北部湾地震的动力学参数与应力场

从震源机制和动力学参数方面讨论了北部湾地震的震源应力场，结果表明，主震是在北东东向构造的作用下发生的，同时计算了动力学参数如破裂长度，地震矩，应力降，破裂面积和平均位错等，并探讨了非线性地震与较大余震的关系。     

用算法复杂性分析地震活动演化特征

以非线性动力学理论为依据，用非线性动力学中分析时间序列的算法复杂性研究地震活动规律和构成地震活动复杂现象的动力学特征。提出了按震级计算的地震算法复杂性ＡＣ值和按发震时间计算的地震算法复杂性ＴＡＣ值。选取１９７０年以来中国东部ＭＳ≥６．０地震，西部ＭＳ≥６．５的强震，对ＡＣ值和ＴＡＣ值进行回顾性分析；利用１９７０￣１９８０年大华北地区展望性空区识别结果，对ＡＣ值和ＴＡＣ值进行展望性检验分析，并进行了     

应用非线性理论和方法探讨地震与地震前兆的复杂性

本文应用非线性理论和方法讨论了产生地震现象的动力学机制、地震与地震前兆的复杂性,并就地震本身表现出来的自相似层次结构、分形与分维的非线性整体特征以及产生分形结构的重要物理机制,给出了一组与地震分维有关的公式。     

大陆地震的动力学模型研究

应用非线性动力学模型，以大陆构造构体为参照对象，对大陆地震的成组孕育和发生过程进行模拟研究，通过对６×８弹簧－滑块－阻尼器组合单元非线性动力学模型的理论计算及其结果的分析，得到了一系列与实际地震较类似的人工地震图像，如模型中的地震活动在时间上有轮回怀，在地点上有条带性，并在不同轮回中有条过移的现象。模型中应力变化十分复杂，但仍能为预测地震提供概略性的信息。     

粘性力在地形变动力学模型演化过程中的作用

本文分别利用Ｌｙａｐｕｎｏｖ指数方法和特征值方法，对摸拟地震过程的线性粘弹性动力学模型的稳定性进行了分析，并讨论了粘性力在地形变动力学系统演化过程中的作用，采用Ｒｕｎｇｅ－Ｋｕｔｔａ格式的Ｍｅｒｓｏｎ修改方法模拟了在不同粘性系数时线性和非线性动力学系统的演化过程，得出了一些有意义的结论和认识。     

地震控制策略

提出了控制地震概念和用时间反转方法实现非均匀地壳中波的聚焦，从而实现动力触发地震的思路。采用了有限元动力学仿真技术，研究了在波的遍历模型、线性不均匀的介质、以至非线性介质中的时间反转，探讨了在潜在震源区域人工聚能的可能性。结果表明这种聚能是可行的，在考虑介质非线性的条件下，波能量至少可以近似地聚焦。     

孕震物理过程探索

本文根据非线性科学观点，从多分形、自组织临界现象和浑沌动力学等三个方面综述了地震孕育过程的动力学演化特征及其系统的不稳定性问题。     

支持向量机方法在地震短期预测中的应用

支持向量机方法是基于统计学习理论提出的一种机器学习方法,在处理小样本、非线性问题方面有着很强的优势。而地震的孕育发生过程是一个复杂的非线性动力学系统,地震数据时间序列的变化更呈现非线性、不规则等特征。本文系统地分析了天津及其周边地区多种前兆现象,选取反映2至3个月短期情况的前兆测项,使用支持向量机分类方法建立地震综合预测模型,初步结果表明这种方法在地震短期预测中有一定的应用前景。     

非线性科学在地震研究中的一些应用

非线性科学应用极其广泛，近年来不少国内外学者将非线性科学应用于地震研究中，对地震现象的非线性问题和复杂性进行了探讨，取得了不少成果。本文对非线性科学在地震的可预测性、地震模型以及地震预报方法的研究方面进行了评述。关于地震的可预测性，有两种观点：一是认为地震是混沌，因而是不可长期确定性预测的；另一种观点认为地震是弱混沌，因而可能是可长期确定性预报的。加卸载响应比地震预报方法抓住了地震的本质，是一种很有希望的方法。     

