial cell is defined as the median value of the temporal history of the smoothed seismicity rate in this cell, circumventing the relatively subjective choice of a declustering algorithm. For short-term forecasts, we simply assume persistence, that is, a constant rate over short time windows. Our long-term forecast performs slightly better than our previous forecast based on spatially smoothing a declustered catalog. Our short-term forecasts are compared with those of the epidemic-type aftershock sequence (ETAS) model. Although our new methods are simpler and require fewer parameters than ETAS, the obtained probability gains are surprisingly close. Nonetheless, ETAS performs significantly better in most comparisons,  and the kernel model with a Gutenberg-Richter law attains larger gains than the kernel model that non-parametrically estimates the magnitude distribution. Finally, we show that combining ETAS and kernel model forecasts, by simply averaging the expected rate in each bin, can provide greater predictive skill than ETAS or the kernel models can achieve individually.

 

60

講演者: Dr. Hasih Pratiwi Sebelas Maret University, Surakarta, Indonesia Lecturer

日 時: 2016 8 30() 16:00 -17:00

場 所: 統計数理研究所 A504セミナー室7

 

Title: ESTIMATING EARTHQUAKE RISK BY USING EPIDEMIC TYPE AFTERSHOCK SEQUENCE MODEL APPROACH (Case Study in Java Island, Indonesia)  (Hasih Pratiwi and Respatiwulan)

 

Abstract: 

Physical losses caused by earthquakes are death or casualties and damage to buildings and areas. Therefore, efforts to reduce the risk of earthquake are very necessary. Relating to risk or loss generated by earthquake it is of course does not get out of insurance world. Insurance as nonbank financial institution can give guarantee or protection as done by banking sector. This research discusses a method to estimate earthquake risk by using epidemic type aftershock sequence model. Calculation of earthquake risk can be determined through a damage probability matrix. The information contained in the damage probability matrix and in the damage ratios can be combined for defining the mean damage ratio. Then, based on the estimation of intensity function in epidemic type aftershock sequence model we can formulate the expected annual damage ratio, and the existing method for calculating earthquake risk is modified to obtain earthquake insurance premium rates. We use earthquakes data in Java Island obtained from U.S. Geological Survey which consists of time of occurrence, longitude, latitude, magnitude, depth, and catalogue source. The time span of this research is from January 1, 1973, to December 31, 2010. Zonation map of earthquake generated in this research is different from the zonation map SNI 2010 issued by Indonesian Ministry of Public Works. The difference lies on the distribution of earthquake zone, especially in regencies and cities with high risk. The earthquake insurance premium rates for high and medium intensities obtained from this research are significantly greater than the premium rates issued by PT Reasuransi Maipark Indonesia. The current premium rates are relatively small when compared with the rates in Turkey and from this research.

 

Keywords: earthquake insurance, intensity function, epidemic type aftershock sequence model, damage probability matrix.

 

59

講演者: Prof. 陳 玉英(Chen, Yuh-Ing (台湾国立中央大学, 統計研究所・特聘教授)

日 時: 2016 7 19() 16:00 -17:00

場 所: 統計数理研究所 D312Aセミナー室3

 

Title: Statistical evaluation of short-term hazard of earthquakes after 1999 M 7.3 Chi-Chi shock in Taiwan

 

Abstract: 

The temporal-spatial hazard of the earthquakes in a continental region of Taiwan after the 1999 September 21 MW =7.7 Chi-Chi shock is investigated. The Reasenberg-Jones (RJ) model (Reasenberg and Jones, 1989) that combines the frequency-magnitude distribution (Gutenberg and Richter, 1944) and time-decaying occurrence rate (Utsu et al., 1995) is conventionally employed for assessing the earthquake hazard after a large shock (Wiemer, 2000). However, it is found that the b values in the frequency-magnitude distribution of the earthquakes in the studyregion dramatically decreased from background values after the Chi-Chi shock, and then gradually increased up. The observation of a time-dependent distribution of magnitude motivated us to propose a modified RJ model (MRJ) to assess the earthquake hazard (Chen et al. 2015). To incorporate the possible impact of previous large earthquakes on thefollowing ones, a simplified epidemic-type aftershock sequence (ETAS) model (Ogata, 1988, Ogata and Zhunag, 2006) is further considered. A modified ETAS (METAS) model that combines the simplified ETAS model and the time-dependent distribution of magnitude is then suggested for the hazard evaluation. The MRJ and METAS models are further separately used to make one-day forecast of large earthquakes in the study region. To depict the potential rupture area for future large earthquakes, we also develop the space-time MRJ and METAS models and construct the corresponding relative hazard (RH) maps. The Receiver Operating Characteristics (ROC) curves (Swets, 1988) demonstrate that the RH map based on the MRJ model is as good as the one based on the METAS model for exploring the spatial hazard of earthquakes in a short time after the Chi-Chi shock.

 

58

講演者: Dr. Zhuang, Jiancang ( 建倉) (統計数理研究所 モデリング研究系・准教授)

日 時: 2016 6 29() 16:00 -16:40

場 所: 統計数理研究所 D313D314セミナー室5

 統計数理研究所・統計数理セミナー平成28年度 (2016年度)

 

Title: 欠測のあるマーク付き点過程時系列データの補充法(Replenishing missing data in the observation record of mark point processes)

 

Abstract: 

This presentation illustrates a fast approach for replenishing missing data in the record of a temporal point process with time independent marks. The basis of this method is that, if such a point process is completely observed, it can be transformed into a homogeneous Poisson process by using a biscale empirical transformation. This approach includes three key steps: (1) Obtain the transformed process by using the empirical transformation and find a time-mark range that likely contains missing events; (2) Estimate a new empirical distribution function based on the data in the time-mark range inside which the events are supposed to be completely observed; (3) Generate events in the missing region. This method is tested on a synthetic dataset and applied to the data missing problem in the JMA record of the Kumamoto aftershock sequence, occurring from 2016-4-15 in Japan. The influence of missing data on the MLE of the ETAS parameters is studied by comparing the analysis results on the original and replenished datasets. The results show that the MLEs of the ETAS parameters vary when the ETAS model is fitted to the recorded catalog with different cut-off magnitudes, while when the replenished dataset is used the MLE of the ETAS parameters keep stable.

 

57

講演者: Dr. Shcherbakov, Robert Department of Earth Sciences, Western University(Ontario), Canada Associate Professor
統計数理研究所 モデリング研究系 ・客員准教授166-7月)

日 時: 2016 6 22() 16:40 -17:20

場 所: 統計数理研究所 D313D314セミナー室5

 統計数理研究所・統計数理セミナー平成28年度 (2016年度)

 

Title: Statistics and Physics of Aftershocks

 

Abstract: 

Aftershocks are ubiquitous in nature. They are the manifestation of relaxation phenomena observed in various physical systems. In the studies of seismicity, aftershock sequences are observed after moderate to large main shocks. Empirical observations reveal that aftershocks obey power-law scaling with respect to their energies (seismic moments) which in magnitude domain can be modelled by the Gutenberg-Richter law. The decay rate of aftershocks above a certain magnitude is typically inversely proportional to the time since the main shock and is approximated by the modified Omori law. The largest aftershocks in a sequence constitute significant hazard and can inflict additional damage to infrastructure that is already affected by the main shock. Therefore, the estimation of the magnitude of a possible largest aftershock in a sequence is of high importance. In this presentation, a Bayesian predictive distribution and the corresponding confidence intervals for the magnitude of the largest expected aftershock in a sequence are derived using the framework of Bayesian analysis and extreme value statistics. The analysis is applied to several well-known aftershock sequences world-wide to construct retrospectively the confidence intervals for the magnitude of the subsequent largest aftershock by using the statistics of early aftershocks in the sequences. In order to infer the physical mechanisms of triggering and time delays responsible for the occurrence of aftershocks, a nonlinear viscoelastic slider-block model is considered. It is shown that nonlinear viscoelasticity plays a critical role in the triggering of aftershocks. The model reproduces several empirical laws describing the statistics of aftershocks, which are observed in the studies of systems with relaxation dynamics, specifically, for earthquakes.

 

56

講演者: Dr. Strader, Anne GFZ German Research Centre for Geosciences, Germany 特別研究員) 

日 時: 2016 6 7() 16:00 -17:00

場 所: 統計数理研究所 A508セミナー室6

 

Title: Evaluation of Current CSEP Testing Methods: Case Studies for Japan and California

 

Abstract: 

The Collaboratory for the Study of Earthquake Predictability (CSEP) was developed to rigorously test earthquake forecasts retrospectively and prospectively through reproducible, completely transparent experiments within a controlled environment (Zechar et al., 2010).  Forecasts are individually evaluated using a set of likelihood-based consistency tests, which measure the consistency between the number, spatial and magnitude distribution of the observed and forecasted seismicity during the testing period (Schorlemmer et al., 2007; Zechar et al., 2010). Additionally, the classical paired t-test and non-parametric w-test are used to directly compare two forecasts' performances at target earthquake locations. These tests rely on a hypothesis testing framework, resulting in a final decision (to reject or not reject a forecast), rather than quantifying the model's lack-of-fit or localized performance. Residual methods are employed by the CSEP to discern spatial variation in model performance compared to the observed seismicity distribution and other models, but are not currently incorporated into decision-making processes. To illustrate what can be learned from commonly utilized current CSEP tests, we present two case studies. The first is a retrospective evaluation of a rate-and-state forecast for the Japan CSEP testing classes, where spatiotemporal seismicity rate fluctuations are inverted for Coulomb stress changes. Although the model underestimates the number of earthquakes following the M9.0 Tohoku mainshock, it displays positive information gain over baseline ETAS seismicity rates (Ogata, 2011) within the rupture region. The second forecasting experiment is a continued prospective evaluation of the time-independent California earthquake forecasts tested in the Regional Earthquake Likelihood Model (RELM) experiment, from 2011-2016. Additionally, we test two models developed by the United States Geological Survey (USGS): the time-dependent Uniform California Earthquake Rupture Forecast (UCERF2) and time-independent National Seismic Hazard Mapping Project (NSHMP) models.  To reduce bias from expert-based decision making utilized in current testing methods, we introduce the framework of a Dynamic Risk Quantification (DRQ) platform, that will be developed to combine and optimize ensemble forecasts and hazard models using a data-driven approach, and updated as new data become available.

 

55

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講演者: Dr. 一村Guo, Yicun (北京大学 地球宇宙科学研究科 博士後期課程)

日 時: 2016 3 22() 16:00 -17:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Iterative finiteETAS model and some results of the histETAS model of the North China Craton

 

Abstract: 

We introduce a iterative algorithm to refine the finite sources of main shocks in the finite ETAS model, in which the weight of triggering ability for each subfault is its productivity divided by the whole productivity of the main shock. Also we apply histETAS model to North China Craton. It turns out that the b value and background seismicity patterns coincide with the static coulomb stress change induced by historical big earthquakes, and p value variation in space is in agreement with velocity structure of the lithosphere under major fault zones. Therefore we infer the statistical characteristics of seismicity reflect the properties of medium to some extent, and make some discussion of future earthquake hazard.

 

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講演者:尾形 良彦 (統計数理研究所 名誉教授/東京大学地震研究所 地震火山情報センター ・特任研究員

日 時: 2016 3 22() 17:00 -18:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: 3D spatial models for seismicity beneath Kanto region

 

Abstract: 

Development of point-process models for the seismicity in 3D space (longitude, latitude and depth) beneath Kanto area down to 100km depth is more required than for seismicity in the rest of the world. This is because the three tectonic plates meet beneath Kanto plain; and interactions among the interplate and intraplate earthquakes are too complex to make detailed analysis and forecasts in 2D space that ignores the depths.

 

We consider the 3D hierarchical space-time ETAS (epidemic-type aftershock sequence) model. Among the characterizing parameters, the background seismicity rate \mu and aftershock productivity K are highly sensitive to the locations, so that these parameters should be location-dependent. Furthermore, the impact of the 2011 Tohoku-Oki earthquake of M9.0 to the seismicity beneath the Kanto region has been so large that we need a space-time function for representing the amount of the induced seismicity beneath Kanto by this giant earthquake. Specifically, we adopt the Omori-Utsu function as the effect of induced earthquakes, started after the occurrence time of the Tohoku-Oki earthquake, where we assume that the aftershock productivity parameter KM9 of the Omori-Utsu function is also location-dependent. For forecasting future large earthquakes, we further need to estimate the location-dependent b-value of the Gutenberg-Richter law.

 

The spatial variations of the characteristic parameters \mu(x,y,z), K(x,y,z) , KM9(x,y,z) and b(x,y,z) of our model are inverted to visualize the regional changes of the seismic activity. For this objective, we make 3D Delaunay tessellation of the Kanto volume, where every earthquake belongs to vertices of a tetrahedron. Each of the above mentioned parameter function is a 3-dimensional piecewise linear function defined by the values at the four Delaunay tetrahedral vertices.

 

The estimates of the focal parameter functions are obtained by an optimal trade-off between the goodness of fit to the earthquake data and the smoothness constraints (or roughness penalties) of the variations of parameter values. Strengths of the constraints of or the penalties to respective parameter functions can be simultaneously adjusted from the data by means of an empirical Bayesian method using the Akaike’s Bayesian information criterion (ABIC).

 

Key words: ABIC, aftershock productivity, background seismicity rate, b-values, Delaunay function, Delaunay tessellation, empirical Bayesian method, Omori-Utsu function for induced seismicity, penalized log-likelihood.

