Multifractal and Chaotic Analysis of Vrancea (Romania) Intermediate-depth Earthquakes: Investigation of the Temporal Distribution of Events

The Vrancea seismic region contains an isolated cluster of events beneath the Carpathian Arc Bend in Romania, dipping to about 200 km depth. Seismic activity mainly occurs at intermediate depths (h > 60 km). The main goal of the paper is to perform an in-depth, complex analysis of the occurrence times of these intermediate-depth events. We also try to show the versatility of the methods used to characterize different aspects of the seismicity evolution and to offer a user-friendly software toolbox to do most of the related computations. The earthquake catalog used in this study spans from 1974 to 2002 and includes only the intermediate-depth events. In the first part of the paper, we analyze the multifractal characteristics of the temporal distribution of earthquakes. The study reveals two distinct scaling regimes. At small scales we found a clear nonhomogeneous, multifractal pattern, while at large scales the temporal distribution of events shows a monofractal, and close to Poissonian (random), behavior. The multifractal behavior at small scales (minutes-hours) is shown to be clearly an effect of the short aftershock sequences that occurred after some major Vrancea earthquakes. In the second part of the paper we analyze whether our temporal series shows a persistent (or anti-persistent) long-term behavior, by using the Detrended Fluctuation Analysis (DFA) method. The results suggest that the analyzed temporal series of Vrancea earthquakes is a non-correlated process. In part three of the paper we seek to determine whether the dynamics of our earthquake system (described by the occurrence time of Vrancea earthquakes) is deterministically chaotic, deriving from a rather simple evolution law, or whether it is stochastic and is generated by a system that possesses many degrees of freedom. The results suggest that our signal is stochastic (probably does not possess an attractor). The limited time-span of the catalog and the analysis performed in this paper cannot rule out the emergence of an interesting, quasi-deterministic and low-dimensional structure in the case of major Vrancea earthquakes.Acknowledgement One of the authors (BE) is grateful to the Japanese Ministry of Education for providing him a Monbusho scholarship for studying in DPRI, Kyoto University. We thank Z.R. Struzik, M Holschneider, J. Mori and D. Kaplan for their useful comments, and acknowledge the support of the staff of DPRI, Kyoto University and the National Inst. for Earth Physics, Bucharest. We thank the two reviewers, M.B. Geilikman and M. Anghel, for their useful suggestions which improved the quality of this work.     

Collective resonant phenomena on small bodies in the solar system

For both asteroids and meteor streams, and also for comets, resonances play a major role for their orbital evolutions but on different time scales. For asteroids both mean motion resonances and secular resonances not only structure the phase space of regular orbits but are mainly at the origin for the inherent chaos of planet crosser objects.For comets and their chaotic routes temporary trapping into orbital resonances is a well known phenomenon. In addition for slow diffusion through the Kuiper belt resonances are the only candidates for originating a slow chaos.Like for asteroids, resonances with Jupiter play a major role for the orbital evolution of meteor streams. Crossing of separatrix like zones appears to be crucial for the formation of arcs and for the dissolution of streams. In particular the orbital inclination of a meteor stream appears to be a critical parameter for arc formation. Numerical results obtained in an other context show that the competition between the Poynting-Robertson drag and the gravitational interaction of grains near the 2/1 resonance might be very important in the long run for the structure of meteor streams.     

A sequential sparse polynomial chaos expansion using Bayesian regression for geotechnical reliability estimations

Polynomial chaos expansions (PCEs) have been widely employed to estimate failure probabilities in geotechnical engineering. However, PCEs suffer from two deficiencies: (a) PCE coefficients are solved by the least-square minimization method which easily causes overfitting issues; (b) building a high order PCE is often computationally expensive. In order to overcome the aforementioned drawbacks, the Bayesian regression technique is employed to evaluate PCE coefficients, which not only provides a sparse solution but also avoids overfitting. With the aid of the predictive means and variances given by Bayesian analysis, a learning function is proposed to sequentially select the most informative samples that are critical to build a PCE. This sequential learning scheme can highly enhance the computational efficiency of PCEs. Besides, importance sampling (IS) is incorporated into the sequential learning (SL)-PCEs to deal with geotechnical problems with small failure probabilities. The proposed method of SL-PCE-IS is applied to three illustrative examples, which shows that the improved PCE method is more effective and efficient than the common PCEs method, leading to accurate estimations of small failure probabilities using fewer training samples.     

