Earthquake Forecasting Using Hidden Markov Models

This paper develops a novel method, based on hidden Markov models, to forecast earthquakes and applies the method to mainshock seismic activity in southern California and western Nevada. The forecasts are of the probability of a mainshock within 1, 5, and 10 days in the entire study region or in specific subregions and are based on the observations available at the forecast time, namely the interevent times and locations of the previous mainshocks and the elapsed time since the most recent one. Hidden Markov models have been applied to many problems, including earthquake classification; this is the first application to earthquake forecasting.     

Recurrence Interval Statistics of Cellular Automaton Seismicity Models

The recurrence interval statistics for regional seismicity follows a universal distribution function, independent of the tectonic setting or average rate of activity (Corral, 2004). The universal function is a modified gamma distribution with power-law scaling of recurrence intervals shorter than the average rate of activity and exponential decay for larger intervals. We employ the method of Corral (2004) to examine the recurrence statistics of a range of cellular automaton earthquake models. The majority of models has an exponential distribution of recurrence intervals, the same as that of a Poisson process. One model, the Olami-Feder-Christensen automaton, has recurrence statistics consistent with regional seismicity for a certain range of the conservation parameter of that model. For conservation parameters in this range, the event size statistics are also consistent with regional seismicity. Models whose dynamics are dominated by characteristic earthquakes do not appear to display universality of recurrence statistics.     

Continuous Hidden Markov Models: Application to automatic earthquake detection and classification at Las Canãdas caldera,Tenerife

A possible interaction of (volcano-) tectonic earthquakes with the continuous seismic noise recorded in the volcanic island of Tenerife was recently suggested. Also recently the zone close to Las Canadas caldera shows unusual high number of near (< 25 km), possibly volcano-tectonic, earthquakes indicating signs of reawakening of the volcano putting high pressure on the risk analyst. Certainly for both tasks consistent earthquake catalogues provide valuable information and thus there is a strong demand for automatic detection and classification methodologies generating such catalogues. Therefore we adopt methodologies of speech recognition where statistical models, called Hidden Markov Models (HMMs), are widely used for spotting words in continuous audio data. In this study HMMs are used to detect and classify volcano-tectonic and/or tectonic earthquakes in continuous seismic data. Further the HMM detection and classification is evaluated and discussed for a one month period of continuous seismic data at a single seismic station. Being a stochastic process, HMMs provide the possibility to add a confidence measure to each classification made, basically evaluating how “sure” the algorithm is when classifying a certain earthquake. Moreover, this provides helpful information for the seismological analyst when cataloguing earthquakes. Combined with the confidence measure the HMM detection and classification can provide precise enough earthquake statistics, both for further evidence on the interaction between seismic noise and (volcano-) tectonic earthquakes as well as for incorporation in an automatic early warning system.     

A Hidden Markov Model Based Tool for Geophysical Data Exploration

--Unsupervised learning techniques provide a way of investigating scientific data based on automated generation of statistical models. Because these techniques are not dependent on a priori information, they provide an unbiased method for separating data into distinct types. Thus they can be used as an objective method by which to identify data as belonging to previously known classes or to find previously unknown or rare classes and subclasses of data. Hidden Markov model based unsupervised learning methods are particularly applicable to geophysical systems because time relationships between classes, or states of the system, are included in the model. We have applied a modified version of hidden Markov models which employ a deterministic annealing technique to scientific analysis of seismicity and GPS data from the southern California region. Preliminary results indicate that the technique can isolate distinct classes of earthquakes from seismicity data.     

Seismicity Models of Moderate Earthquakes in Kanto, Japan Utilizing Multiple Predictive Parameters

We construct a single hazard function from multiple predictive parameters independently developed for moderate earthquakes in Kanto, Japan, during a learning period from 1990 to 1999, and applied to a testing period from 2000 to 2005. Here, we consider as predictive parameters the a and b values of the Gutenberg–Richter relation, the ν value (change in b value), and the Every Earthquake a Precursor According to Scale (EEPAS) model rate. To study the correlations among the parameters, we prepare two groups of space–time coordinate sets for assessment, namely the background and conditional groups selected from the learning period. The background group contains ten thousand sets of coordinates randomly selected from the space–time volume of our study. The conditional group contains 33 sets of space–time coordinates corresponding to the epicenters of the target earthquakes (M ≥ 5.0) just before their times of occurrence. Each parameter for the background group is transformed so that its distribution conforms to the standard Normal function. The mean and variance of the conditional distribution is then estimated after applying the same transformation to the conditional group. Using the means and variances of b values, ν values and EEPAS rates and the correlation matrices in the background and conditional distributions, we construct a combined hazard function following the procedure developed for normally distributed parameters. The information gain per event (IGpe) of the new hazard function is 0.26 and 0.3 units larger than that of the EEPAS rate for the learning and testing period, respectively. The R-test confirms the statistical significance of the difference in the IGpe value for the testing period.     