 

54

講演者: Dr. 婷(Wang, Ting Department of Mathematics and Statistics, University of Otago, New Zealand Lecturer

日 時: 2016 2 9() 16:00 -17:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Identification of seismic phases using Markov-modulated marked Hawkes processes

 

Abstract: 

Based on a temporal Markov-modulated Hawkes process that we developed earlier to investigate long-term patterns of seismic activity with multiple mainshocks, we made extensions to this temporal model to include spatial variation of the seismic activity and the earthquake magnitudes. Our aim is to categorize spatiotemporal seismic hazards holistically, using the entire earthquake record in a selected region to identify patterns correlated with subsequent large earthquakes, rather than the traditional way of selecting individual foreshock-mainshock or mainshock-aftershock sequences. I will use several case studies to illustrate how this model works and discuss about the problems that we had with the model fitting.

 

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講演者: Dr. Yin, Fengling (中国地震局 地球物理研究所・助理研究員(助教相当)

日 時: 2016 1 27() 13:30 -14:30

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Coulomb stress evolution along the middle segment of Redriver fault zone over the past 180 Years due to coseismic, postseismic and interseismic deformation Yin,Fengling, Jiang, Changsheng and Han, Libo

 

Abstract: 

The Redriver fault zone, for it being as the boundary of Sichuan-Yunnan rhombic block and southeastern margin of the Tibetan plateau, and near the Central Yunnan city group, its seismic activity deserves attention. The Redriver fault zone within Yunnan has experienced at least 9 earthquakes of M≥6 in recent 180 years. Using stratified viscoelastic lithospheric model, we calculate the coulomb failure stress evolution along the redriver fault zone over the past 180 years due to coseismic, postseismic and interseismic deformation. By analyzing 25 earthquakes occurred along the Redriver fault zone and ajacent faults, we find that the middle segment of Redriver fault zone remains low seismic activity in recent two hundred years. This is consistent with the observed ‘seismic gap’ as earthquake catalog shows. Assuming there is no earthquake within about 30 years around the Redriver fault zone, this ’seismic gap’ may remain due to postseismic and interseismic deformation.

 

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講演者: Dr. Taroni, Matteo Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy Post-doctoral fellow

日 時: 2016 1 27() 14:30 -15:30

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Some recent techniques to improve earthquake forecasting (Taroni, Matteo, Marzocchi, Warner, Zechar, Jeremy and Werner, Maximilian)

 

Abstract: 

In this presentation I will show some recent results regarding the earthquake forecasting techniques. In particular I will show:

i) How to consider aftershocks and foreshocks in the seismic hazard computation, with an application to the Italian case.

ii) How to merge different catalogues to obtain a better estimation of the Tapered Gutenberg-Richter distribution parameters, with an application to the global and Italian case.

iii) How to create an ensemble model to improve the performance of the short-term earthquake forecasting models, with an application to the New Zealand case.

 

52

講演者: Dr. Guillas, Serge Department of Statistical Science, University College London, U.K. Reader/東京大学地震研究所・特任准教授) 

日 時: 2015 11 17() 16:00 -17:00

場 所: 統計数理研究所 A508セミナー室6

 

Title: Dimension reduction for the quantification of uncertainties in tsunami and climate models

 

Abstract: 

VOLNA, a nonlinear shallow water equations solver, produces high resolution simulations of earthquake-generated tsunamis. However, the uncertainties in the bathymetry (from irregularly-spaced observations) have an impact on tsunami waves. We first employ a stochastic partial differential equation (SPDE) approach to quantify uncertainties in these boundary fields. These uncertainties are then parametrized to be used as inputs of an emulator of VOLNA. However, the dimension of these boundary fields is large and must be reduced. We apply the gradient-based kernel dimension reduction approach (gKDR) by Fukumizu and Leng (2014) and construct an Gaussian Process emulator on this reduced input space. We propagate uncertainties in the bathymetry to obtain an improved probabilistic assessment of tsunami hazard.

In a separate climate application, we employ the Bayesian calibration of complex computer models using Gaussian Processes, introduced by Kennedy and O'Hagan (2001), that has proven to be effective in a wide range of applications. However, the size of the outputs, such as climate models' spherical outputs, leads to computational challenges in implementing this framework. Covariance models for data distributed on the sphere also present additional challenges compared to covariance models for data distributed over an Euclidean space. To overcome these various challenges, we make use of the spherical harmonics (SHs) decomposition of the computer model output, and then apply a Gaussian process assumption to the coefficients in the decomposition. Furthermore, using the SPDE approach, we can capture non-stationarity in the spatial process. Hence, we generalize further the spherical correlation framework by expanding the SPDE parameters used to quantify the nonstationary behavior in the functional space spanned by the SHs. We illustrate our findings on several synthetic examples. In particular, our method can outperform the calibration based on principal components. Finally we show that our technique has the potential to calibrate the Whole Atmosphere Community Climate Model (WACCM).

 

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講演者: Dr. Gerstenberger, Matthew GNS Science, New Zealand Risk and Engineering Team Leader, Senior Seismologist

日 時: 2015 9 1() 16:00 -17:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: The New Zealand National Seismic Hazard Model: Rethinking PSHA

 

Abstract: 

We are currently revising the New Zealand National Seismic Hazard Model. In this revision we are exploring some of the fundamental assumptions of the model and investigating how uncertainties in earthquake source and ground motion estimation propagate through to the end uses of the model. Uncertainties related to the source modelling that come from a paucity of data and from different methods that can be used to model the seismic sources are currently not fully quantified in the way we model seismic hazard. Additionally, seismic sources are generally assumed to be a stationary Poisson process and earthquake clustering is ignored. Including these uncertainties in the way risk is modelled based on the outputs of the National Seismic Hazard Model will likely lead to more robust estimates of risk for use by industry and in the development of design standards.

 

Notice: This email and any attachments are confidential. If received in error please destroy and immediately notify us. Do not copy or disclose the contents. 

 

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講演者: Dr. 石(Chen, Shi (中国地震局地球物理研究所・准教授)

日 時: 2015 9 1() 17:00 -18:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: A study on the regional gravity changes before large earthquakes from the statistical perspectives

 

Abstract: 

The repeated gravity surveys, also called mobile gravity measurements, have been carried out for decades in the Chinese mainland. Significant gravity changes have been detected before some cases of great earthquakes, such as the 1976 Tangshan Ms7.8 Earthquake, 2008 Wenchuan Ms8.0 earthquake, etc. The main aim of the repeated gravity surveys is to monitor the geophysical field variations in some major seismic hazard zones. By this sort of in-situ gravimetric network, the yearly changes of regional gravity can be obtained. Through the Molchan Error Diagram tests, we found that observed gravity changes are statistically correlated to the occurrence of future large earthquakes, i.e., the gravity changes are more powerful than a seismicity rate model in forecasting large earthquakes. These results imply that gravity changes before earthquake include precursory information of future large earthquakes.

 

Key words: Gravity changes, Earthquake prediction, Molchan error diagram, Repeated gravity measurement, Chinese mainland.

 

50

講演者: Dr. Kagan, Yan Y. Department of Earth and Space Sciences, University of California, Los Angeles (UCLA), U.S.A. Researcher

日 時: 2015 8 4() 16:00 -18:00

場 所: 統計数理研究所 D208会議室2

 

Title: Statistics of earthquake focal mechanisms

 

Abstract: 

I. Double-couple earthquake source: symmetry and rotation

 

We analyze earthquake focal mechanisms and their forecast both analytically and statistically. This problem is complex because source mechanisms are tensor-valued variables, thus their analysis requires applying sophisticated mathematical and statistical tools, many of which are not yet fully developed. We describe general and statistical properties of the seismic moment tensor, in particular, its most important form -- the double-couple (DC) mechanism. We establish a method for the analysis of a DC source, based on the quaternion technique, and then apply quaternions for the statistical analysis of earthquake catalogs. The important property of the focal mechanism is its symmetry. We describe the classification of the mechanism symmetry and the dependence of the DC orientation on its symmetry. Four rotations exist in a general case of a DC with the nodal-plane ambiguity, there are two transformations if the fault plane is known, and there is one rotation if the sides of the fault plane are known. A statistical analysis of symmetrical objects has long been the subject of crystallographic texture investigations. We describe the application of crystallographic methods to focal mechanism analysis and consider theoretical statistical distributions appropriate for the DC orientation approximation. Uniform random rotation distributions for various DC sources are discussed, as well as two non-uniform distributions: the rotational Cauchy and von Mises-Fisher. We discuss how the parameters of these rotations can be estimated by a statistical analysis of earthquake source properties in global seismicity using the GCMT catalog. We also show how earthquake focal mechanism orientations can be displayed on the Rodrigues vector space.

 

II. Statistical earthquake focal mechanism forecasts

 

In the focal mechanism forecast, the sum of normalized seismic moment tensors within a 1000 km radius is calculated and the P- and T-axes for the predicted focal mechanism are evaluated on the basis of the sum (Kagan and Jackson 1994, JGR). Simultaneously we calculate an average rotation angle between the forecasted mechanism and all the surrounding mechanisms. This average angle shows tectonic complexity of a region and indicates the accuracy of the prediction. Recent interest by CSEP and GEM has motivated some improvements, particularly a desire to extend the previous forecast to polar and near-polar regions. The major problem in extending the forecast is the focal mechanism calculation on a spherical surface. In a modified program focal mechanisms have been projected on a plane tangent to a sphere at a forecast point. A comparison with the old 75S-75N forecast shows that in equatorial regions the forecasted focal mechanisms are almost the same, and the difference in the forecasted focal mechanisms rotation angle is close to zero. However, closer to the 75 latitude degree the difference in the rotation angle is large (around a factor 1.5 in some places). The Gamma-index was calculated for the average focal mechanism moment. A non-zero Index indicates that earthquake focal mechanisms around the forecast point have different orientations. Thus deformation complexity displays itself both in the average rotation angle and in the Index. However, sometimes the rotation angle is close to zero, whereas the Index is large, testifying to a large CLVD presence. Both new 0.5x0.5 and 0.1x0.1 degree forecasts are posted at http://eq.ess.ucla.edu/~kagan/glob_gcmt_index.html

 

III. Evaluating focal mechanisms forecast skill

 

We discuss the ways to test the focal mechanism forecast efficiency. We start with several verification methods, first based on ad-hoc, empirical assumptions. However their performance is questionable. In the new work we apply a conventional likelihood method to measure the skill of a forecast. The advantage of such an approach is that an earthquake rate prediction can be adequately combined with a focal mechanism forecast, if both are based on the likelihood scores. This results in a general forecast optimization. To calculate the likelihood score we need to compare actual forecasts or occurrences of predicted events with the null hypothesis that the mechanism's 3-D orientation is random. To better understand the resulting complexities we calculate the information (likelihood) score for two rotational distributions (Cauchy and von Mises-Fisher), which are used to approximate earthquake source orientation patterns. We then calculate the likelihood score for earthquake source forecasts and for their validation by future seismicity data. Several issues need to be explored when analyzing observational results: their dependence on the forecast and data resolution, internal dependence of scores on the forecasted angle, and random variability of likelihood scores. We propose a preliminary solution to these complex problems, as these issues need to be explored by a more extensive theoretical and statistical analysis.

 

IV. Future focal mechanisms studies

 

1. Statistical earthquake focal mechanism forecasts, rigorous    likelihood methods for evaluating forecast skill.

2. Likelihood analysis of GCMT catalog, including focal mechanisms.

3. Focal mechanism clustering.

4. Collapsing focal mechanism patterns.

5. Influence of Earth surface on focal  mechanisms interaction (Morawiec,Ch8).

6. Integrating Cauchy distribution on Rodrigues space, Morawiec, pp.116-119.

7. Calculating Cauchy and von Mises-Fisher distributions for 120 degrees rotation limit.

8. Investigating the sign-change symmetry of a DC earthquake source.

9. Studies of statistics of earthquake focal mechanisms in the Rodrigues space.

10. Rotation-translation distribution of double-couples as different from arbitrary symmetric deviatoric second-rank tensor. 

 

49

講演者: Prof. Künsch, Hans R. Department of Mathematics, ETH Zurich, Switzerland Emeritus Professor

日 時: 2015 4 7() 16:00 -17:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Data assimilation in seismology ?

 

Abstract: 

The accuracy of weather forecasts has increased substantially over the past decades. This is due to at least three factors: The increase in computing power which allows a higher accuracy in solving the equations of the underlying physical model, a denser set of observations of the state of the atmosphere and better methods for data assimilation, that is the use of these observations to adjust the initial conditions of the model sequentially. In order to represent the uncertainty in assimilation and forecasting, ensembles are used whose members represent different states of the atmosphere that are compatible with the observations and the physical dynamics. Such ensemble methods should be viewed as Monte Carlo methods which provide the link to statistics.

 

Recently there has been interest in using these data assimilation tools also in seismology in order to improve forecasts and quantify their uncertainty. In this talk I will discuss some of the attempts in this direction. Time permitting, I will also present some new ideas for ensemble data assimilation. 

 

48

講演者: 石辺 岳男 (東京大学地震研究所 地震火山情報センター ・特任研究員)

日 時: 2015 2 24() 16:00 -17:00

場 所: 統計数理研究所 A508セミナー室6

 

Title: Overview of Seismicity Changes in Inland Japan after the 2011 Tohoku-Oki Earthquake and Its Interpretation

 

Abstract: 

In this presentation, I overview the widespread changes in seismicity rate and distribution of focal mechanism after the Tohoku-Oki earthquake (Mw9.0) and summarize the possible contributing factors. In Tohoku, westward from the Tohoku-Oki source, significant increases in seismicity rate were observed in N. and S. Akita, SW off Oga peninsula, and Yamagata/Fukushima and Ibaraki/Fukushima boundary regions as well as other surrounding areas. On the other hand, aftershock activities in the source regions of recent large earthquakes such as the 2008 Iwate-Miyagi earthquake have been suppressed. In Kanto, southwest of the Tohoku-Oki source, interplate earthquakes were typically activated, while belt-like seismicity along the western edge of slab-slab contact zone and shallow earthquakes in some areas were also activated.

