用于检测同相轴的Duffing型系统恢复力项的讨论

在用于检测同相轴的Duffing型系统中,非线性恢复力项的选取至关重要．针对具有不同非线性恢复力项的混沌系统,本文首先就非线性恢复力项的来源进行了说明,然后通过对哈密顿系统和耗散系统的仿真实验分析,以及理论推导,确定了势能—哈密顿多项式方程中可用于混沌振子检测系统的各项幂次和各项系数组合关系,即非线性恢复力项的选取规则：幂次最高项为奇次,其系数大于零．     

检测地震勘探微弱同相轴的混沌振子算法

针对地震勘探资料湮没在随机噪声中的微弱同相轴问题提出基于混沌理论的混沌振子检测算法. 利用修正的Duffing_Holmes方程建立检测微弱同相轴的混沌振子系统,之后经过对同相轴的扫描处理,构成新子波等时间间隔序列W(t),与此同时对随机噪声也进行相同的截断. 截断的随机噪声在混沌振子系统中可以具有与周期信号相同的表现;经过大量仿真实验确定出满足通常地震勘探子波延续时间的使混沌振子检测子波不呈现周期相态的随机噪声截断时间范围. 选用与松辽盆地T1、T2反射层类似的子波函数并构成待检微弱周期信号,经过MATLAB仿真试验成功地检测出该弱信号,信噪比达到约-10.3dB.     

微弱正弦信号检测模型混沌解的判定

运用Melnikov方法就混沌检测模型的混沌判据问题进行研究,证明并推导该数学模型为非线性混沌系统及系统出现混沌状的临界值。为正弦信号的混沌检测和混沌振子法用于准周期信号检测提供理论依据,也为从低信噪比地震勘探资料中提取有效信息建立理论基础。     

关于地震震级-频度关系式及其非线性项的讨论

研究了震级频度关系式中非线性项产生的原因,指出由于地震孕育过程是非线性的,很多地震现象都服从分形和混沌规律,因此传统的震级频度关系式中应含有非线性项,才能全面描述地震过程的非线性规律．得出了新的含有非线性项的震级频度关系式．讨论了该公式中非线性项的含义．     

Ricker子波视主频的变化对混沌振子检测效果的影响

针对地震勘探资料中存在加性强随机噪声干扰,已经提出用混沌振子系统处理的方法技术.为完善该方法,需要研究诸如地震勘探同相轴完整程度、组成同相轴的地震子波变化等对系统检测效果的影响.本文以Ricker子波模拟地震子波,研究Ricker子波视主频变化的相应检测效果.研究结果：随着Ricker子波视主频的升高,检测SNR逐渐变差,在高频部分SNR的变化明显比低频部分缓慢;在通常地震勘探频率范围内,混沌振子系统检测SNR有可能部分补偿由于地震波传播引起的幅度降低;为检测由畸变子波构成的同相轴提供一定的可能.     

Automatic Interpretation of Magnetic Data Using Euler Deconvolution with Nonlinear Background

The voluminous gravity and magnetic data sets demand automatic interpretation techniques like Naudy, Euler and Werner deconvolution. Of these techniques, the Euler deconvolution has become a popular choice because the method assumes no particular geological model. However, the conventional approach to solving Euler equation requires tentative values of the structural index preventing it from being fully automatic and assumes a constant background that can be easily violated if the singular points are close to each other. We propose a possible solution to these problems by simultaneously estimating the source location, depth and structural index assuming nonlinear background. The Euler equation is solved in a nonlinear fashion using the optimization technique like conjugate gradient. This technique is applied to a published synthetic data set where the magnetic anomalies were modeled for a complex assemblage of simple magnetic bodies. The results for close by singular points are superior to those obtained by assuming linear background. We also applied the technique to a magnetic data set collected along the western continental margin of India. The results are in agreement with the regional magnetic interpretation and the bathymetric expressions.     

Characterization of Earthquake Dynamics in Northeastern India Regions: A Modern Nonlinear Forecasting Approach

— The Northeastern India (NEI) region, is seismotectonically one of the most active regions of the world. Earlier studies of NEI earthquake data have provided contrasting evidence for the presence of randomness and low-dimensional strange attractor. Here, in the present study, we assess the dimensionality of an earthquake-generating mechanism by nonlinear predictability analyses on phase portrait constructed by monthly frequency earthquake time series which was obtained from the NOAA catalogue. The result of nonlinear forecasting analyses suggests that the earthquake processes in the NEI region evolve on a non-random high-dimensional chaotic system. Such a complex high-dimensional earthquake behavior is indicative of heterogeneous geological structures in which weak fault zones and/or individual fault interactions might have strength fluctuations due to pore pressure variation. Further, K₂ entropy analysis was performed to isolate the non-random component from the data. The analysis reveals a quasi-coherent time structure, (K₂ 0.08/month) which corresponds to a seasonal time scale of about 12 months. We argue that stochastic resonance created by seasonality bias may have combined with noise to affect the pore pressure variation leading to subsequent earthquake triggering. It is interesting to note that most earthquakes and swarm activities occurred during or after the monsoon season. Geological and geophysical evidence also reconciles with the above view. Evidence for high-dimensional chaos associated with seasonal bias in the NEI region may provide useful constraints for testing models and criteria to assess earthquake hazards on a more rigorous and quantitative basis.Received: 1 September 2001     

地球空间稳定核素的趋势分析方程与物质的超光速运动规律

通过讨论地球空间已有稳定核素内质子数与中子数的分布趋势,介绍了稳定核素的趋势分析方法及其有关周期性分布方程形式,给出了理论方程曲线与地球空间稳定核素实验数据分布点的对比结果,进而给出了稳定核素极限值和元素周期表中化学元素极限,以及其与正负粒子对的可能对应关系方程,包括位于电子中微子层面附近的粒子质量量级初步估计.随后通过建立真空物质能量状态的二个假设,及基于等效Binet方程,给出了与Einstein狭义相对论有关结论相融合的物质粒子以光速及超光速运动的质量及能量方程;作为推论,对这些方程与暗物质及暗能量的可能对应关系予以了初步探讨.     

n维非线性波动方程对应的线性方程Cauchy问题解的一个估计式

对于地震波在地球介质中传播的传播非线性而言,在求解n维非线性波动方程Canchy问题时,需要求解其对应的线性波动方程Cauchy问题和建立一些解的估计式。我们已经求得了其对应的线性波动方程Canchy问题解的表达式。在此基础上,本文应用函数空间L^1(R^n)、L^∞（R）的范数,建立了n维非线性波动方程对应的线性波动方程Cancny问题解的一个估计式,为求解n维非线性波动方程莫定了基础。     

固体介质中非线性波的能量初探

本文从能源问题与勘探问题的密切关系出发,提出进行深入的非线性波研究的必要性——进一步提供可靠而详实的地质资料,以解决实际地质问题.说明了非线性科学与非线性波动的关系和特点,非线性波动是非线性科学的一个重要的分支,而地球本身的特点也决定了非线性科学是解决地质问题的重要基础.回顾了波动理论的研究历程及当今国内外非线性研究的进展情况.通过上述认识,提出了非线性波动问题中能量的重要性,然后分别从震源与冲击波的形成,界面处的能量分配,介质中能量的衰减,波的相互作用四个方面讨论了非线性波的能量问题.通过对能量问题的讨论,进一步讨论了影响非线性波能量的因素.从能量的角度出发,探讨了以后进行固体中非线性波研究的重点.最后对非线性波在地学应用中的可能性进行了探讨.