Koichi Katsura

LIKELIHOOD ANALYSIS OF SPATIAL INHOMOGENEITY FOR MARKED POINT PATTERNS

An objective method is developed for estimations of both spatial intensity of the point locations and spatial variation of a characteristic parameter of the distributions for the attached marks. Its utility is demonstrated by means of analyses of seismological and ecological data sets.

Modelling heterogeneous space–time occurrences of earthquakes and its residual analysis

Earthquake intensities are modelled as a function of previous activity whose specific form is based on established empirical laws in seismology, but whose parameter values can vary from place to place. This model is used for characterizing regional features of seismic activities in and around Japan, and also for exploring regions where the actual seismicity rate systematically deviates from that of the modelled rate. Copyright 2003 Royal Statistical Society.

Empirical Bayes Age-Period-Cohort Analysis of Retrospective Incidence Data

We analyse the (age, time)-specific incidence of diabetes based on retrospective data obtained from a prevalent cohort only including survivors to a particular date. From underlying point processes with intensities corresponding to the (age, time)-specific incidence rates the observed point pattern is assumed to be generated by an independent thinning process with parameters (assumed known) depending on population density and survival probability to the sampling date. A Bayesian procedure is carried out for the optimal adjustment and comparison of isotropic and anisotropic smoothing priors for the intensity functions, as well as for the decomposition of the intensity on the (time, age) Lexis diagram into the three factors of age, period and cohort.

Fast likelihood computation of epidemic type aftershock‐sequence model

The Epidemic Type Aftershock-Sequences (ETAS) model is a point process representing the temporal activity of earthquakes in a certain geophysical region. A method for fast and accurate computation of the likelihood is suggested for the ETAS model. Double sums of variables in the logarithm of the likelihood function with respect to the earthquake occurrence data is reduce to a single sum by using the recursive relation of the integrands in the Gamma transformation of the modified Omori functions. Then the integral is computed in unusually high accuracy by using the Double Exponential transformation followed by an application of the trapezoidal rule with an equal mesh size. The computing run time is greatly improved to be proportional to the number of recorded earthquakes N compared to the order of N² for the naive computation method. The present numerical procedures put the parameter estimation of the ETAS model to practical use in large number of occurrence records.

Point-Process Models with Linearly Parametrized Intensity for Application to Earthquake Data

It is demonstrated that linear parametrization of the conditional intensity provides systematic classes of flexible models which are reasonably useful for calculating maximum likelihoods. To exemplify the modelling, seismic activity around Canberra is decomposed into components of evolutionary trend, clustering and periodicity. The causal relationship between earthquake sequences from two seismic regions is also analysed for a certain Japanese earthquake data set. Some technical aspects of the modelling and calculations are descrnbed.

Comparing foreshock characteristics and foreshock forecasting in observed and simulated earthquake catalogs

In this paper, we compare the empirical results regarding foreshocks obtained from the Japan data with results for synthetic catalogs in order to clarify whether or not the corresponding results are consistent with the description of the seismicity by a superposition of background activity and epidemic-type aftershock sequence (ETAS) models. This question is important, because it is still controversially discussed whether the nucleation process of large earthquakes is driven by seismically cascading (ETAS type) or by aseismic accelerating processes. To explore the foreshock characteristics, we first applied the same clustering algorithms to real and synthetic catalogs and analyzed the temporal, spatial, and magnitude distributions of the selected foreshocks. Most properties are qualitatively the same in the real data and in synthetic catalogs. However, we find some quantitative differences particularly in the temporal acceleration, spatial convergence, and magnitude dependence, which also depend on the assumed synthetic catalogs. Furthermore, we calculated forecast scores based on a single-link cluster algorithm which could be appropriate for real-time applications. We find that the Japan Meteorological Agency catalog yields higher scores than all synthetic catalogs and that the ETAS models having the same magnitude sequence as the original catalog performs better (more close to the reality) than ETAS models with randomly picked magnitudes. We also find that the ETAS model that takes account of the triggering effect by small earthquakes below threshold magnitude performs more closely to the reality.

Correction of earthquake location estimation in a small-seismic-array system

An array of regularly spaced seismic stations can estimate the location of a distant earthquake using arrival times at the stations of seismic waves generated by the earthquakes. However, the accuracy decreases as the distance to the epicentre of the earthquake from the array increases. This paper is concerned with the modification of the estimated location by removing its bias which is locally systematic but globally complex, reflecting the structure of the Earths interior. Spline surfaces are used to model such biases. Then a Bayesian procedure is carried out not only to tune the smoothness constraints but also to select the best combination among various sums of squares of differently weighted residuals and various roughness penalties for the smoothing. Using the estimated splines of the posterior mode, the newly determined epicentre locations are transformed to confirm its practical utility. Residual distributions show that our procedure improves the modification by the conventional procedure. A spatial pattern of the residuals reveals some geophysical characteristics.

Exploring Magnitude Forecasting of the Next Earthquake

Almost all forecasting of the magnitude of the next earthquake has assumed the same independent probability distribution, such as the Gutenberg–Richter law, with the same b-value (b = 0.9 in Japan region standard), throughout an earthquake sequence. Identifying a broadened forecasting procedure for general models of space-time magnitude sequences may enhance the information gain of earthquake forecasts. This manuscript explores and evaluates three such models for earthquake magnitude forecasting. The first model forecasts magnitudes by location-dependent b-values; the second model forecasts magnitudes by space-time weighted moving average of the short-term past and neighboring magnitude sequence; and the third forecasts based on short-term tightness of clustering among earthquakes. The forecasting performances of these models estimated in a learning periods are shown at each time in the CSEP Japan testing period, from November 1, 2008 till October 31, 2017. Except for the last example, the forecasts do not outperform the baseline G–R law with the b value of 0.9. We discuss the reasons by some residual analysis.