 

The most plausible factor is the static changes in the Coulomb stress, which seems to be valid for retrospectively forecasting the changes in seismicity on some level, while some activated seismicity showed clear counter-evidence. Remotely triggered local events, whose origin times are well coincided with the arrivals of mainshock seismic waves, suggest that dynamic stress changes also contribute. Some swarm-like activities, showing temporal expansion of the focal area which is attributed to fluid diffusion, suggest that changes in pore fluid pressure should be another possible factor. The contribution of indirectly triggered earthquakes might be important in some regions because stress changes imparted by neighboring indirect aftershocks could be comparable with those from a distant mainshock. Postseisimc slip and viscoelastic effect would play an important role for long-term hazard assessments.

 

47

講演者: Dr. Segou, Margaret National observatory of Athens, Greece Researcher

日 時: 2015 2 10() 16:00 -17:00

場 所: 統計数理研究所 4階ラウンジ

 

Title: The Future of Earthquake Predictability

 

Abstract: 

The last decade dense seismological networks around the world provide the opportunity to study more aftershock sequences in seismically active areas across the world such as California (San Andreas Fault), Japan, New Zealand (Canterbury Fault, Christchurch) and continental rift systems (Corinth Gulf, Greece). The importance behind that is evident; the 2008 M7.9 Sichuan event continues having catastrophic aftershocks (2013 Lushan M6.6) after five years. The above provide the necessary motivation for geophysicists to develop short and long-term earthquake forecasts for providing to scientists and the public authoritative information on seismic hazard and answer ultimately the question When the next big earthquake will occur. Static and dynamic triggering are often described as the two primary mechanisms for earthquake clustering in time and space. Recent studies have provided evidence that physics-based earthquake forecast models, combining fault aging laws and the static stress triggering hypothesis, can accurately predict (80%) transient seismicity rates. Static triggering plays an important role in spatial clustering at distances 2-3 rupture lengths away from the seismic source whereas dynamic triggering studies usually focus on larger distances (>1000 km). But how dependent are our calculations on our incomplete knowledge of the ambient stress of a region? What are the implications behind the time dependent fault behavior? The last two questions are the key for reducing the uncertainties of physical forecast models. Quite often the development of such quantitative and testable models is followed by extensive statistical performance evaluation, which is critical for understanding their merits and pitfalls.

 

In this seminar I focus on recent development on physics-based earthquake models using worldwide examples and how they compare with statistical models. Furthermore, I discuss how we can reduce their uncertainties and sketch the future of our scientific predictability. Is it possible to hope on higher information gains in the near future? and, How these forecast models could be most effective in Japan? 

 

 

46

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講演者: 熊澤 貴雄 (統計数理研究所 リスク解析戦略研究センター 地震予測解析プロジェクト ・特任研究員)

日 時: 2015 1 27() 15:00 -16:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Predicting Offshore Swarm Rate by Volumetric Strain Changes in Izu Peninsula, Japan

 

Abstract: 

The eastern offshore of Izu peninsula is one of the well known volcanic active regions in Japan, where magma intrusions have been observed several times since 1980s monitored by strain-meters located nearby. Major swarm activities have been synchronously associated with coseismic and preseismic significant sizes of volumetric strain changes (Earthquake Research Committee, 2010).  We investigated the background seismicity changes during these earthquake swarms using the nonstationary ETAS model (Kumazawa and Ogata, 2013, 2014), and have found the followings. The volumetric strain change data, modified by removing the effect of earth tides and precipitation as well as removing coseismic jumps, have much higher cross-correlations to the background rates of the ETAS model than to the whole seismicity rate change of the ETAS. Furthermore the strain changes precede the background seismicity by lag of about half a day. This relation suggests an enhanced prediction of earthquakes in this region using volumetric strain measurements. Thus we propose an extended ETAS model where the background seismicity rate is predicted by the time series of preceding volumetric strain changes. Our numerical results for Izu region show consistent outcomes throughout the major swarms.

 

-2

講演者: Dr. 婷(Wang, Ting Department of Mathematics and Statistics, University of Otago, New Zealand Lecturer

日 時: 2015 1 27() 16:30 -17:30

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Marked point process modeling with missing data in volcanic eruption records

 

Abstract: 

Despite ongoing efforts to compile new data, eruption records, particularly those of earlier time periods, are pervasively incomplete. The probability of missing an ancient eruption is much higher than a recent eruption. We consider modeling both the times and sizes of the eruptions using a marked point process. We propose to model the marks (the sizes of the events) as having a time-varying distribution which takes the higher proportion of missing smaller events in earlier records into consideration. We then estimate the proportion of detected events over time based on the assumption that the most recent record is complete and that the record of eruptions with the largest size in the considered catalog is complete. With this information, we can then estimate the true intensity of volcanic eruptions.

 

45

講演者: Dr. Schehr, Grégory Laboratoire de Physique Théorique et Modèles Statistiques, Orsay-University Paris-Sud, France
CNRS-Researcher

日 時: 2014 10 14() 11:00 -12:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Exact Statistics of the Gap and Time Interval Between the First Two Maxima of Random Walks and Lévy Flights

 

Abstract (PDF)

 

 

44

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講演者: Prof. 周 仕勇 (Zhou, Shiyong) (北京大学 地球空間科学学院 ・教授)

日 時: 2014 8 5() 16:00 -17:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Seismicity simulation in Western Sichuan of China based on the fault interactions and its implication on the estimation of the regional earthquake risk

 

Abstract: 

Seismicity over 10000 years in Western Sichuan of China has been simulated based on the mechanical synthetic seismicity model we developed. According to the analysis of the simulated synthetic seismic catalogue , the occurrence of strong earthquakes with Ms ≥710 in the whole region of Western Sichuan is rather random , very close to the Poisson process with seismic rate 010454Pyear , which means it is reasonable to estimate the regional earthquake risk with Poisson model in Western Sichuan. However, the occurrence of strong earthquakes with Ms ≥710 on the individual faults of Western Sichuan is far from Poisson

process and could be predicted with a time2dependent prediction model. The fault interaction matrices and earthquake transfer possibility matrices among the faults in Western Sichuan have been calculated based on the analysis of the simulated synthetic catalogues. We have also calculated the static change in Coulomb failure stress (CFS) on one fault induced by a strong earthquake on another fault in Western Sichuan to discuss the physical implications of the earthquake transfer possibility matrices inferred from the synthetic catalogue.

 

Keywords: Simulation of earthquake generation , Poisson model , Coulomb stress , Seismic hazard

 

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講演者: Dr. (Wang, Dun) (東京大学地震研究所/日本学術振興会 特別研究員)

日 時: 2014 8 5() 17:00 -18:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Rupture speeds for recent large earthquakes

 

Abstract: 

Studying the rupture speeds of earthquakes is of broad interesting for earthquake research because it has a large effect on the strong near-field shaking that causes damage during earthquakes. Also rupture speed is a key observation for understanding the controlling stresses and friction during an earthquake, yet the speed and its variations are usually difficult to determine. Using only far-field seismic waveforms, which is the only data available for many large earthquakes, there are problems for estimating the rupture speed with standard waveform inversions, due to trade-off between the rupture speed and the slip location.

 

Here we applied a back projection method to estimate the rupture speeds of Mw ≥ 7.5 strike-slip earthquakes since 2001 which could be analyzed using Hi-net in Japan. We found that all events had very fast average rupture speeds of 3.0-6.0 km/s, which are near or greater than the local shear wave velocity (supershear). These values are faster than for thrust and normal faulting earthquakes that generally rupture with speeds of 1.0-3.0 km/s. Considering the depth-dependent shear-wave velocity, the average propagation speeds for all of the strike-slip events are closer to or greater than the shear wave velocity. For large strike-slip events, transition from subshear to supershear usually occurs within distances of 15 to 30 km from the initiation, which is probably the reason for the scarcity of observed supershear earthquakes for smaller magnitudes.

 

Earthquakes with supershear ruptures can cause more damage than events with subshear ruptures because of the concentration of energy in the forward direction of the rupture. Numerical modeling shows strong focusing and other effects of energy at the rupture front which can intensify the ground motions. A recent example is the April 13, 2010 Qinghai, China earthquake (Mw 6.9), where a moderate-size event caused extensive damage in the Yushu region at the southeastern end of the fault. Careful evaluation of long and straight strike-slip faults should be emphasized for predicting strong ground motions due to supershear rupture.

 

43

講演者: Dr. Aiken, Chastity Georgia Institute of Technology, U.S.A. National Science Foundation Graduate Fellow, ARCS Scholar

日 時: 2014 7 8() 16:00 -18:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Triggered Seismic Activity in Geothermal Regions and on Strike-Slip Faults

 

Abstract: 

Dynamic stresses caused by large earthquakes are capable of triggering a wide range of seismic/aseismic responses at remote distances.  These responses include instantaneously triggered microearthquakes, deep tectonic tremor, earthquake swarms, slow-slip events, and near-surface icequakes.  Systematic studies of these triggered phenomena not only help us to understand how large earthquakes affect seismic/aseismic processes at remote distances but also help improve our understanding of the necessary physical conditions responsible for the generation of seismic activity.  In this talk I present two recent studies:  (1) a comparison of triggered microearthquakes in three geothermal regions of California and (2) a comparison of triggered tremor on four strike-slip faults in the Western Hemisphere.  Triggered seismic activity is characterized as being triggered by the surface waves of large, distant earthquakes.  Triggered earthquakes in geothermal regions are generally small magnitude (M<4) and have distinct P and S waves, whereas triggered tremor is a low-amplitude, emergent signal with no distinct P wave.  After identifying the large earthquakes that trigger seismic activity, we analyze and compare the peak ground velocities, seismic wave incidence angles, amplitude spectra of all distant earthquakes we examined, as well as the background activity in each region to determine the factors that promote triggering in geothermal regions and on strike-slip faults.

 

42

講演者: Dr. Aranha, Claus (筑波大学大学院システム情報工学研究科 助教

日 時: 2014 5 27() 16:00 -17:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Using Evolutionary Algorithms to optimize earthquake risk models: Early Ideas

 

Abstract: 

Evolutionary Algorithms are a class of meta-heuristics that use genetic principles to sample good solutions from a search space. They have shown great promise in a wide variety of optimization problems, specially in problem domains where the search space is multi modal and/or non-continuous. However, evolutionary algorithms have not yet seen a lot of use in the optimization of statistical models for earthquake forecasting. Our goal is to explore this combination.

 

In this talk, we will (briefly) explain what evolutionary algorithms are, and then proceed to outline our early proposals and results regarding their use for the generation of an RELM based earthquake forecast model.

 

41

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講演者: Dr. 敏真(Wang, Min-Zhen (統計数理研究所 リスク解析戦略研究センター 特任研究員)

日 時: 2014 3 4() 15:00 -16:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Distributions on Torus, Cylinder and Disc  Wang, Min-Zhen and Shimizu, Kunio

 

Abstract: 

Statistics for data which include angular observations is known as directional statistics. Bivariate circular data such as wind directions measured at two points in time are modeled by using bivariate circular distributions or distributions on the torus. Likewise circular-linear data are modeled by using distributions on the cylinder and disc. We propose some extensions of distributions on the torus, cylinder and disc in the framework of directional statistics. A new circular distribution (Wang and Shimizu, 2012) is also introduced, which is obtained by applying the Mӧbius transformation to a univariate cardioid random variable. The distribution function, trigonometric moments, and conditions for unimodality and symmetry are studied. Kato and Jones (2010) study a family of distributions which is obtained by applying the Mӧbius transformation to a von Mises random variable, and we discuss the relationship between our model and the Kato--Jones model. The bivariate circular case (Wang and Shimizu, 2012) which is generated from a circular-circular structural model linked with Mӧbius transformation or a method of trivariate reduction. The joint probability density function, trigonometric moments and circular-circular correlation coefficient are explicitly expressed. An illustration is given for wind direction data at 6 a.m. and noon as an application of the bivariate cardioid distribution. The distributions on the cylinder we proposed is generated from a combination of von Mises and transformed Kumaraswamy distributions. It is an extension of the Johnson and Wehrly (1978) model.

   The marginal and conditional distributions of the proposed distribution are given. A distribution using the method of generating a cylindrical distribution with specified marginals is also proposed. We generate skew or asymmetric distributions on the disc by using the Mӧbius transformation and modified Mӧbius transformations as extensions of the Mӧbius distribution proposed by Jones (2004). The new distributions called the modified Mӧbius distributions have six parameters. They can be reduced to the Mӧbius and uniform distributions as special cases, but many members of the family are skew distributions for both the linear and the angular random variables. Some properties such as the joint probability and marginal density functions of the proposed distributions are obtained.

 

References:

[1] Johnson, R. A. and Wehrly, T. E. (1978). Some angular-linear distributions and related regression models. Journal of the American Statistical Association, 73, 602–606.

[2] Jones, M. C. (2004). The Mӧbius distribution on the disc. Annals of the Institute of Statistical Mathematics, 56, 733–742.

[3] Kato, S. and Jones, M. C. (2010). A family of distributions on the circle with links to, and applications arising from, Mӧbius transformation. Journal of the American Statistical Association, 105, 249–262.

[4] Wang, M.-Z. and Shimizu, K. (2012). On applying Mӧbius transformation to cardioid random variables. Statistical Methodology, 9, 604–614.

 

-2

講演者: Dr. Llenos, Andrea L. US Geological Survey, Earthquake Science Center  Postdoctoral

日 時: 2014 3 4() 16:30 -17:30

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Statistical modeling and identification of potentially induced seismicity rate changes

 

Abstract: 

TBA  

 

40

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講演者: Dr. Varini, Elisa Institute of Applied Mathematics and Information Technology, National Research Council (IMATI-CNR), Italy
Professional Researcher

日 時: 2014 2 18() 15:00 -16:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Bayesian estimation of doubly stochastic Poisson processes: a particle filtering approach

 

Abstract: 

TBA  

 

-2

講演者: Dr. Harte, David GNS Science, New Zealand  Statistical Seismologist and Hazard Modeller

日 時: 2014 2 18() 16:30 -17:30

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Stochastic Earthquake Models: Ways to Improve and Insights into the Physical Process

 

Abstract: 

1.  Bayesian estimation of doubly stochastic Poisson processes: a particle filtering approach

We aim to explore the hypothesis that the earthquakes of a seismic region occur under different physical conditions, corresponding to as many seismicity phases characterized by different occurrence rates.

