Statistical analysis and long-term prediction of seismicity for linear zones

The model of the Poisson point process is too vague for earthquake locations in space and time: earthquakes tend to cluster in middle distances and to repulse in large ones. The Poisson point model with variable density makes it possible to describe the tendency for clustering but does not reveal the periodicity of clusters. The author proposes the point-process model where locations of points are determined not by densities of point distribution, but by densities of interpoint differences distribution. In the model, a latent periodicity is revealed and used for prediction of a point process. In 1983, the point-process model prediction was made for the Kuril Islands for 1983–1987 and two signs of danger in time and location were determined. Then they were confirmed by strong earth-quakes. In 1989, a similar prediction was made for North Armenia. The Spitak earthquake in 1988 is clearly seen from the data of previous earthquakes.     

Estimating work-magnitude associations in earth surface processes

Magnitude-frequency concepts in earth surface processes have found widespread application following the publication of the well-known paper Wolman and Miller. Of particular interest in such studies is the determination of those event magnitudes which make the most important long-term contributions to the total work of a given process. However, there has been little discussion to date concerning an appropriate estimator of the parameter , where is the long-term work achieved by events within a specified magnitude range, expressed as a proportion of the long-term work achieved by events of all magnitudes. The estimation of is straightforward for the time-independent case where short-duration events occur randomly in time, and event magnitudes are independent random variables from a common distribution. For this model, exists as a true parameter which can be estimated by , where is the sample proportion of work contributed by events within the specified magnitude range. This estimator is biased, but it is almost median-unbiased for large samples. An approximate expression for var ( ) can be obtained from standard results. A similar approach to the estimation of can be applied to estimating the long-term work contribution of the largest events in consecutiveR-year periods. An example is presented using riverbank erosion data. Within the constraints of the time-independent model, the estimation procedure is quite general and can be applied with or without prior specification of the probability distribution of event magnitudes. In some situations, estimation can also be achieved indirectly by using a sample of the causal events which generate the individual work events. This indirect estimation is particularly simple if work magnitude is a power transformation of causal magnitude, and the distribution of causal event magnitudes can be approximated by a lognormal distribution or a Weibull distribution. The relative work achieved by events within ever-smaller magnitude ranges leads in the limit to the work intensity function,P(y). A plot of this function shows the relative importance ofy—magnitude events with respect to their long-term work contributions. Estimation ofP(y) is carried out by first fitting a probability distribution to a sample of event magnitude data. The functionP(y) is unimodal with respect to the following probability distributions of event magnitudes: lognormal, Weibull, unimodal beta, gamma, and inverse Gaussian. A lognormal distribution of event magnitudes produces the maximum work intensity at the lognormal median. In a strict mathematical sense, the long-term work contribution of very large and very small events is insignificant. However, little can be deduced concerning the pattern of work intensity between these two extremes. In particular, there appears no reason to suppose that the maximum work intensity will coincide with work magnitudes classified as intermediate.     

A statistical method for detecting spatiotemporal co-occurrence patterns

Spatiotemporal co-occurrence patterns (STCOPs) are subsets of Boolean features whose instances frequently co-occur in both space and time. The detection of STCOPs is crucial to the investigation of the spatiotemporal interactions among different features. However, prevalent STCOPs reported by available methods do not necessarily indicate the statistically significant dependence among different features, which is likely to result in highly erroneous assessments in practice. To improve the reliability of results, this paper develops a statistical method to detect STCOPs and discern their statistical significance. The proposed method detects STCOPs against the null hypothesis that the spatiotemporal distributions of different features are independent of each other. To construct the null hypothesis, suitable spatiotemporal point-process models considering spatiotemporal autocorrelation are employed to model the distributions of different features. The performance of the proposed statistical method is assessed by synthetic experiments and a case study aimed at identifying crime patterns among multiple crime types in Portland City. The experimental results demonstrate that the proposed method is more effective for detecting meaningful STCOPs than the available alternative methods.     

A Point-process Analysis of the Matsushiro Earthquake Swarm Sequence: The Effect of Water on Earthquake Occurrence

Temporal characteristics of the famous Matsushiro earthquake swarm were investigated quantitatively using point-process analysis. Analysis of the earthquake occurrence rate revealed not only the precise and interesting process of the swarm, but also the relation between pore water pressure and the strength of the epidemic effect, and the modified Omori-type temporal decay of earthquake activity. The occurrence rate function (t) for this swarm is represented well aswhere f(t) represents the contribution of the swarm driver, which was the erupting water from the deep in this case, and the second term represents an epidemic effect of the modified Omori type. Based on changes in the form of f(t), this two-year long swarm was divided into six periods and one short transitional epoch. The form of f(t) in each period revealed the detail of the water erupting process. In the final stage, f (t) decayed according to the modified Omori-formula form, while it decayed exponentially in the brief respite of the water eruption in the fourth period. When an exponential decay of swarm activity is observed, we have to be cautious of a sudden restart of the violent activity. The epidemic effect is stronger when the pressure of the pore water is higher. Even when the pressure is not high, the p value in the epidemic effect is small, when there is plenty of pore water. However, the epidemic effect produced about a quarter of the earthquakes even though there was not much pore water in the rocks.