时空序列预测误差的敏感性试验分析

利用33模Lorenz系统得到的"理想"混沌时空序列,作为时空混沌序列"发生器".通过状态空间重构,建立"场时间序列"局域近似预测模型,对资料空间分辨率,资料的长度、噪音,以及模型的参数选取等因素进行敏感性试验分析,了解时空混沌序列预测中误差产生和增长的一些影响因素.得到以下初步结论:对于理想混沌时空序列(33模Lorenz系统)而言,与系统相适应的资料空间分辨率和较长的资料长度都将会提高预测精度;可预报时效与资料长度之间近似服从指数关系.另外,在建立预测模型时,适当的邻近点数目,以及采用二阶映射关系和迭代法都可以有效地改善预测精度.对于加入噪音的混沌时间序列,通过"场时间序列"的局域近似方法和4阶自回归方法的预测试验的对比表明,前者显示了更强的抗"干扰"能力.以上结论可以有分析地应用于短期气候预测中.     

岩性储集层的混沌识别技术研究

本文从动力学系统原理出发,论述了混沌理论中的李指数法,并从地震剖面上提取李指数,并应用李指数来区分和识别储集层的岩性变化特征和含油气性。计算和应用研究表明,李指数随着相空间维数的增加容易趋于稳定值,这就使它预测地震序列横向变化的可靠性增大,这正是李指数预测岩性和含油气性的一个优越性。成功地应用实例表明,混沌识别技术是岩性储集层的一种有效识别技术,并具有广阔的应用前景。     

Prediction of weather parameters on a very short time scale by an Auto Regressive process for aviation flight planning

Forecasting weather parameters such as temperature and pressure with a reasonable degree of accuracy three hours ahead of the scheduled departure of an aircraft helps economic and efficient planning of aircraft operations. However, these two parameters exhibit a high degree of persistency and have nonstationary mean and variance at sub-periods (i.e. at 0000, 0300, 0600,…, 2100UTC). Hence these series have been standardised (to have mean 0 and variance 1) and thereafter seasonal differenced (lag 8) to achieve almost near stationarity. An attempt has been made to fit the standardised and seasonal differenced series of Chennai (a coastal station) and Trichy (an inland station) airport into an Auto Regressive (AR) process. The model coefficients have been estimated based on adaptive filter algorithm which uses the method of convergence by the steepest descent. The models were tested with an independent data set and diagnostic checks were made on the residual error series. An independent estimation of fractal dimension has also been made in this study to conform the number parameters used in the AR processes. The models contemplated in this study are parsimonious and can be used to forecast surface temperature and pressure.     

Polynomial chaos expansion and response surface method for nonlinear modelling of reference evapotranspiration

The feasibility of polynomial chaos expansion (PCE) and response surface method (RSM) models is investigated for modelling reference evapotranspiration (ET₀). The modelling results of the proposed models are validated against the M5 model tree and multi-layer perceptron neural network (MLPNN) methods. Two meteorological stations, Isparta and Antalya, in the Mediterranean region of Turkey, are inspected. Various input combinations of daily air temperature, solar radiation, wind speed and relative humidity are constructed as input attributes for the ET₀. Generally, the modelling accuracy is increased by increasing the number of inputs. Including wind speed in the model inputs considerably increases their accuracy in modelling ET₀. Mean absolute error (MAE), root mean square error (RMSE), agreement index (d) and Nash-Sutcliffe efficiency (NSE) are used as comparison criteria. The PCE is the most accurate model in estimating daily ET₀, giving the lowest MAE (0.036 and 0.037 mm) and RMSE (0.047 and 0.050 mm) and the highest d (0.9998 and 0.9999) and NSE (0.9992 and 0.9996) with the four-input PCE models for Isparta and Antalya, respectively.     