This hypothesis can be modeled by doubly stochastic Poisson processes in which the observed process of the occurrence times of the earthquakes is a point process whose conditional intensity function is assumed to be dependent on both the past history and the current hidden state.

By assuming some of the possible choices for the observed point process and the hidden state process, a Bayesian analysis is carried out in which the likelihood function is approximated by the particle filtering method.

 

2.  Stochastic Earthquake Models: Ways to Improve and Insights into the Physical Process

We present a version of the ETAS model where the offspring rates vary both spatially and temporally. This is in response to deficiencies discussed in [1]. This is achieved by distinguishing between those space-time volumes where the interpoint space-time distances are small, and those where they are considerably larger. In the process of modifying a stochastic earthquake model, one needs to justify assumptions made, and these in turn raise questions about the nature of the underlying physical process. We will use this version of the ETAS model as the basis for our discussion, and by focussing on aspects where the model does not perform so well, attempt to find physical explanations for such lack of fit. Some possible discussion points are as follows.

 

What is the nature of the so called background process in the ETAS model? Is it simply a temporal boundary (t=0) correction or does it represent an additional tectonic process not described by the aftershock component? Or are these two alternatives on completely different time scales?

 

An epidemic (the basic analogy underpinning the ETAS model), or a living organism, can evolve by reproducing offspring that are slightly different to that of their parents - randomness or gene mutation. Certain "modified" individuals will be able to adapt to the environment better and tend to survive over others. In the ETAS context, a lower value of $\alpha$ will cause more "generations" in the aftershock sequence. This allows for a richer and more complex evolution of the process, both spatially and temporally. Alternatively, if alpha is large, then more of the aftershocks are direct offspring of the mainshock. In the epidemic context, this implies that the mainshock contains much more of the "DNA" which governs the evolution of the overall sequence.

 

What is the relationship between fractal dimension and clustering? Does the fractal dimension provide a better discrimination between those space-time volumes with higher offspring rates and the others? If so, does the fractal dimension provide a more obvious physical description of the difference between these high rate volumes and the lower rate volumes, and hence a suggestive physical explanation?

 

[1] Harte, D.S. (2013). Bias in Fitting the ETAS Model: A Case Study Based on New Zealand Seismicity. Geophys. J. Int. 192(1), 390-412.

 

39

-1

講演者: 松浦 充宏 (統計数理研究所 リスク解析戦略研究センター 地震予測解析プロジェクト 外来研究員)

日 時: 2014 1 14() 13:00 -14:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Inversion of GPS Data using ABIC

 

Abstract: 

To monitor crustal movements of the Japanese Islands, a nation-wide dense GPS network (GEONET) has been operated by Geographical Survey Institute of Japan (now Geospatial Information Authority of Japan) since 1996. We developed an inversion method to estimate unbiased interseismic slip-deficit rates at plate interfaces from GPS displacement rate (velocity) data with an elastic dislocation model. In this method, first, we subtract theoretical surface velocities due to known steady relative plate motion from the observed GPS data, and presume the residuals to be caused by slip deficit at plate interfaces. However, the observed GPS data always include rigid block translation and rotation, which cannot be explained by the elastic dislocation model. We treated the rigid block translation and rotation as systematic errors in the analysis, and removed them by transforming the velocity data into the average strain rates of triangle elements composed of adjacent GPS stations. By this transformation, original information about intrinsic deformation is preserved. Applying a general inversion formula using ABIC to the GPS strain data, we can obtain unbiased slip-deficit rate distribution. We demonstrate the applicability of the GPS strain data inversion method through the analyses of coseismic and interseismic GPS data in the Japan region, where the North American, Pacific, Philippine Sea, and Eurasian plates are interacting with each other in a complicated way.

 

-2

講演者: Prof. 周 仕勇 (Zhou, Shiyong) (北京大学 地球空間科学学院 ・教授)

日 時: 2014 1 14() 14:10 -15:10

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Detecting the regional tectonic stress variations in background seismicity data through statistical earthquake modeling

            Yajun Peng, Shiyong Zhou, Jiancang Zhuang and Jia Shi

 

Abstract: 

Large earthquakes could perturb the stress field in regions even thousands of kilometers away, leading to abrupt changes in background seismicity. We have developed a probability based approach, based on the epidemic-type aftershock sequence model and the stochastic declustering method, to invert the smoothed temporal variation of background seismicity rate and to extract useful physical signals from complex seismicity patterns. An iterative algorithm is constructed to estimate the background seismicity simultaneously by using a combination of maximum likelihood estimate and weighted variable kernel estimate. We verify this approach through simulations and confirm that it can sensitively recover the onset of dynamic triggering.

The algorithm is applied to an earthquake catalog in Yunnan Province, China, and successfully identifies a rapid increment of background seismicity rate following the occurrence of the 2004 Sumatra Mw 9.2 earthquake, whereas no remote triggering effect is detected following the occurrence of the 2005 Sumatra Mw 8.7 earthquake. This phenomenon agrees with GPS observations. It is found that the elevated seismic activity within 15 d after the Sumatra earthquake is mostly composed by shallow events, and direct triggering relationship is well established.

We also studied the possible dynamic triggering effect in Northern China, including Tangshan area, when the Japan Tohoku Mw 9.0 earthquake happened at March 11th, 2011 and found out whether the area with large co-seismic displacement would have sudden abnormal seismicity increase. As a result, the Japan Tohoku earthquake has little effect on the total and background seismicity of Tangshan area, which means that the seismic structure of Tangshan area is fundamentally stable.

 

-3

講演者: Dr. 婷(Wang, Ting University of Otago, New Zealand ・助教)

日 時: 2014 1 14() 15:30 -16:30

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Estimating the likelihood of volcanic eruptions with incomplete eruption record

 

Abstract: 

TBA 

 

-4

講演者: 尾形 良彦 (統計数理研究所 名誉教授/東京大学・客員教授)

日 時: 2014 1 14() 16:40 -17:40

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Foreshocks and short-term forecasting: comparisons between in real seismicity and synthetic catalogs

            Yosihiko Ogata and Koichi Katsura

 

Abstract: 

Some statistical characteristics of foreshocks in the JMA earthquake catalog are quantitatively different from those in the catalogs simulated by the space-time epidemic-type aftershock sequence (ETAS) model associated with the Gutenberg-Richter (GR) law. Also, the information gain of a foreshock probability forecasting in the real seismicity is significantly large in comparison with in synthetic catalogs.

 

38

講演者: Prof. 清華(Huang, Qinghua (北京大学 理論応用地球物理研究所・教授)

日 時: 2013 11 12() 16:00 -17:00

場 所: 統計数理研究所 A508セミナー室6

 

Title: Seismicity changes revealed by the Region-Time-Length (RTL) algorithm

 

Abstract: 

The Region-Time-Length (RTL) algorithm, which takes into account the epicenter, time, and magnitude of earthquakes, is an effective technique in detecting seismicity changes, especially the seismic quiescence. Based on the RTL algorithm and the Q-parameter (an average RTL parameter over a certain time window), we can quantify the spatio-temporal characteristics of seismicity changes. In order to reduce the possible ambiguity due to the selection of model parameters in the RTL algorithm, we proposed an improved technique of searching for the optimal model parameters. The applications of the RTL algorithm in various tectonic regions indicated that seismic quiescence anomalies generally started a few years prior to the occurrence of the mainshock. The linear dimension of the seismic quiescence zone could be a few to several times of the rupture dimension of the mainshock. The significance of the seismic quiescence anomalies revealed by the RTL algorithm was supported by the close investigations of model parameter effects and the stochastic test based on randomized earthquake catalogs.

 

37

講演者: Herrmann, Marcus ETH Zurich (チューリッヒ工科大学・スイス), Swiss Seismological Servise 博士後期課程(大学院生)

日 時: 2013 8 27() 16:00 -17:00

場 所: 統計数理研究所 D312Aセミナー室3

 

Title: Forecasting Losses Caused by a M6.6 Scenario Earthquake Sequence in Basel, Switzerland

 

Abstract: 

When people and their environment are not properly prepared, earthquakes pose a serious threat. Recently, the SEISMO-12 earthquake scenario exercise simulated the repeat of the 1356 Basel earthquake. This gave officials, organizations, and the general public an idea of what may be expected in case of a M6.6 earthquake. The present work relates to the scenario and contributes to loss reduction by expressing the potential impact through seismic risk. Reducing the short-term seismic risk requires the evacuation of vulnerable buildings. However, one cannot always evacuate in times of an ongoing seismic sequence. Based on information of the continuous seismicity, probabilistic forecasts show increasing benefit for short-term defense against earthquakes. Forecast probabilities subsequently allow time-varying seismic hazard calculation. Only another combination with time-invariant loss estimation permits the assessment of short-term seismic risk. Seismic risk delivers a more direct expression of the socio-economic impact than seismic hazard, but one must characterize vulnerability and exposure to estimate risk. Risk assessment brings together a variety of data, models and assumptions. Based on the specific earthquake scenario, I perform a probabilistic forecast of human losses. Seismologists may not be responsible for communicating short-term risk information to the public, but they have to support decision-makers to take worthwhile actions that may save lives. However, the low-probability environment and the complexity of involved processes challenge decision-makers. A final cost--benefit analysis constitutes greater benefit than pure statistical approaches by providing objective statements that may justify evacuations. To deliver supportive information in the simplest reasonable form, I propose a warning approach --- in terms of alarm levels --- which allows one to explore worthwhile mitigation actions for each district of the Basel region.

 

36

講演者: Dr. Enescu, Bogdan (筑波大学 生命環境系地球進化科学専攻 ・准教授)

日 時: 2013 7 23() 16:00 -17:00

場 所: 統計数理研究所 D313セミナー室5

 

Title: Dynamic triggering of earthquakes in Japan due to the 2011 Tohoku-oki earthquake: some observations, stress modeling and interpretation

 

Abstract: 

TBA 

 

35

講演者: Dr. Marzocchi, Warner Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy Chief scientist

日 時: 2013 7 3() 16:00 -16:40

場 所: 統計数理研究所 D313セミナー室5

 

Title: Operational Earthquake Forecasting and Decision Making

 

Abstract: 

Traditionally, seismic risk reduction is achieved only through a sound earthquake building code. Nonetheless, some recent seismic disasters have highlighted the need for enlarging the range of risk mitigation actions beyond that. In particular, the occurrence of a seismic sequence may increase the weekly probability of a large shock by orders of magnitude, although the absolute probability usually remains below 1/100. Here, we summarize the state of the art in short-term earthquake forecasting and discuss how these forecasts may be used to mitigate seismic risk in this time horizon. Because of the low probabilities and high false alarm rates of possible advisories, mandatory mitigation actions would not be an effective practical strategy to reduce risk. Alternatively, we propose some low cost strategies, such as increasing vigilance and preparedness, for using probabilistic forecasting to mitigate seismic risk. These are based on the ‘nudging’ principle of devolving decision-making down from civic authorities to the individual level. 

 

34

講演者: Dr. Chen, Xiaowei Scripps Institution of Oceanography, University of California, San Diego Post-Doctoral Fellow

日 時: 2013 4 16() 16:00 -17:00

場 所: 統計数理研究所 D312Bセミナー室4

 

Title: Aspects of earthquake triggering and seismicity clustering

 

Abstract: 

Earthquakes strongly cluster in space and time, driven both by earthquake-to-earthquake triggering and underlying physical processes, such as tectonic stress loading, increased pore pressure, etc.

 

To understand the general characteristics of earthquake clustering from a large dataset of earthquakes, I analyze seismicity in southern California. I use a high-resolution earthquake catalog based on waveform cross-correlation to study the spatial-temporal distribution of earthquakes. Parameters based on event location, magnitude and occurrence time are computed for isolated seismicity clusters. Spatial migration behavior is modeled using a weighted-L1-norm method. Aftershock-like event clusters do not exhibit significant spatial migration compared with earthquake swarms. Two triggering processes are considered for swarms: slow slip and fluid diffusion, which are distinguished based on a statistical analysis of event migration. The results suggest fluid-induced seismicity is found across southern California, particularly within geothermal areas. In the Salton Sea geothermal field (SSGF), a correlation between seismicity and fluid injection activities is seen. Spatial-temporal variations of earthquake stress drops are investigated in different regions, and a distance-dependence of stress drop from the injection source is found in the SSGF, suggesting the influence of increased pore pressure. Temporal variation of stress drops within mainshock source regions shows that foreshocks and earthquake swarms have lower stress drops than background seismicity and aftershocks. These results, combined with the spatial migration observed for some large foreshock sequences, suggests an aseismic transient process is likely involved in foreshock triggering. 

 

33

講演者: Dr. 鵬(Han, Peng (千葉大学・大学院生)

日 時: 2013 2 14() 16:00 -18:00

場 所: 統計数理研究所 D312Aセミナー室3

 

Title: Investigation of ULF seismo-magnetic phenomena in Kanto, Japan during 2000 – 2010

 

Abstract: 

Earthquakes are one the most destructive natural hazards, causing huge damages and high casualties. Especially during the past decade, huge/mega earthquakes have hit many countries. Thus, effective earthquake forecasting is important and urgent. Since the end of last century, ULF seismo-magnetic phenomena have been intensively studied. Recently, it has been considered a promising candidate for short-term earthquake prediction as a number of case studies have been reported.

