Manual hierarchical clustering of regional geochemical data using a Bayesian finite mixture model

Interpretation of regional scale, multivariate geochemical data is aided by a statistical technique called “clustering.” We investigate a particular clustering procedure by applying it to geochemical data collected in the State of Colorado, United States of America. The clustering procedure partitions the field samples for the entire survey area into two clusters. The field samples in each cluster are partitioned again to create two subclusters, and so on. This manual procedure generates a hierarchy of clusters, and the different levels of the hierarchy show geochemical and geological processes occurring at different spatial scales. Although there are many different clustering methods, we use Bayesian finite mixture modeling with two probability distributions, which yields two clusters. The model parameters are estimated with Hamiltonian Monte Carlo sampling of the posterior probability density function, which usually has multiple modes. Each mode has its own set of model parameters; each set is checked to ensure that it is consistent both with the data and with independent geologic knowledge. The set of model parameters that is most consistent with the independent geologic knowledge is selected for detailed interpretation and partitioning of the field samples.     

基于聚类的极光形态分类的探索性研究

极光形态为研究日地物理过程提供了显著、直观和具有可识别性的特征。合理分类对研究各类极光现象与磁层动力学过程之间的关系尤为重要。极光形态分类机制的选择问题是极光有监督分类研究被主要诟病的问题之一。有监督分类实验中人工标记的工作量非常浩大,而且不能保证标记的准确性。更重要的是,高分类正确率只能说明自动分类符合人的认识,有监督分类结果无法验证分类机制的正确性。现有的分类机制是否为极光数据空间的真实划分,是否存在更为合理的分类机制都是我们应该探讨的问题。针对该问题,基于已有的全天空极光图像表征方法,引入聚类算法探究极光特征空间的结构,利用了9种聚类有效性函数选择适合极光数据的聚类个数。实验结果表明,对于从2003—2004年北极黄河站观测的全天空极光数据中随机选取的6 000幅极光图像,两类和四类的划分方式最为合适。两类的划分可以看作是分离度较好的极光类型,并且根据两类分布曲线呈现午前-午后双峰的分布特点,这一类极光可能是弧状极光。对于四类的情况,虽然通过肉眼观察无法用一幅典型的极光图像代表每一类,但是这些由聚类得出的极光类型具有各自的时间分布特点,这一结果从无监督的角度证明了极光类型在形态上是可分的。     

The space/time behaviour of dwelling burglars: Finding near repeat patterns in serial offender data

Whilst analysis of crime for tactical and strategic reasons within the criminal justice arena has now become an established need, predictive analysis of crime remains, and probably always will be, a goal to be desired. Opening a window on this over the last 2 decades, prominent research from academia has focused on the phenomenon of repeat victimisation and more recently ‘near repeat’ victimisation, both firmly grounded in the geography of crime. Somewhat limited to the establishment of near repeat behavioural patterns in whole area data, these can be utilised for crime prevention responses on a local scale. Research reported here however, explores the phenomenon through the examination of serial offending by individual offenders to establish if such spatio-temporal patterns are apparent in the spatial behavioural patterns of the individual burglar, and if so how they may be defined and therefore utilised on a micro rather than macro scale. It is hypothesised that offenders' responsible for more than one series of offences will display consistency across their crime series within time and distance parameters for their closest offences in space. Results improve upon current knowledge concerning near repeat offending being the actions of common offenders. Testing of the extracted data indicates that offenders maintain personal boundaries of ‘closeness’ in time and space even when actions are separated by significant time spans, creating stylised behavioural signatures appertaining to their use of and movement through space when offending.     

Studying Regions by Studying Firms*

This paper presents a method for inferring regional economic structure and prospects from key informant interviews. It describes assumptions which must be made and steps to be taken in moving from individuals to establishment, firm, and industry aggregations. A technique is offered for mapping core relationships among firms and other regional and external actors, and for aggregating firm-centered maps into industrial and regional maps. The mapping technique can be expanded to incorporate historicity and dynamic change.     

Rapid zonation of abrupt mass movement hazard: Part I. General principles

Hazards caused by mass movement cost many human lives and cause severe damage to property. Accurate zonation of such hazards provides an important tool for preventive measures. Previous approaches for mass movement hazard zonation are costly because they require large amounts of data, time and labor, and are only applicable to specific local areas. In this paper, a Rapid Zonation of Abrupt Mass-movement Hazard (RZAMH), applicable to large regions, is proposed. It involves the selection of appropriate zonation principles, routes, units, and indexes that can be used for the classification of reference groups, identification of matching groups of test sites, evaluation of blank test sites, and coalescence of sub-regions into specified zonation areas. The K-means clustering method is used in the classification processes. The applicability of the RZAMH approach to a large area implies that the number of reference sites required to build the reference groups is not of primary importance as long as the reference sites are representative. Therefore, for large areas, the RZAMH approach would be more economical than other conventional methods. The RZAMH approach is probably applicable to all abrupt mass movement hazards including rock falls, landslides, and debris flows.     