震源物理研究的回顾与展望

震源物理的研究是岩石力学、位错理论，断裂力学、电磁学和非线性动力学等学科的渗透与结合。地震的孕育、发生重复的动力学过程是震源物理研究的重要内容。     

基于一种新显式时间积分算法的场地非线性地震反应分析

针对线弹性结构动力学方程,作者已提出一种具有良好稳定性的二阶精度单步显式时间积分算法。本文将该方法推广到求解材料非线性结构动力学方程中,采用带误差控制的修正欧拉算法计算单元应力,提高显式时间积分算法的精度。将求解非线性问题的显式算法应用于地震波垂直入射时非线性地震反应分析中,使用黏性边界模拟场地土层底部半空间基岩的辐射阻尼,并考虑地震动输入。与中心差分法计算结果进行对比,以表明新显式算法的有效性。     

强震动作用下土体非线性动力特征研究发展与展望

浅地表覆盖土层动力特性对地震动影响显著,软厚土层会明显改变地震动强度及频谱特性。由于观测数据匮乏,强震动作用下土体非线性动力特征研究长期以来均以室内试验为主,但在实验室中难以可靠地模拟实际地震历程中土体承受的加载路径、边界条件、排水条件等复杂因素。近二十年来竖向台阵(至少包含一个地表测点和一个井下基岩测点)记录数据大量增加,为土体非线性动力学研究提供了新的基础数据与发展机遇,使基于现场观测的土体非线性动力特征实证研究成为可能。     

Nonlinear dynamics of long-wave perturbations of the Kolmogorov flow for large Reynolds numbers

The nonlinear dynamics of long-wave perturbations of the inviscid Kolmogorov flow, which models periodically varying in the horizontal direction oceanic currents, is studied. To describe this dynamics, the Galerkin method with basis functions representing the first three terms in the expansion of spatially periodic perturbations in the trigonometric series is used. The orthogonality conditions for these functions formulate a nonlinear system of partial differential equations for the expansion coefficients. Based on the asymptotic solutions of this system, a linear, quasilinear, and nonlinear stage of perturbation dynamics is identified. It is shown that the time-dependent growth of perturbations during the first two stages is succeeded by the stage of stable nonlinear oscillations. The corresponding oscillations are described by the oscillator equation containing a cubic nonlinearity, which is integrated in terms of elliptic functions. An analytical formula for the period of oscillations is obtained, which determines its dependence on the amplitude of the initial perturbation. Structural features of the field of the stream function of the perturbed flow are described, associated with the formation of closed vortex cells and meandering flow between them. As a supplement, an asymptotic analysis of nonlinear dynamics of long-wave perturbations superimposed on a damped by small viscosity Kolmogorov flow (very large, but finite Reynolds numbers) is made. It is strictly shown that all velocity components of the perturbed flow remain bounded in this case.     

强震动作用下土体非线性动力特征研究发展与展望

浅地表覆盖土层动力特性对地震动影响显著,软厚土层会明显改变地震动强度及频谱特性。由于观测数据匮乏,强震动作用下土体非线性动力特征研究长期以来均以室内试验为主,但在实验室中难以可靠地模拟实际地震历程中土体承受的加载路径、边界条件、排水条件等复杂因素。近二十年来竖向台阵（至少包含一个地表测点和一个井下基岩测点）记录数据大量增加,为土体非线性动力学研究提供了新的基础数据与发展机遇,使基于现场观测的土体非线性动力特征实证研究成为可能。     

Incorporating the spatio-temporal distribution of rainfall and basin geomorphology into nonlinear analyses of streamflow dynamics

Many recent studies have been devoted to the investigation of the nonlinear dynamics of rainfall or streamflow series based on methods of dynamical systems theory. Although finding evidence for the existence of a low-dimensional deterministic component in rainfall or streamflow is of much interest, not much attention has been given to the nonlinear dependencies of the two and especially on how the spatio-temporal distribution of rainfall affects the nonlinear dynamics of streamflow at flood time scales. In this paper, a methodology is presented which simultaneously considers streamflow series, spatio-temporal structure of precipitation and catchment geomorphology into a nonlinear analysis of streamflow dynamics. The proposed framework is based on “hydrologically-relevant” rainfall-runoff phase-space reconstruction acknowledging the fact that rainfall-runoff is a stochastic spatially extended system rather than a deterministic multivariate one. The methodology is applied to two basins in Central North America using 6-hour streamflow data and radar images for a period of 5 years. The proposed methodology is used to: (a) quantify the nonlinear dependencies between streamflow dynamics and the spatio-temporal dynamics of precipitation; (b) study how streamflow predictability is affected by the trade-offs between the level of detail necessary to explain the spatial variability of rainfall and the reduction of complexity due to the smoothing effect of the basin; and (c) explore the possibility of incorporating process-specific information (in terms of catchment geomorphology and an a priori chosen uncertainty model) into nonlinear prediction. Preliminary results are encouraging and indicate the potential of using the proposed methodology to understand via nonlinear analysis of observations (i.e., not based on a particular rainfall-runoff model) streamflow predictability and limits to prediction as a function of the complexity of spatio-temporal forcing relative to basin geomorphology.     