  However, scientists also found that sometimes a sizeable earthquake happened without magnetic anomalies and sometimes magnetic anomalies followed by no earthquakes. Thus, the relation between magnetic anomalies and seismicity has been queried. Moreover, there are two essential problems puzzling the researchers: (1) what is the exact waveform of electro-magnetic signals associated with earthquakes or underground activities; (2) how are the signals generated. These two questions have not yet been answered clearly and fully. There are still active debates in the geophysical community on the seismo-electromagnetic phenomena. In order to verify, clarify, and evaluate the ULF seismo-magnetic phenomena, long-term continuous monitoring of ULF magnetic field in a seismically active area is required. Therefore, a sensitive observation network has been established in Kanto-Tokai area since the year 2000. Based on eleven years’ observation, plenty of geomagnetic data have been accumulated, which provides an excellent opportunity to find answers to the questions above. Thus, in this study I have conducted an investigation of ULF seismo-magnetic phenomena in Izu and Boso Peninsulas, Japan, based on the data observed from 2000-2010.

  First, case studies of major events have been applied. Energy of ULF geomagnetic signals at the frequency around 0.01 Hz has been investigated by wavelet transform analysis. In order to minimize the influences of artificial noises, only the midnight time data (LT 1:00 ~ 4:00) have been utilized. To indentify anomalous changes from ionospheric disturbances, the standard station Memabutsu has been chosen as a reference station. (1) Case studies of the 2000 Izu Islands earthquake swarm have indicated that there are unusual geomagnetic energy enhancements in vertical component before and during the earthquake swarm. (2) Case studies of the 2005 Boso M 6.1 earthquake have also shown clear geomagnetic energy enhancements in vertical component before the earthquake. (3) Case studies of the 2002 and 2007 slow slip events have demonstrated that there are geomagnetic energy enhancements in both vertical and horizontal components during the slip events.

Then, to verify and clarify the relation between ULF geomagnetic anomalies and seismicity, statistical studies by superposed epoch analysis (SEA) have been carried out. The results have indicated that before a sizeable earthquake there are clearly higher probabilities of ULF anomalies than after the earthquake: for Seikoshi (SKS) station in Izu, about 20~30 days before, one week and few days before, and one day after the event statistical results of daily counts are significant; for Kiyosumi (KYS) station in Boso around two weeks before, few days before, and one day after the event.

  Finally, to find out the detailed waveform of anomalous magnetic signals, waveform analysis has been performed. The results show that there are mainly two kinds of seismo-magnetic signature. (1) Noise-like signals: Compared with the background, the signals exhibit small increases of amplitudes at a wide frequency range. (2) Transient/quasi-rectangular signals: the signals have transient/quasi-rectangular waveforms with amplitudes of several nT (~ 10-9 T). The noise-like signals usually persist for several days or even a few weeks, and are mainly associated with large earthquakes; the transient/quasi-rectangular signals have durations of few seconds to few ten seconds, and are registered mainly during slow slip events.

  Based on the results obtained above, we conclude that: (1) there is a correlation between ULF geomagnetic anomalies and local sizeable earthquakes in Izu and Boso Peninsulas, Japan, and the common period of significant results is few days before and one day after a sizeable earthquake; (2) there are mainly two kinds of seismo-magnetic signature registered in Izu and Boso Peninsulas: noise-like signals and transient/quasi-rectangular signals. The mechanisms of the anomalous geomagnetic signals are still unclear and need further studies.

 

 

32

講演者: Prof. Savage, Martha School of Geography, Environment and Earth Sciences, Victoria University of Wellington, New Zealand Professor

日 時: 2012 11 13() 16:00 -18:00

場 所: 統計数理研究所 D312Aセミナー室3

 

Title: Towards Predicting Earthquakes and Volcanic Eruptions using Statistical Techniques

 

Abstract: 

Predicting natural hazards is fraught and statistical techniques are necessary to put such studies on a firm standing.  Here we discuss two methods that we have applied to volcanic areas.  Analysis of the rates of earthquake activity (CURATE) is used to determine the characteristics of earthquake swarms to try to determine how they develop over time.  The technique compares favourably to other declustering techniques and allows us to consider whether some swarms are triggered by underlying processes that create diffuse seismicity that is not well modelled by Omori’s law. We also analyse waveforms of earthquakes to determine seismic anisotropy, which depends upon stress orientation and magnitude, which in turn can be influenced by earthquake and volcanic activity.  Seismic waves travel faster when their particle motion is along the cracks, which orient with the principal stress direction.  At volcanoes around the world, we discovered significant changes in seismic anisotropy strength and orientation that correlate with magma movement.  Detecting and evaluating such changes is complicated by scattered measurements, which sometimes have 90 degree ambiguities and we have been considering ways to make the techniques more robust.  These observations will provide the data that may eventually lead to prediction tools. 

 

31

講演者: 近江 崇宏 (東京大学 JST 博士研究員)

日 時: 2012 10 25() 16:00 -17:00

場 所: 統計数理研究所 4階ラウンジ 

 

Title: A state-space model for estimating the time-varying detection rate of earthquakes and its application to immediate probabilistic prediction of aftershocks

 

Abstract: 

After a large earthquake, the detection rate of earthquakes temporarily decreases, and a lot of earthquakes are missed from a catalog. Such incompleteness of the catalog prevents us from estimating statistical models of aftershock activity accurately. To overcome this difficulty, Ogata and Katsura (2005) modeled the incomplete catalog by using a parametric model of a time-varying detection rate of earthquakes.

In this talk, we propose a state space model for estimating the time-varying detection rate. In our model, the estimation problem is recursively solved, by using Kalman filter and a Gaussian approximation of the posterior probability distribution. Thus our model has an advantage in real-time computation. Finally our model is combined with the Omori-Utsu law to predict the occurrence rate of underlying aftershocks. We present some results on the immediate probabilistic prediction of aftershocks.

 

30

講演者: Dr. 婷(Wang, Ting University of Otago, New Zealand Lecturer

日 時: 2012 7 24() 16:00 -17:00

場 所: 統計数理研究所 D312Bセミナー室4 

 

Title: Hidden Markov models in modelling earthquake data

 

Abstract: 

Earthquakes are processes in which the internal workings (such as the accumulation of tectonic stress) are only observed indirectly, although the final effects are all too observable! Hidden Markov models (HMMs, a general statistical framework for modelling partially observed systems) are an intuitively attractive idea for analysing seismicity. I will briefly introduce the idea of using HMMs to investigate earthquake cycles, and then focus on one case study incorporating GPS data into earthquake forecasting.

 

A new model we developed, the Markov-modulated Hawkes process with stepwise decay (MMHPSD), can capture the cyclic parent-generating-offspring feature of the temporal behaviour of earthquakes. The decomposition of the earthquake cycle motivated the construction of a non-linear filter measuring short-term deformation rate-changes to extract signals from GPS data. This filter was applied to a) deep earthquakes in central North Island, New Zealand, and b) shallow earthquakes in Southern California. The study examines the use of HMMs to extract possible precursory information that indicates an elevated probability of large earthquakes occurrence. This study is controversial and still requires further tests. Japan is an ideal place to carry out this test.

 

29

-1

講演者: Prof. Daley, Daryl Department of Mathematics and Statistics, The University of Melbourne 名誉教授)

日 時: 2012 7 6() 14:30 -15:30

場 所: 統計数理研究所 D312Aセミナー室3 

 

Title: Dimension walks and Schoenberg spectral measures for isotropic random fields

 

Abstract: 

Schoenberg (1938) showed how Bochner's basic representation theorem for positive definite functions (e.g. correlation function of a stationary stochastic process) `simplifies' for spatial processes (d-dimensional random fields) which are isotropic: the standard Fourier kernel function is replaced by the characteristic function of a random direction in d-space and the spectral measure, instead of being on d-space, is on the positive half-line.

 

The talk describes how Wendland's `dimension walks', which were defined earlier by Matheron as Descente and Montee in studying relations between d-D and either (d+2)-D or (d-2)-D correlation functions, are equivalent to simple modifications of their d-Schoenberg measures.

 

Another family of dimension walks arises from projections from unit d-spheres to lower dimensional spheres, first via the kernel functions in the Schoenberg representation and then more generally, for d-Schoenberg measures.

 

-2

講演者: Dr. Adrian Baddeley CSIRO Mathematics, Informatics & StatisticsResearch Scientist

日 時: 2012 7 6() 15:30 -16:30

場 所: 統計数理研究所 D312Aセミナー室3 

 

Title: Leverage, influence and residual diagnostics for point process models

 

Abstract: 

For a spatial point process model fitted to spatial point pattern data, we develop diagnostics for model validation, analogous to the classical measures of leverage and influence and residual plots in a generalized linear model. The diagnostics can be characterised as derivatives of basic functional of the model. They can also be derived heuristically (and computed in practice) as the limits of classical diagnostics under increasingly fine discretizations of the spatial domain. We apply the diagnostics to example datasets where there are concerns about model validity.

 

-3

講演者: 島谷 健一郎 (統計数理研究所 データ科学研究系・准教授)

日 時: 2012 7 6() 16:30 -17:30

場 所: 統計数理研究所 D312Aセミナー室3 

 

Title: Inferring parameters in inhomogeneous Neyman-Scott processes using the Palm likelihood

 

Abstract: 

Plant populations often exhibit spatially clustering distributions, in which the two processes, limited seed dispersal and limited safe sites, are primary mechanisms. The inhomogeneous Neyman-Scott process can combine and model these two ecological processes. Estimating the model parameters allows evaluation of the relative effects of dispersal and safe sites retrospectively from spatial individual distribution data along environmental gradients. Here we propose a likelihood-based method for this spatial point process by extending the recently developed method, the Palm likelihood. Our approach was applied to even-aged black spruce forests in Canada. We obtained a set of model parameters that well reproduced the observed spatial patterns, and the fitted point processes predicted the reassembly pathway of the boreal forests.

 

27

講演者: Dr. 長勝(Jiang, Changsheng (中国地震局地球物理研究所 ・副研究員(准教授)

日 時: 2012 6 19() 16:00-17:00 14:30-15:30

場 所: 統計数理研究所 4階ラウンジ 

 

Title: Background sesismicty and its application in the study of Accelerating Moment release (AMR) and Pattern Informatics (PI) method

            Changsheng Jiang, Zhongliang Wu and Jiancang Zhuang

 

Abstract: 

 

 

26

講演者: Dr. Chan, Chung-Han Department of Geosciences, National Taiwan University Postdoctoral Fellow

日 時: 2012 5 29() 16:00 -18:00

場 所: 統計数理研究所 D312Aセミナー室3 

 

Title: Short-term earthquake forecasting through a smoothing Kernel and the rate-and-state friction law: Application to Taiwan and the Kanto region, Japan

 

Abstract: 

An earthquake forecasting approach was employed for estimating the spatio-temporal distribution of seismicity density in Taiwan and the Kanto region, Japan. To evaluate long-term seismicity rate, a smoothing Kernel function based on the distribution of past earthquakes was proposed. With the use of the rate-and-state friction model, short-term rate evolution according to the fault-interaction stress disturbance was forecasted. To test feasibility of this model, it was applied using a catalog for the area surrounding Taiwan. It leads to good agreement between the model forecast and actual observations to prove its forecasting accuracy. To check its stability, we estimated the deviation of the models according to different parameters used in the approach. We conclude that deviations within each parameter had an insignificant impact on forecasting stability. For the application to the Kanto region, we proposed a 3D forecasting model due to its complex tectonic setting. The seismicity patterns at various depths are illustrated and the seismicity rate in the crust and along the subduction zones can be distinguished. The high seismicity rate offshore in the east at the depth of 20-50 km can be associated with stress increase imparted by the 2011 Tohoku sequence. This phenomenon can be forecasted according to the rate-and-state friction model. The proposed approach, with verified applicability for seismicity forecasts, could be useful for seismic hazard mitigation. The application could provide a warning before the occurrence of consequent earthquakes and would be valuable for consequent studies, e.g., probabilistic seismic hazard assessment.

 

25

講演者: Dr. Guillas, Serge Department of Statistical Science, University College London Reader

日 時: 2012 5 18() 16:00 -18:00

場 所: 統計数理研究所 D312Aセミナー室3 

 

Title: Earthquake occurrence: emulation and climate forcing

 

Abstract: 

In earthquake occurrence studies, the so-called q value can be considered both as one of the parameters describing the distribution of interevent times and as an index of non-extensivity. Using simulated datasets, we compare four estimators, based on principle of maximum entropy, method of moments, maximum likelihood, and probability weighted moments (PMW) of the parameters of the distribution of inter-events times, assumed to be a generalized Pareto distribution. We then use the unbiased version of PWM estimators to compute the q value for the distribution of inter-event times in a realistic earthquake catalogue simulated according to the epidemic type aftershock sequence (ETAS) model. Finally, we use these findings to build a statistical emulator of the q values of ETAS model. We employ treed Gaussian processes to obtain partitions of the parameter space so that the resulting model respects sharp changes in physical behaviour. The emulator is used to understand the joint effects of input parameters on the q value, exploring the relationship between ETAS model formulation and distribution of inter-event times.

 

We then present statistical evidence for a temporal link between variations in the El NioSouthern Oscillation (ENSO) and the occurrence of earthquakes on the East Pacific Rise (EPR). We adopt a zero-inflated Poisson regression model to represent the relationship between the number of earthquakes in the Easter microplate on the EPR and ENSO (expressed using the southern oscillation index (SOI) for east Pacific sea-level pressure anomalies) from February 1973 to February 2009. We also examine the relationship between the numbers of earthquakes and sea levels, as retrieved by Topex/Poseidon from October 1992 to July 2002. We observe a significant positive influence of SOI on seismicity: positive SOI values trigger more earthquakes over the following 2 to 6 months than negative SOI values. There is a significant negative influence of absolute sea levels on seismicity (at 6 months lag). We propose that increased seismicity is associated with ENSO-driven sea-surface gradients (rising from east to west) in the equatorial Pacific, leading to a reduction in ocean-bottom pressure over the EPR by a few kilopascal. This relationship is opposite to reservoir-triggered seismicity and suggests that EPR fault activity may be triggered by plate flexure associated with the reduced pressure.