Physical and stochastic models of earthquake clustering

The phenomenon of earthquake clustering, i.e., the increase of occurrence probability for seismic events close in space and time to other previous earthquakes, has been modeled both by statistical and physical processes.From a statistical viewpoint the so-called epidemic model (ETAS) introduced by Ogata in 1988 and its variations have become fairly well known in the seismological community. Tests on real seismicity and comparison with a plain time-independent Poissonian model through likelihood-based methods have reliably proved their validity.On the other hand, in the last decade many papers have been published on the so-called Coulomb stress change principle, based on the theory of elasticity, showing qualitatively that an increase of the Coulomb stress in a given area is usually associated with an increase of seismic activity. More specifically, the rate-and-state theory developed by Dieterich in the ′90s has been able to give a physical justification to the phenomenon known as Omori law. According to this law, a mainshock is followed by a series of aftershocks whose frequency decreases in time as an inverse power law.In this study we give an outline of the above-mentioned stochastic and physical models, and build up an approach by which these models can be merged in a single algorithm and statistically tested. The application to the seismicity of Japan from 1970 to 2003 shows that the new model incorporating the physical concept of the rate-and-state theory performs not worse than the purely stochastic model with two free parameters only. The numerical results obtained in these applications are related to physical characters of the model as the stress change produced by an earthquake close to its edges and to the A and σ parameters of the rate-and-state constitutive law.     

Evaluation of earthquake potential along the Northern Anatolian Fault Zone in the Marmara Sea using comparisons of GPS strain and seismotectonic parameters

Seismotectonic parameters including the Gutenberg-Richter b-value and multifractal dimensions D₂ and D₁₅ of seismicity patterns (both spatial and temporal) were compared to GPS-derived maximum shear and dilatation strains measured in the Marmara Sea region of western Turkey along the Northern Anatolian Fault Zone (NAFZ). Comparisons of seismotectonic parameters and GPS-derived maximum shear and dilatation strain along the NAFZ in the vicinity of the 1999 M7.4 Izmit earthquake reveal a positive correlation (r = 0.5, p = 0.05) between average dilatation and the Gutenberg-Richter b-value. Significant negative correlation (r = − 0.56, p = 0.03 and r = − 0.56, p = 0.02) was also observed between the spatial fractal dimension D₂ and GPS-derived maximum geodetic and shear strain. This relationship suggests that, as maximum geodetic and shear strains increase, seismicity becomes increasingly clustered.Anomalous interrelationships are observed in the Marmara Sea region prior to the Izmit event along a bend in the NAFZ near the eastern end of the Marmara Sea known as the Northern Boundary Fault (NBF). An asperity is located near the northwest end of the NBF. Along the 50-km length of the NBF, GPS strains become slightly compressive. The correlation between b-value and GPS-derived dilatation suggests that regions in compression have increased probability of larger magnitude rupture. The NBF appears to serve as an impediment to the transfer of strain from east to west along the NAFZ. Recurrence times for large earthquakes along the NBF are larger than in surrounding areas. Temporal clustering of seismicity in the vicinity of the NBF may represent foreshocks of an impending rupture.     

单键群方法与昆仑山—阿尔金山弧型构造顶部地震时空群集特征

本文以单键群分析方法为基础，进行以下研究；１．对一个地区的地震目录进行分析得到特征键开，并用其对该区地震的时空群集性和离散性进行分析，进而建立分类子目录，以便作针对性的细致处理；２．定义了几个描述ＳＬＣ构架特点的参数，发展和实现了按时间逐段滑移计算ＳＬＣ构架和这些参数的办法及程序，考察这些参数随时间的变化；３．用以上各软件处理昆仑山阿尔金山弧型顶部区域的地震目录，得到了一些有意义的结果。     

Multi-resolution clustering analysis and 3-D visualization of multitudinous synthetic earthquakes

We use modern and novel techniques to study the problems associated with detection and analysis of multitudinous seismic events, which form the background for isolated great earthquakes. This new approach involves multivariate analysis of low and large magnitude events recorded in space over a couple of centuries in time. We propose here the deployment of the clustering scheme both for extracting small local structures and large-scale trends in synthetic data obtained from four numerically simulated models with: uniform properties (U), a Parkfield-type asperity (A), fractal brittle properties (F), and multi-size-heterogeneity fault zone (M). The mutual nearest neighbor (mnn) clustering scheme allows for extraction of multi-resolutional seismic anomalies in both the spatio-temporal and multi-dimensional feature space. We demonstrate that the large earthquakes are correlated with a certain pathway of smaller events. Visualization of the anomalies by using a recently introduced visualization package Amira reveals clearly the spatio-temporal relationships between clusters of small, medium and large earthquakes, indicating significant stress relaxation across the entire fault region. We demonstrate that this mnn scheme can extract distinct clusters of the smallest events, which precede and follow a singularly large magnitude earthquake. These clusters form larger spatio-temporal structures comprising a series of large earthquakes. The link between the large and medium magnitude events is not so clearly understood. Short-ranged correlations are dominated by strong spatio-temporal anomalies, thus reflecting the global seismic properties of the entire fault zone.Electronic Supplementary Material Supplementary material is available for this article if you access the article at . A link in the frame on the left on that page takes you directly to the supplementary material.