切变基本纬向流中非线性赤道Rossby长波

为了解决观测和理论研究中的一些问题以及更好地了解热带大气动力学 ,有必要进一步研究基本气流的变化对大气中赤道Rossby波动的影响 .本文研究分析基本气流对赤道Rossby长波的影响 ,利用一个简单赤道 β平面浅水模式和摄动法 ,研究纬向基本气流切变中非线性赤道Rossby波 ,推导出在切变基本纬向流中赤道Rossby长波振幅演变所满足的非线性KdV方程并得到其孤立波解 .分析表明 ,孤立波存在的必要条件是基本气流有切变 ,而且基流切变不能太强 ,否则将产生正压不稳定 .     

A new look at the response surface method for reliability analysis using chaos theory

To overcome excessive computation errors and convergence failures encountered in an iterative calculation of the reliability index using the response surface method （RSM） for some nonlinear limit state functions, this study investigates an essential factor based on chaotic dynamics theory. The bifurcation diagrams of the reliability index are presented for some typical nonlinear limit state functions, and the computation results from the mapping functions due to the RSM iterations show the complicated dynamic phenomena such as the periodic oscillation, as well as bifurcation and chaos. From the numerical examples, it is concluded that the parameter of selection range fplays an important role in the convergence of the RSM iteration, and an improved RSM iterative algorithm is proposed with regard to the incorporation of the iterative sequential function of selection rangef The proposed method is shown to be efficient and to yield accurate results.     

Long Nonlinear Surface and Internal Gravity Waves in a Rotating Ocean

Nonlinear dynamics of surface and internal waves in a stratified ocean under the influence of the Earth's rotation is discussed. Attention is focussed upon guided waves long compared to the ocean depth. The effect of rotation on linear processes is reviewed in detail as well as the existing nonlinear models describing weakly and strongly nonlinear dynamics of long waves. The influence of rotation on small-scale waves and two-dimensional effects are also briefly considered. Some estimates of the influence of the Earth's rotation on the parameters of real oceanic waves are presented and related to observational and numerical data.     

Characterization of ground motions using recurrence plots

The current analysis of earthquakes is typically based on linear mathematical models that may fail to describe and forecast particular behaviors, because in many cases the data complexity may induce a highly non linear behavior. In this paper the implementation of an alternative method for seismic time series analysis is presented. The RPs (Recurrence Plots) enables recognition and treatment of measured accelerations. An RP obtained from seismic data allows a more efficient interpretation of the ground motions and this explanation contributes to characterize materials and responses. The nonlinear attributes from RPs analysis can be used as filters to reveal patterns or be combined to predict a seismic property. Automated seismic data characterization, based on nonlinear seismic attributes, could rewrite the rules of earthquake phenomena interpretation. The objective of this work is to establish a new methodology for practical application of nonlinear dynamics in seismic pattern/attributes recognition, an evolving and challenging engineering field.     

Nonlinear analysis of seasonality and stochasticity of the Indus River

Abstract

One of the world's largest irrigation networks, based on the Indus River system in Pakistan, faces serious scarcity of water in one season and disastrous floods in another. The system is dominated both by monsoon and by snow and glacier dynamics, which confer strong seasonal and inter-annual variability. In this paper two different forecasting methods are utilized to analyse the long-term seasonal behaviour of the Indus River. The study also assesses whether the strong seasonal behaviour is dominated by the presence of low-dimensional nonlinear dynamics, or whether the periodic behaviour is simply immersed in random fluctuations. Forecasts obtained by nonlinear prediction (NLP) and the seasonal autoregressive integrated moving average (SARIMA) methods show that the performance of NLP is relatively better than the SARIMA method. This, along with the low values of the correlation dimension, is indicative of low-dimensional nonlinear behaviour of the hydrological dynamics. A relatively better performance of NLP, using an inverse technique, may also be indicative of the low-dimensional behaviour. Moreover, the embedding dimension of the best NLP forecasts is in good agreement with the estimated correlation dimension. This provides evidence that the nonlinearity inherent in the monthly river flow due to the snowmelt and the monsoon variations dominate over the high-dimensional components and might be exploited for prediction and modelling of the complex hydrological system.

Citation Hassan, S. A. & Ansari, M. R. K. (2010) Nonlinear analysis of seasonality and stochasticity of the Indus River. Hydrol. Sci. J. 55(2), 250–265.