 

24

講演者: 寺川 寿子 (名古屋大学 環境学研究科 附属地震火山研究センター・助教)

日 時: 2012 5 11() 14:00-17:00

場 所: 統計数理研究所 D312Aセミナー室3

 

Title: Temporal Changes in Fault Strength and Pore Fluid Pressures Following the 2011 off the Pacific Coast of Tohoku Earthquake

 

Abstract: 

Extensive aftershocks and triggered seismic events are ubiquitous following large earthquakes, but the controlling mechanisms are not yet understood. Focal mechanisms of these events can provide insight into physical triggering mechanisms because they reflect friction coefficient and pore fluid pressure on the fault as well as the tectonic stress pattern. In the present study we investigate physical processes triggering seismic events in inland region of the northeast Japan following the 2011 off the Pacific Coast of Tohoku earthquake (Mw = 9.0) by examining focal mechanisms to the tectonic stress pattern and changes in the Coulomb failure function (DCFF). The local excitation of seismicity rate in the regions with negative DCFF indicates that these aftershocks would have been triggered by decrease of fault strength due to the increase of pore fluid pressures. We show a plausible explanation that seismic events on unfavourably oriented pre-existing faults relative to the tectonic stress pattern, or focal mechanisms inconsistent with the tectonic stress pattern, would be evidence for drastic decrease of fault strength due to increase of pore fluid pressures.

 

23

講演者: Prof. Khmaladze, Estate V. School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, New Zealand.Professor

日 時: 20111212() 16:00 -17:00

場 所: 統計数理研究所 D312-Aセミナー室3 (立川)

 

Title: Infinitesimal analysis of set-valued functions and applications to spacial statistics and image analysis

 

Abstract: →PDF

The problem under consideration started with a study of spacial change-point problem, or change-set problem as we called it: suppose there is a set $K$, such that our observations inside this set behave differently then anywhere outside it. Given $n$ observations, how can we test that a given $K$ is the correct one against its small perturbation $K(\varepsilon)$ as an alternative?

 

 In huge amount of publications on the change-set problem, almost all devoted to the estimation of the change-set, we could not find such an object as an "alternative set" $K(\varepsilon)$. One reason for this porbably is that it is not easy to realize how to describe small changes in sets.

 

We developed an appropriate notion of the derivative of set-valued function  in (Khmaladze, 2007) and used it to build a version of contiguity theory in (Einmahl, Khmaladze, 2011) for statistical problems where the parameter of interest is a set.

 

One single result here is that if $\Phi_n$ is a point process with increasing intenstiy $n$, and the symmetric difference $K(\varepsilon)\Delta K$ shrinks and "vanishes" as $\varepsilon \to 0$, then the sequence $\Phi_n(K(\varepsilon)\Delta K)$ lives in the limit on the derivative set $dK(\varepsilon)/d\varepsilon$:

 

$$\Phi_n( K(\varepsilon)\Delta K) \to \Psi (dK(\varepsilon)/d\varepsilon, {\rm as} n\to\infty, \varepsilon\to 0.$$

 

In the talk we present the main framework of this approach. We hope that some discussions would lead to further applications.

 

22

講演者: 岩田 貴樹 (統計数理研究所 予測発見戦略研究センター 地震予測解析グループ・特任准教授)

日 時: 2011 11 25() 13:30-14:30

場 所: 統計数理研究所 D312Bセミナー室4 (立川)

 

Title: The slip distribution of the 2011 Tohoku-oki earthquake inferred from the spatial distribution of its aftershocks

 

Abstract: 

We have developed a method to estimate the spatial slip distribution of a large earthquake based on its on-fault aftershock activity and the rate- and state-dependent friction model (Dieterich, 1994, JGR). This talk will represents the application of this method to the 2011 Tohoku-oki earthquake. The outline of the method is as follows. First, we divided the source area of the destructive earthquake into 450 subfaults of which size is 20 x 20 km. Next the slips of each subfault were optimized to make the expected spatial distribution of aftershocks fit to the observed distribution during one day after the mainshock. The expected distribution was derived from the Dieterich’s formulation and the goodness-of-fit between the expected and observed distributions was evaluated by means of the likelihood for point-process model. Then we constructed a Bayesian model incorporating smoothness constraint on the spatial slip distribution, because optimizing such a huge number of parameters is unstable; the incorporation of the constraint enhances the stability of the optimization. To compute the posterior distribution of the parameters in this Bayesian framework, the Markov Chain Monte Carlo method was used. The result of this approach found an asperity close to the hypocenter and some small asperities located to the southwest of the hypocenter. This feature is consistent with the results of some slip inversions based on seismograph, geodetic, and/or tsunami data, suggesting that seismic activity data would play an important role in the estimation of rupture process of an earthquake.

 

21 

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講演者: Prof. Schorlemmer, Danijel GFZ German Research Centre for Geosciences, Potsdam, Germany Professor

日 時: 20111018() 15:00 -16:00

場 所: 統計数理研究所 D312-Aセミナー室3 (立川) 

 

Title: Advancements in Probabilistic Seismic Network Completeness Studies

 

Abstract: 

An important characteristic of any seismic network is its detection completeness, which should be considered a function of space and time. Many researchers rely on robust estimates of detection completeness, especially when investigating statistical parameters of earthquake occurrence.

 

We present the Probability-based Magnitude of Completeness (PMC) method for computing the spatial variation and temporal evolution of detection capability of seismic networks based on empirical data only: phase data, station information, and the network specific attenuation relation. New developments are extending this method to complex 3D structures like mining environments.

 

We present studies of regional networks from California, Switzerland, Italy, Japan, New Zealand, and compare the result with estimated completeness levels of other methods. We report on the time evolution of monitoring completeness in these regions. Scenario computations show the impact of different possible network failures and offer estimates of possible network optimization strategies. Optimizations are reducing the necessary processor time for computing. All presented results are published on the CompletenessWeb (www.completenessweb.org) from which the user can download completeness data from all investigated regions, software codes for reproducing the results, and publication-ready and customizable figures.

 

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講演者: Prof. Rundle, John B. Department of Physics and Geology, University of California, Davis, U.S.A.Distinguished Professor

日 時: 20111018() 16:00 -18:00

場 所: 統計数理研究所 D312-Aセミナー室3 (立川) 

 

Title: Forecasting Large Earthquakes: Problems, Pitfalls and Promise

 

Abstract: 

Forecasting the future behavior of a stochastic complex system is a necessary and critical activity with wide applications.  As the mathematician Edward Thorp showed many years ago [1,2], forecasting has applications in games of chance as well as in financial markets.  Both fields represent applications of statistics, stochastic random walks, and probability theory.  Objective evaluation of forecasts by established tests and measures is also a necessary and important component of a forecasting system.  Many of the modern tests have been tabulated at [3].  Earthquake forecasts are a special case of the forecasting problem, particularly as applied to large earthquakes such as the March 11, M9 Off the Pacific Coast of Tohoku earthquake.  Forecasts of future events in complex systems are in general plagued by incomplete information, a problem that must be considered in constructing forecasts.  In addition to these problems, delivery of real-time forecast information to the scientific community and to the public is an issue as well.  Here, web 2.0 technology is helpful in allowing rapid dissemination of information.  In this lecture, I shall discuss these general aspects of the forecasting problem as applied to earthquake forecasting.  I will discuss ideas based on the Natural Time Weibull method of earthquake forecasting, recently developed by our group.  I will also discuss our experiences with numerical earthquake simulations, as well as with public outreach using the World Wide Web (see www.openhazards.com). 

 

[1] E. Thorp and S. Kassouf, Beat the Market: A Scientific Stock Market System,  Random House (1967)

[2] E. Thorp, Beat the Dealer: A Winning Strategy for the Game of Twenty-One, Random House (1962)

[3] http://www.cawcr.gov.au/projects/verification/

 

20

講演者: Dr. Kagan, Yan Y. Department Earth and Space Sciences (ESS), UCLA, U.S.A.Researcher

日 時: 201192() 16:00 -17:00

場 所: 統計数理研究所 D312-Bセミナー室4 (立川)

 

Title: Statistical properties of earthquake occurrence and their application for earthquake forecasting

 

Abstract: 

Earthquake occurrence exhibits scale-invariant statistical properties:

(a) Earthquake size distribution is a power-law (the Gutenberg-Richter relation for magnitudes or the Pareto distribution for seismic moment). Preservation of energy principle requires that the distribution should be limited on the high side; thus we use the generalized gamma or tapered Pareto distribution. The observational value of the distribution index is about 0.65. However, it can be shown that empirical evaluation is upward biased, and the index of 1/2, predicted by theoretical arguments, is likely to be its proper value. The corner (maximum) moment has an universal value for shallow earthquakes occurring in subduction zones. We also determined the corner moment values for 8 other tectonic zones.

(b) Earthquake occurrence has a power-law temporal decay of the rate of the aftershock and foreshock occurrence (Omori's law), with the index 0.5 for shallow earthquakes. The short-term clustering of large earthquakes is followed by a transition to the Poisson occurrence rate. In the subduction zones this transition occurs (depending on the deformation rate) after 7-15 years, whereas in active continents or plate-interiors the transition occurs after decades or even centuries.

(c) The spatial distribution of earthquakes is fractal: the correlation dimension of earthquake hypocenters is equal to 2.2 for shallow earthquakes.

(d) The stochastic 3-D disorientation of earthquake focal mechanisms is approximated by the rotational Cauchy distribution.

 

On the basis of our statistical studies, since 1977 we have developed statistical short- and long-term earthquake forecasts to predict earthquake rate per unit area, time, and magnitude. The forecasts are based on smoothed maps of past seismicity and assume spatial and temporal clustering. Our recent program forecasts earthquakes on a 0.1 degree grid for a global region 90N--90S latitude. For this purpose we use the PDE catalog that reports many smaller quakes (M>=5.0). For the long-term forecast we test two types of smoothing kernels based on the power-law and on the spherical Fisher distribution. We employ adaptive kernel smoothing which improves our forecast in seismically quiet areas. Our forecasts can be tested within a relatively short time period since smaller events occur with greater frequency. The forecast efficiency can be measured by likelihood scores expressed as the average probability gains per earthquake compared to the spatially or temporally uniform Poisson distribution. The other method uses the error diagram to display the forecasted point density and the point events.

 

As an illustration of our methods, we are trying to answer a question: was the Tohoku mega-earthquake of 2011/3/11 a surprise? We consider three issues related to the 2011 Tohoku earthquake:

(1) Why was the magnitude limit for the Tohoku region so badly underestimated, and how can we estimate realistic limits for subduction zones in general?

(2) How frequently can such large events occur off Tohoku?

(3) Could short-term forecasts have offered effective guidance for emergency preparation?

 

Two methods can be applied to estimate the maximum earthquake size in any region: statistical analysis of available earthquake records, and the moment conservation principle -- how earthquakes release tectonic deformation. We have developed both methods since 1991. For subduction zones, the seismic record is usually insufficient (in fact it failed badly for Tohoku), because the largest earthquakes are so rare. However, the moment conservation principle yields consistent estimates for all subduction zones. Various measurements imply maximum moment magnitudes of the order 9.0--9.7. A comparison of the inter-earthquake secular strain accumulation and its release by the coseismic slip implies a similar maximum earthquake size estimate. Beginning in 1999

we used our statistical short- and long-term earthquake forecasts, based on the GCMT catalog, for the western Pacific, including Japan. We have posted them on the web and included expected focal mechanisms as well. Long-term forecasts indicate that the average frequency for magnitude 9 earthquakes in the Tohoku area is about 1/400 years. We have archived several forecasts made before and after the Tohoku earthquake. As expected, the Tohoku mega-earthquake changed the forecasted long-term rate by just a few percent. However, the magnitude 7.5 foreshock increased the short term rate to about 100 times the long-term rate, and the magnitude 9 event increased it briefly to more than 1000 times the long-term rate. These results could well justify the development of an operational earthquake forecasting plan.

 

19

日 時: 201134() 15:00 -16:00

場 所: 統計数理研究所 D312Aセミナー室3 (立川)

-1

講演者: Dr. Talbi, Abdelhak (東京大学地震研究所 ・外国人研究員)

 

Title: Analysis of Earthquake Inter-event Times

 

Abstract: 

Understanding temporal behavior of earthquakes is a fundamental step towards building reliable statistical model fitting observed seismicity. A successful class of models assume two seismicity components corresponding to stable backgroundand varying triggeredrates or inter-event times. In this study, the distribution of inter-event times is modeled assuming triggered events governed by a non-homogenous Poisson process, and background events governed by different hypothetical distribution (Exponential, Gamma and Weibull). The model is analytically introduced using Palm-Khinchine equations and fitted in practice to seismicity data from southern California, Japan and Turkey. The analytic form of the distribution is discussed when different priory hypotheses are adopted.In a second step, the temporal clustering of events is studied using the distance between the whole distribution of inter-event times, and the residual distributions obtained using different declustering approaches. Short and long range correlations are studied in space and time. The residual background process is found dominant around the mean inter-event time and the mean inter-event distance. The former analysis describes seismicity as the accumulation of local perturbations related to a unique mean field backgroundprocesses characterized by the mean inter-event time and the mean inter-distance.