加卸载响应比在Poisson模型下的随机分布

本文在地震的发生时间服从Ｐｏｉｓｓｏｎ过程,而地震震级服从Ｇｕｔｅｎｂｅｒｇ－Ｒｉｃｈｔｅｒ关系的前提下,对不同定义的加卸载响应比Ｙ值的随机分布进行了探讨。结果表明：当在计算窗口的地震发生的期望数目较大（〉４０）时,Ｙ１￣Ｙ５值的分布基本稳定,出现高加卸载响应比的概率极低。然而当计算窗口的地震期望数目过小时,Ｙ２￣Ｙ５值则变得不太稳定。也就是说,服从Ｐｏｉｓｓｏｎ过程的地震序列,在计算窗口的地震期     

Rapid computation of directional wellbore drawdown in a confined aquifer via Poisson resummation

We have derived a rapidly computed analytical solution for drawdown caused by a partially or fully penetrating directional wellbore (vertical, horizontal, or slant) via Green's function method. The mathematical model assumes an anisotropic, homogeneous, confined, box-shaped aquifer. Any dimension of the box can have one of six possible boundary conditions: 1) both sides no-flux; 2) one side no-flux – one side constant-head; 3) both sides constant-head; 4) one side no-flux; 5) one side constant-head; 6) free boundary conditions. The solution has been optimized for rapid computation via Poisson Resummation, derivation of convergence rates, and numerical optimization of integration techniques. Upon application of the Poisson Resummation method, we were able to derive two sets of solutions with inverse convergence rates, namely an early-time rapidly convergent series (solution-A) and a late-time rapidly convergent series (solution-B). From this work we were able to link Green's function method (solution-B) back to image well theory (solution-A). We then derived an equation defining when the convergence rate between solution-A and solution-B is the same, which we termed the switch time. Utilizing the more rapidly convergent solution at the appropriate time, we obtained rapid convergence at all times. We have also shown that one may simplify each of the three infinite series for the three-dimensional solution to 11 terms and still maintain a maximum relative error of less than 10⁻¹⁴.     

Use of Statistical Models to Analyze Periodic Seismicity Observed for Clusters in the Kanto Region, Central Japan

—A periodic pattern of seismicity has been reported for the Kinugawa cluster in the Kanto region, where several earthquake clusters are observed at depths between 40 and 90 km. To analyze this periodicity, statistical studies are performed for the Kinugawa cluster together with eight other clusters. Hypocentral parameters of the earthquakes with magnitudes 4.5 and larger for the period between 1950 and 1995 are taken from the JMA catalogue. The simple sinusoidal function, the exponential of sinusoidal function and the stress release model are applied as the intensity function. Model parameters are determined by the maximum likelihood method and the best model for each cluster is selected by using the Akaike Information Criterion (AIC). In six cases the sinusoidal model or the exponential of the sinusoidal model is selected as the best option and achieves AIC reductions of values between 2.4 and 13.2 units from the simple Poisson model. The stress release model is selected for two clusters. The three clusters, the Kinugawa, Kasumigaura, and Choshi clusters, have a similar optimal period of about 10 years, and align in the northwest–southeast direction at a similar depth range of 40 to 70 km. A model modified from the stress release model is applied to the three clusters so to analyze the relationship among them. In the modified model, an earthquake occurrence in one zone increases the stress in the other zone, which is different from the original stress release model which assumes a linear increase with time. Applying the modified model to the Kinugawa cluster, an AIC reduction from the Poisson model is significantly larger than the value obtained with the sinusoidal model. This suggests that the periodic seismicity observed for the Kinugawa cluster can be explained with the more comprehensive model than the sinusoidal model.     

The Random Distribution of the Loading and Unloading Response Ratio Under the Assumptions of Poisson Models

This paper discussed the random distribution of the loading and unloading response ratio(LURR) of different definitions(Y_1～Y_5)using the assumptions that the earthquakes occurfollowing the Poisson process and their magnitudes obey the Gutenberg-Richter law.Theresults show that Y_1～Y_5 are quite stable or concentrated when the expected number of eventsin the calculation time window is relatively large(>40);but when this occurrence ratebecomes very small,Y_2～Y_5 become quite variable or unstable.That is to say,a high value ofthe LURR can be produced not only from seismicity before a large earthquake,but also from arandom sequence of earthquakes that obeys a Poisson process when the expected number ofevents in the window is too small.To check the influence of randomness in the catalogue tothe LURR,the random distribution of the LURR under Poisson models has been calculated bysimulation.90%,95% and 99% confidence ranges of Y_1 and Y_3 are given in this paper,which is helpful to quantify the random influe