大气和植被生态及土壤系统水文过程相互作用的一些研究

利用我国测站的降水资料、卫星测得的OLR和高云量资料、SST和137°E次表层海温资料以及NCEP/NCAR再分析资料,分析了东亚夏季风的爆发和北进的年际变化特征及其与热带西太平洋热状态的关系.分析结果表明:当春季热带西太平洋处于暖状态,菲律宾周围对流活动强,在这种情况下,南海上空对流层下层有气旋性距平环流,西太平洋副热带高压偏东,从而使得南海夏季风爆发早;并且,当夏季热带西太平洋也处于暖状态,菲律宾周围对流活动也很强,在这种情况下,西太平洋副热带高压北进时,在6月中旬和7月初存在明显的突跳,从而使得东亚季风雨带在6月中旬明显由华南北跳到江淮流域,并于7月初由江淮流域北跳到黄河流域、华北和东北地区.这将引起江淮流域和长江中、下游夏季风降水偏少,并往往发生干旱,而黄河流域、华北和东北地区的夏季降水正常或偏多.相反,当春季热带西太平洋处于冷状态,菲律宾周围对流活动弱,在这种情况下,南海上空对流层下层有反气旋性距平环流,西太平洋副热带高压偏西,从而使得南海夏季风爆发晚;并且,当夏季热带西太平洋也处于冷状态,菲律宾周围对流活动也很弱,在这种情况下,西太平洋副热带高压北进时,在6月中旬或7月初向北突跳并不明显,而是以渐进式向北移动,从而使得东亚季风雨带一直维持在长江流域和淮河流域.这将引起此两流域夏季风降水偏多,并往往发生洪涝,而黄河流域、华北和东北地区的夏季降水偏少,发生干旱.作者还从非线性多平衡态动力理论说明了菲律宾周围对流活动强弱对西太平洋副热带高压北进时以突跳或渐进式向北移动起到重要作用.     

边坡可靠度分析的非侵入式随机有限元法

提出基于非侵入式随机有限元法的边坡可靠度分析方法,并编写计算程序NISFEM。采用有限元滑面应力法计算边坡安全系数,将Hermite随机多项式展开与SIGMA/W和SLOPE/W模块有机结合实现边坡可靠度非侵入式随机分析。根据随机多项式展开系数,给出边坡安全系数前4阶统计矩（均值、标准差、偏度和峰度）和Sobol指标解析表达式,并采用Sobol指标进行边坡可靠度参数敏感性分析。最后,以均质土坡可靠度问题为例,证明该方法在边坡可靠度分析中的有效性。结果表明,边坡可靠度分析的非侵入式随机有限元法能够有效地考虑边坡变形对边坡可靠度的影响,计算效率远远高于蒙特卡罗模拟方法（MCS）,是解决复杂边坡可靠度问题一种有效地分析手段;黏聚力和内摩擦角变异性对边坡安全系数前四阶统计矩具有明显的影响,重度变异性对安全系数前4阶统计矩几乎没有影响;抗剪强度参数间负相关性对边坡安全系数均值几乎没有影响,但对安全系数标准差、偏度和峰度均有明显的影响。此外,随着抗剪强度参数间负相关性的增加,边坡安全系数由近似正态分布逐渐变为明显的非正态分布。     

庐山风景区功能演化的混沌特征及其启示

在构建风景区演化周期、混沌模型的基础上,对庐山风景区功能演化的混沌特征进行了实证研究。庐山风景区主要经历了古代旅游风景名胜区的探索、形成、发展、成熟期和近现代大众旅游的度假、观光、科考旅游地的探索、形成、发展期,其功能演化体现了分形、初始条件与蝴蝶效应、混沌边缘、间歇变换、同步锁模和锁定效应等混沌特征,说明风景区演化是周期和非周期的相对统一。现阶段呈现的旅游消费需求不稳定、景区城市化、行政管理体制不顺、景区发展与社区矛盾等是庐山发展的混沌要素,控制这些混沌要素,有助于促进景区健康发展。