 

-2

講演者: Prof. Console, Rodolfo National Institute of Geophysics and Volcanology, Rome, Italy Senior Scientific Advisor

 

Title: Short-term earthquake forecasting before and during the L'Aquila (Central Italy) seismic sequence of April 2009

 

Abstract: 

The M5.9 earthquake occurred on April 6th 2009, which caused more than 300 casualties in the city of L'Aquila and neighboring villages in Central Italy, immediately generated a lot of discussions about the potential practical use of foreshocks and other kind of information for mitigating seismic risk among the population. These discussions triggered studies related to the validity of statistical clustering models such as the ETAS model, not only for forecasting aftershocks, but also mainshocks following potential foreshocks. In the frame of the above mentioned studies, this presentation reports preliminary results of the statistical analysis of the L'Aquila seismic sequence by means of a version of the group of ETAS models. The free parameters used in the algorithm are obtained through the maximum likelihood method from a learning data set of instrumental seismicity collected from 2005 up to March 2009 in the region of L'Aquila. Our method includes statistical declustering of the background seismicity by an iterative process until the maximum likelihood of the learning data set under the ETAS model is obtained. For testing purposes, an algorithm for producing simulations of seismic series has been developed and applied to produce synthetic catalogues, the statistical properties of which are compared with those of the real one. Finally, the daily forecasts of earthquakes at different threshold magnitudes were produced for a testing period including the L'Aquila 2009 mainshocks and its largest aftershocks. The results show that the probability of occurrence of an M5.9 computed from the ETAS algorithm at the midnight preceding the L'Aquila 2009 mainshock, even if it was much higher than the background Poisson probability, was quite low if compared with reasonable expectations for a practical operational forecast. Moreover, the comparison between the daily rate expected by the ETAS forecast method, and the real daily number of aftershocks shows a systematic underestimation of such rate.

 

18

講演者: Dr. Falcone, Giuseppe National Institute of Geophysics and Volcanology Rome, Italy Researcher

日 時: 2011217() 15:00 -16:00

場 所: 統計数理研究所 D313セミナー室5 (立川)

 

Title: Earthquake occurrence models and their validation

 

Abstract: 

This presentation describes the tests and the forecast verification procedures of three earthquake occurrence models applied to the various regions of the globe (Italy, California, Japan) to assess the occurrence probabilities of future earthquakes: two as short-term (24 hour) models, and one as long-term (5 and 10 years). The first model for short-term forecasts is a purely stochastic epidemic type earthquake sequence (ETES) model. The second short-term model is an epidemic rate-state (ERS) forecast based on a model that is physically constrained by the application to the earthquake clustering of the Dieterich rate-state constitutive law. The third forecast is based on a long-term stress transfer (LTST) model that considers the perturbations of earthquake probability for interacting faults by static

Coulomb stress changes. The forecast verification procedures have been carried out in forward-retrospective and in real time way making use of statistical tools as the Relative Operating Characteristics (ROC) diagrams, Log-likelihood, N-Test, L-Test and Observed and forecasted number of events. The seismic hazard modeling approach so developed, after a suitable period of testing and refinement, is expected to provide a useful contribution to earthquake hazard assessment, even with a possible practical application for decision making and public information.

 

These models have been submitted to the Collaboratory for the Study of Earthquake Predictability (CSEP) for forecast testing for Italy (ETH Zurich) and Japan (ERI Tokyo).

 

17

講演者: Dr. 卉瑄(Chen, Kate Huihsuan (国立台湾師範大学 ・助教)

日 時: 2011128() 15:00 -16:00

場 所: 統計数理研究所 D313セミナー室5 (立川)

 

Title: Triggering effect of small to large earthquakes on earthquake cycle of small repeating events

 

Abstract: 

Knowledge of what governs the timing of repeating earthquakes is essential to understanding the nature of the earthquake cycle and to determining earthquake hazard, yet the variability and controls of earthquake recurrences are not well established. Several unsolved problems regarding the recurrence properties of natural earthquake sequences remain: How do the repeating sequences respond to static and dynamic stress perturbations associated with nearby earthquakes? To what degree does fault interaction influence the timing of repeating earthquakes? Do spatially adjacent repeating sequences communicate with each other in a way that is clearly evident in similar occurrence times or recurrence patterns?

 

Here we use a large population of small, characteristically repeating earthquakes at Parkfield provides to study how the interaction of nearby earthquakes affects their recurrence properties. We analyze 114 M -0.4 ~ 3.0 repeating earthquake sequences (RES) to examine the triggering effect from nearby microseismicity. We find that close-by-events influence RES’s timing in a matter of minutes or hours by short-term triggering. Events that occurred within less than 1 day of an RES often imposed or experienced high stress changes. A stress increment of 10 kPa appears to be needed to produce such effectively immediate triggering.

 

16

講演者: Prof. Console, Rodolfo National Institute of Geophysics and Volcanology Rome, Italy Senior Scientific Advisor

日 時: 2011117() 15:00 -16:00

場 所: 統計数理研究所 4F ラウンジ (立川)

 

Title: Renewal modeling and co-seismic stress transfer for seismic hazard assessment in the Corinth Gulf, Greece, fault system

 

Abstract: 

Earthquake forecasts have always been a difficult task because they can be affected by uncertainty in terms of the most appropriate model and the involved parameter values. The models adopted in this study belongs to the category of the renewal models, based on the characteristic earthquake hypothesis, the necessary ingredients of which are a fixed geometry and the knowledge of the slip rate on the faults. Both the BPT and the Weibull distribution have been tested. The hazard rate so obtained is then modified by the inclusion of a permanent effect due to the Coulomb static stress change caused by failure of neighboring faults that occurred since the latest characteristic earthquake on the concerned fault. I apply this method along the Corinth gulf extension zone, a place that is rich with observations of strong-earthquake recurrence behavior, to assess their relative forecast applicability. The validity of the renewal models is assessed in retrospective way on the data of the last 300 years by comparison with a plain time independent Poisson model. This is done by means of statistical tools as the ROC diagram, the R-score and the log-likelihood ratio. I find that the renewal models perform better than the Poisson hypothesis. It seems also that the BPT distribution works slightly better than the Weibull distribution, while little advantage is achieved by the introduction of the Coulomb static stress change in the forecasting algorithm.

 

15

講演者: Dr. Parsons, Tom United States Geological Survey, U.S.A. Research Geophysicist

日 時: 201114() 14:00 -15:00

場 所: 統計数理研究所 D312Bセミナー室4 (立川)

 

Title: What causes aftershocks?

 

Abstract: 

Despite decades of research devoted to this question, we still do not know how mainshocks cause aftershocks. In this presentation I show recent research that attempts to isolate static and dynamic stressing signals so that we can learn more about their abilities to trigger other earthquakes. We hope someday to combine physical models with statistical models for forecasting, but I show that the physical models still have problems when used prospectively.

 

14

講演者: 遠田 晋次 (京都大学防災研究所 地震予知研究センター・准教授
統計数理研究所 予測発見戦略研究センター 地震予測解析グループ ・客員教授)

日 時: 20101117() 13:30-14:30

場 所: 統計数理研究所 D312Bセミナー室4 (立川)

 

Title: Rate/state Coulomb stress transfer model for the CSEP Japan seismicity forecast

 

Abstract: 

Numerous studies retrospectively found that seismicity rate jumps (drops) due to coseismic Coulomb stress increase (decrease). The Collaboratory for the Study of Earthquake Predictability (CSEP) instead provides us an opportunity for prospective testing of the Coulomb hypothesis. Here we adapt our stress transfer model incorporating rate and state dependent friction law to the CSEP Japan seismicity forecast. We demonstrate how to compute the forecast rates of large shocks in 2009 using the large earthquakes during the past 120 years. The time dependent impact of the coseismic stress perturbations explains qualitatively well the occurrence of the recent moderate size shocks. Such ability is partly similar to that of statistical earthquake clustering models. However, our model differs

from them as follows: the off-fault aftershock zones can be simulated using finite fault sources; the regional areal patterns of triggered seismicity are modified by the dominant mechanisms of the potential sources; the imparted stresses due to large earthquakes produce stress shadows that lead to a reduction of the forecasted number of earthquakes. Although the model relies on several unknown parameters, it is the first physics based model submitted to the CSEP Japan test center and has the potential to be tuned for short-term earthquake forecasts.

 

13

講演者: Dr. Bansal, Abhey Ram National Geophysical Research Institute, Council of Scientific and Industrial Research (NGRI, CSIR) (India)
E1クラス研究員/日本学術振興会 外国人招へい研究者(長期) ; 統計数理研究所・外来研究員

日 時: 2010  716() 15:00-16:00

場 所: 統計数理研究所 D312Bセミナー室4 (立川)

 

Title: Statistical seismology of Sumatra: before and after the mega-earthquake of 26 December 2004

 

Abstract: 

We examine the effect of the Sumatra-Andaman Islands mega-earthquake of 26 December 2004 on Sumatran seismicity. Irrespective of time window the inter-event time distribution exhibits Omori-Utsu decay at short time intervals, followed by a gamma distribution at intermediate and long time intervals.  The mean inter-event time drops significantly after the event, associated with an increase in the fractal dimension of the time series sequence from 0.07 ± 0.01 to 0.19 ± 0.01, and a doubling of the coefficient of variation of inter-event time. Epidemic Type Aftershock Sequence (ETAS) model parameters are used to quantify changes in the statistical properties. These changes can be significant: the background random seismicity rate drops to be indistinguishable from zero after the mega-earthquake (indicating a single dominant aftershock sequence) whereas the productivity factor K is ~13.4 times higher. The magnitude sensitivity parameter increases after the earthquake, indicating larger aftershocks are proportionately easier to trigger, and the Omori-Utsu exponent p decreases (to ~1), consistent with a longer duration of aftershock sequences. When examined in retrospect, a non-stationary ETAS model provides a better fit to the seismicity data prior to the main shock, the best fitting model being one with a change point to enhanced rates 4.3 years before the mega-earthquake, most likely due to a localised swarm at that time.

 

特別セミナー

講演者: Prof. Vere-Jones, David Statistics Research Associates Limited (SRA), New Zealand Director

日 時: 2010  6 30() 15:00-16:00

場 所: 統計数理研究所 D312Bセミナー室4 (立川)

 

Title: The Evolution of Statistical Seismology

 

Abstract: 

Some account is given of the early days of statistical seismology, and some issues raised for future consideration in this field.

 

12

講演者: 菅谷 勝則 (統計数理研究所 予測発見戦略研究センター 地震予測解析グループ・特任研究員)

日 時: 2010  4 23() 15:00-16:00

場 所: 統計数理研究所 D312Bセミナー室4 (立川)

 

Title: Coseismic change and recovery of scattering environment in the crust after a large earthquake

(Sugaya, K., Hiramatsu, Y., Furumoto, M. and Katao, H.)

 

Abstract: 

The coda waves mainly consist of scattered S waves in the crust. The attenuation property of coda waves, coda Q^-1 or Qc^-1, reflects the scattering and absorption environments in the crust and is supposed to be a good tool to investigate medium properties in the crust. Furthermore, Qc^-1 is a good indicator of the stress condition in the crust.

 

We observe a unique temporal variation in crustal heterogeneity from the analysis of Qc^-1 for 14 years in the Tamba region, northeast to the rupture zone of the 1995 Hyogo-ken Nanbu earthquake (Mjma 7.3) in southwest Japan. The values of Qc^-1 at lower frequencies (1.5-4.0 Hz) that increased coseismically due to the static stress change decreased back to the pre-event values in about two years. No such variations are found at higher frequencies (5.0-24.0 Hz). We confirm that no tectonic events that cause a significant stress change occurred during the recovery period. The time required for the recovery of the scattering environment, such as the number density of cracks and cracks opened by the stress change, observed here is consistent with those of previous studies focused on the brittle shallower crust. This suggests a possibility that a similar mechanism of the recovery operates both in the brittle and the ductile parts of the crust.

 

11

講演者: Prof. Kuensch, Hans R.ETH Zurich, Switzerland Professor

日 時: 2010  4  9() 15:00-16:00

場 所: 統計数理研究所 D312Bセミナー室4 (立川)

 

Title: Particle and Ensemble Kalman filtering (Kuensch, Hans R. and Frei, Marco)

 

Abstract: 

Ensemble and particle filtering are two sequential Monte Carlo methods for approximating the filter distributions in nonlinear and/or non-Gaussian state space models. They differ in the way a new observation is taken into account in the update step. The particle filter is non-parametric and works by weighting and resampling. The Ensemble Kalman filter (EnsKF) requires a linear Gaussian observation model and proceeds by a Monte Carlo implementation of the linear

Kalman filter update. In a different version of the ENSKF called the square root filter, updates are done by a linear transformation of the prediction sample (without any additional randomness). Even though the EnsKF is based on unwarranted assumptions, it is extremely robust in many high dimensional applications where the number of particles is small because of computational limitations. In contrast, the particle filter degenerates quickly as the dimension of the observations increases.

 

I will discuss some of the following issues: EnsKF for nonlinear observation equations, the use of the EnsKF for parameter estimation, regularization of the estimated prediction covariance, bias due to estimation of the prediction covariance, localization of the EnsKF update, behavior of the EnsKF for Gaussian mixture predictions and ideas for combining the EnsKF and the particle filter.

 

10

講演者: 祺(Wang, Qi Department of Earth and Space Sciences, University of California, Los Angeles, U.S.A.

日 時: 2010  2 19() 15:00-16:00

場 所: 統計数理研究所 D312Aセミナー室3 (立川)

 

Title: An optimized five-year large earthquake forecast in California based on smoothed seismicity (Qi Wang, D.D.Jackson and Y.Y. Kagan)

 

Abstract: 

Earthquake forecasting models based on seismic, geologic, tectonic and geodetic information have been discussed a lot. We tried to state a five year forecast of California earthquakes with magnitude above 5.0 based on smoothed seismicity. We used extended sources to represent large earthquakes. Kagan and Jackson (2007) have presented a five-year forecast of southern California earthquakes with magnitude 5 or larger. Here we extend the forecast region from southern California to all of California using the new California earthquake catalog with estimated moment magnitude, and in one case we include historic earthquakes as well as instrumentally recorded ones after considering catalog incompleteness. This forecast model differs from others like it because larger events are represented by multiple point sources and because the parameters in the spatial smoothing kernel have been optimized in learning period by using maximum likelihood estimation. We tried to answer two basic questions: (1) whether the anisotropic and magnitude-dependent smoothing kernels outperform the isotropic and magnitude-independent ones; (2) whether including large historical earthquakes could improve the forecast.  Moreover, earthquake data have errors in location, magnitude and focal mechanism that can influence the results of earthquake studies. Neglecting these errors, or estimating them poorly, could cause valid hypotheses to be rejected or invalid ones to be accepted. We tried to estimate how the uncertainty of catalog data especially uncertainty of magnitude influences our testable forecast results.

 

9

講演者: Dr. Terakawa, Toshiko (寺川 寿子)Geodynamics, Steinmann-Institute, University of Bonn, Germany

日 時: 2010  1 29() 15:00-16:00

場 所: 統計数理研究所 D312Aセミナー室3 (立川)

 

Title: Identification of the high fluid pressure source driving the 2009 L’aquila earthquake sequence

(Toshiko Terakawa, Anna Zoporowski, Boris Galvan, and Stephen A. Miller)

 

Abstract: 

The April 6, 2009 L’aquila intraplate earthquake (Mw=6.3) in the Central Apennines occurred at the boundary separating regions of diffuse CO_2 degassing and regions where degassing is not observed. The same tectonic and geologic environment hosted the 1997 Colfiorito sequence to the north, which was shown to be driven by degassing of a high-pressure fluid source at depth with a fluid diffusion model [Miller et al. 2004]. Here we show the 3D fluid pressure field in the

L’aquila region, applying a new analysis technique termed Focal Mechanism Tomography [Terakawa et al. 2009 (submitted)] to actual seismic data.  We identify three large-scale pockets of high fluid pressure at depths of 7-10 km, and show a very strong correlation between these high fluid pressure regions and both foreshock and aftershock hypocenters. The shape of over-pressured regions and the evolution of aftershock locations indicate that aftershocks are being driven in part by fluid flow associated with volumetric compression from the main-shock acting upon the over-pressured poro-elastic reservoir [e.g., Nur & Booker 1982; Bosl & Nur 2002], and by fracturing and subsequent flow from trapped high pressure pockets [Miller et al. 2004].  The mapped 3D fluid pressure field inferred from our analysis provides an important boundary condition for forward modelling of fluid flow and stress evolution for a mechanistic assessment of the continuing seismic hazard in the region. These results also form a baseline hypothesis against which other geophysical and geochemical measurements can be tested.

 

8

講演者: 姫野 哲人 (極地研究所 新領域融合研究センター・特任研究員)

日 時: 2010  1 15() 15:00-16:00

場 所: 統計数理研究所 A508セミナー室 (立川)

 

Title: Time variation of background seismicity on ETAS model

 

Abstract: 

The Epidemic Type Aftershock Sequence (ETAS) model introduced by Ogata (1988) is one of statistical method for seismicity. This model classifies earthquake sequence into aftershocks and background seismicity. For the frequency of aftershocks, some empirical relations is assumed. On the other hand, background seismicity rate is constant. Therefore, the main shock sequence is distributed according to stationary Poisson process. In this study, we focus the time variation of background seismicity and expand the background seismicity.

 

7

講演者: Dr. Chu, Annie (統計数理研究所 予測発見戦略研究センター 地震予測解析グループ 特任研究員)

日 時: 2009 12  4() 15:00-16:00

場 所: 統計数理研究所 D312Aセミナー室3 (立川)

 

Title: Comparison of ETAS parameter estimates across different global tectonic zones

 

Abstract: 

Branching point process models such as the ETAS (Epidemic-Type Aftershock Sequence) models introduced by (Ogata 1988, 1998) are often used in the description, characterization, simulation, and declustering of modern earthquake catalogs. The present work investigates how the parameters in these models vary across different tectonic zones. After considering divisions of the surface of the Earth into several zones based on the plate boundary model of Bird (2003), ETAS models are fit to the occurrence times and locations of shallow earthquakes within each zone. Computationally, the EM-type algorithm of Veen and Schoenberg (2008) is employed for the purpose of model fitting.  The fits and variations in parameter estimates for distinct zones are compared.  Seismological explanations for the differences between the parameter estimates for the various zones are considered, and implications for seismic hazard estimation and earthquake forecasting are discussed.

 

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講演者: Prof. 周 仕勇 (Zhou, Shiyong) (北京大学 地球空間科学学院 ・教授)

日 時: 2009 10 30() 15:00-16:00

場 所: 統計数理研究所 D304セミナー室(立川)

 

Title: Was the Ms 8.0 Long Men Shan (Wenchuan) Earthquake in 2008 induced by the Zipingpu Reservoir?

 

Abstract: 

According to the Coulomb failure criterion the variation of either shear stress, normal stress, or pore pressure can result in earthquake occurrences. Abnormal seismicity increases around reservoirs are often thought to be induced by the water piled behind the dam, which leads to increases in crustal pore pressure and Coulomb stress nearby, and so promote the nearby faults to fail. To investigate how much the Zi-Ping-Pu reservoir, whose dam is just a few hundreds of meters from the Long Men Shan fault, influenced the May 12, 2008 Wenchuan earthquake Ms8.0, we calculated the Coulomb stress variation induced by the filling of the Zipingpu reservoir, beginning in December 2004, and analyzed the correlation between the seismicity variations and the induced Coulomb stress variations. Both the calculated Coulomb stress variations and the observed seismicity analysis suggest that the probability that the huge Long Men Shan earthquake Ms8.0 was induced by the Zipingpu reservoir is very low. The filling of the Zipingpu reservoir could only result in a small increase in the rate of shallow earthquakes with hypocenter depth smaller than 5km near the reservoir region.

 

5

講演者: 野村 俊一 (総合研究大学院大学 大学院生)

日 時: 2009 10  2() 15:00-16:00

場 所: 統計数理研究所 D312セミナー室(立川)

 

Title: Composing prior distributions of BPT distribution with slip rates in renewal process of recurrent earthquakes

 

Abstract: 

Renewal process with Brownian Passage Time (BPT) distribution is mainly used in the long-term evaluation of active faults by the Earthquake Research Committee, the Headquarters of Earthquake Research Promotion (ERC/HERP). In ERC/HERP (2001), two parameters of BPT distribution, called mean parameter and aperiodicity (shape) parameter, are estimated as follows: mean parameter is estimated by either recurrence intervals or slip rates of active faults, and aperiodicity parameter is commonly set at 0.24. The value of aperiodicity parameter is derived from the active faults on which more than four recurrence intervals are detected, but recent researches showed the value of aperiodicity parameter is inappropriate to apply for all active faults.

 

In this seminar, we propose an alternative method to estimate the parameters of BPT distribution of recurrence intervals. First, we normalize the intervals by mean recurrence time derived from slip size and slip rate of the fault. Then we can use both intervals and slip rate to estimate its mean parameter. Second, we use Bayesian inference to estimate the parameters. Bayesian predictive distribution gives stable prediction when there are few data in the fault. Prior distributions and their parameters are estimated by maximizing their marginal likelihood. We simulate recurrence intervals from a virtual fault and compare our model and ERC/HERP's model by their relative entropy.

 

4

講演者: 熊澤 貴雄 (統計数理研究所 予測発見戦略研究センター 地震予測解析グループ リサーチ・アシスタント)

日 時: 2009  8 28() 15:00-16:00

場 所: 統計数理研究所 第2セミナー室(330号室)

 

Title: Seismicity changes in Tohoku District before the 2008 Iwate-Miyagi Inland Earthquake

            Kumazawa, Takao (The Graduate University for Advanced Studies), Ogata, Yoshihiko (The Institute of Statistical Mathematics) and
Toda, Shinji (
Disaster Prevention Research Institute Kyoto Univ.)

 

Abstract: 

The 2008 Iwate-Miyagi Nairiku earthquake of M7.2 (JMA) is one of the largest inland earthquakes  occurred in the northern part of Honshu island. We examined seismicity rate changes in the surrounding areas prior to this earthquake for around 10 years in relation to the ∆CFF values of it. We selected a number of regions according to the sign of the ∆CFF from the Iwate-Miyagi inland earthquake, then examined the series of earthquakes in each region by fitting ETAS models and examined if the changes of seismicity, if any, were significant and consistent with the ∆CFF.  We confirmed the pre-seismicity by transient anomalies in GPS measurement of several stations.

 

Five years prior to the event, a M7.1 earthquake of 2003 occurred at 71km. depth in the subducting Pacific plate, beneath Sanriku coast, Miyagi prefecture.  This fault’s movement activated the reverse fault system in inland Tohoku District including the one responsible for Iwate-Miyagi inland earthquake, raising the seismicity there. The activated area also covered the fault of M6ǒ5Ņinland earthquake occurred two months afterward. It as well likely contributed to the activation.

 

Here we hypothesize these two large earthquake in 2003 enhanced the precursory slow slip in the fault of our interest, including its deeper extension, and explain the observed pre-seismic patterns. This hypothesis is in concordance with the GPS location measurement from several stations on and around the fault. The rate of distance shrinkage between the two stations, one being right on the fault, can only be well explained by assuming that the active site moved deeper at some point.

 

We fitted ETAS model to the observed seismic activity in each selected area and see if there are meaningful changing points of time, across which the seismicity being changed significantly in terms of AIC. The search for the changing points were done first by dividing the whole period either at points of known events, or at suspicious points with some systematical shifting of them, then to each divided period ETAS was refitted. Among these combined ETAS models, the best performed model was compared with the single ETAS without divisions and examined if its improvement was significant.  We finally checked these changing points are consistent with ∆CFFs.

 

3

講演者: 松浦 充宏 (統計数理研究所 予測発見戦略研究センター 地震予測解析グループ 特任教授)

日 時: 2009  8 14() 15:00-16:00

場 所: 統計数理研究所 第2セミナー室(330号室)

 

Title: Inversion of seismic and geodetic data to estimate tectonic stress fields in the Earth's crust

 

Abstract: 

The Earth's crust is macroscopically treated as a linear elastic body, but it includes a number of defects. The occurrence of inelastic deformation such as brittle fracture at the defects, which can be generally represented by moment tensor, brings about elastic deformation in the surrounding regions. Since the moment tensor is mathematically equivalent to the volume integral of stress release over the whole elastic region surrounding the source, we can quantitatively relate the centroid moment tensor (CMT) solutions of seismic events with a true but unknown tectonic stress field. On the basis of such an idea, we developed an inversion method to estimate tectonic stress fields from CMT data using Akaike's Bayesian information criterion (ABIC) [1]. We show the 3-D tectonic stress pattern in and around Japan, obtained by applying the CMT data inversion method to 15,000 seismic events within the magnitude range of 3.5-5.0 in the period of 1997-2007. The inverted 3-D stress pattern illuminates the present-day (Quaternary) complex tectonic motion of Japanese Islands. On the other hand, the crustal deformation observed through geodetic measurements is the sum of the inelastic deformation as source and the elastic deformation as effect. Representing the sources by moment density tensor distribution, we created a theory of physics-based strain analysis, and developed an inversion method to separately estimate 3-D elastic and inelastic strain fields from GPS data [2]. In this method, first, we determine the optimum distribution of moment density tensor from observed GPS array data by using Akaike's information criterion (AIC). Converting the optimum moment density tensor distribution with elastic compliance tensor, we can directly obtain 3-D inelastic strain fields. Given the optimum moment density tensor distribution, we can theoretically compute 3-D elastic strain fields. We applied the inversion method to GPS horizontal velocity data (1996-2000) in the Niigata-Kobe transformation zone, central Japan, and succeeded in estimating 3-D elastic and inelastic

strain rate fields separately.

 

References:

1. Terakawa, T. and M. Matsu'ura (2008), CMT data inversion using a Bayesian information criterion to estimate seismogenic stress fields, Geophys. J. Int.,
172, 674-685.

2. Noda, A. and M. Matsu'ura (2009), Physics-based GPS data inversion to estimate 3-D elastic and inelastic strain fields, Geophys. J. Int., submitted.

 

2

講演者: Dr. Zhuang, Jiancang ( 建倉) (統計数理研究所 モデリング研究系・助教)

日 時: 2009  7 31() 15:00-16:00

場 所: 統計数理研究所 第2セミナー室(330号室)

 

Title: Gambling with reputation: On scoring earthquake forecasts and predictions

 

Abstract: 

This seminar 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 magnitudes, this new scoring method compensates the risk that the forecaster has taken. Once a forecaster makes a prediction or forecast, he is assume to have bet some points of his reputations. The reference model, which plays the role of the house, determines how many reputations the forecaster can gain if he succeeds, according to a fair rule, and also takes away the reputations bet by the forecaster if he loses. From the viewpoints of both the reference model and the forecaster, the rule for rewarding and punishment is fair. This method is also extended to the continuous cases  of point process models, where the reputations bet 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.

 

1

講演者: Dr. Harte, David Director of Statistics Research Associates Limited (SRA), New Zealand

日 時: 2009  7  3() 15:00-16:00

場 所: 統計数理研究所 第2セミナー室(330号室)

 

Title: Using R for Modelling Marked Point Processes Indexed by Time

 

Abstract: 

A unified approach will be described for the fitting and analysis of a large class of point process models. The models discussed will be those that are indexed by time and contain additional marks. These include many of the point process models used for describing earthquake processes, e.g. stress release model, ETAS model, spatial ETAS model and the linked stress release model. By exploiting characteristics of their conditional intensity function, the log-likelihood function can be reduced to a more simple form. This simplified structure can also be used to calculate the residual process and perform simulations. The method involves "decomposing" these models into more elementary parts, and then utilising these parts in an object orientated manner within the R programming language. The longer term purpose in such an approach is to lessen programming effort involved in fitting such models. This should give us a better ability to more easily make modifications to existing models, and hence test alternative hypotheses. I will show R programming code for some fitted models to earthquake data.