高阶统计量方法在地震勘探中的应用

高阶统计量方法是研究非高斯过程，非最小相位信号和非线性系统的有力工具，其应用领域已涉及通信、地球物理、生物医学、故障诊断等。本文就近年来高阶统计量在地震勘探中的应用现状进行简要的综述，并根据高阶统计量在相关领域的应用特点展望了它在地球物理领域的应用前景。     

陇西及周边地区地震活动与震磁效应的高阶统计量研究

高阶统计量是研究非高斯过程,非最小相位信号和非线性系统的有力工具,其应用领域已涉及通信、地球物理、生物医学、故障诊断等。本文对嘉峪关和乾陵2个地磁台站1998～2002年期间的地磁垂直分量(Z)资料运用高阶统计量方法进行处理,探讨陇西及其周边地区地震活动与地磁场变化之间相互关系,并将其结果与相关分析和线性拟合方法的结果进行对比。结果发现,高阶统计量异常一般早于两台Z分量相关系数和嘉峪关台Z分量线性拟合差异常1～2个月出现,且三阶矩(三阶累积量)的异常变化幅度在5～10之间,四阶矩的异常幅度在50以上,甚至达到150,四阶累积量的异常幅度在10～60之间。这些表明在震磁效应的统计分析研究中引入高阶统计量方法的必要性及其在地震预报中的潜力和良好前景。     

关于大地电磁信号非最小相位性的讨论

由于信号的功率谱仅包含振幅信息而不包含相位信息,因此传统功率谱方法仅能处理最小相位信号,难于适用于非最小相位信号．本文对不同地区的实际大地电磁(MT)信号作了分析,结果表明,不同测点MT信号在Z平面上的零点分布并不全部位于单位圆之内,可以判定MT信号一般具有非最小相位的特点,因此有必要改进传统处理方法,发展新的资料处理方式．实际信号分析,理论和数值模型实验证明,信号的高阶统计量包含其相位信息,因此,高阶统计量方法能够有效处理具有非最小相位特征的MT信号．     

泾阳Ms4.8地震磁效应的高阶统计量方法研究

以陕西关中地区泾阳、乾陵、周至3个地磁台站的地磁场垂直分量(Z)日均值及3个台站地磁场垂直分量变化与1998年1月5日泾阳Ms4．8地震之间关系为基础,探讨利用高阶统计量分析方法提取与地震活动相关的震磁信息。结果表明,在震前3个月,3个台站的三阶矩(三阶累积量)异常变化幅度在10～20,四阶矩异常幅度在120以上,最高达到260,四阶累积量异常幅度在80～105,与加卸载响应比法结果对比发现,高阶统计量方法在突出震前中长期地磁异常方面具有一定的优越性,提出在震磁效应统计分析研究中引入高阶统计量方法的必要性及其在地震预报中的潜力和良好前景。     

高阶统计量在大地电磁测深数据处理中的应用研究

在大地电磁（MT）测深法中,大地电磁响应函数经常出现个别频点分散、误差棒较大、形态异常等现象,在作反演解释时,许多地质特征难以有效提取出来,这些问题严重阻碍了MT的实际应用效能和发展.本文利用高阶统计量方法检验了MT信号的高斯性. 结果表明,MT信号是非高斯的. 根据任何高斯过程,其高阶统计量（高阶累积量,高阶谱）均为零的性质,通过信号的高阶谱恢复功率谱,再由功率谱估算MT响应函数,能有效抑制高斯有色噪声的影响,提高MT资料的处理质量. 从应用效果看,这种方法在抑制高斯有色噪声、提取信号中有用信息方面优于传统功率谱方法.     

高阶统计量在形变固体潮汐异常信息提取中的应用

将高阶统计量方法运用到形变固体潮汐资料处理中,对2006年4月9日山东莘县与河南濮阳交界的濮阳ML4.6地震前泰安地震台的潮汐形变观测资料进行了处理与分析。发现在地震前的一段时间内有异常信号介入,分析结果中的低点对地震异常信息的提取有指导意义。此方法能较好的提取潮汐形变短临异常。     

地震资料非高斯信息分析提取方法及油气预测

从讨论实际地震记录高阶累积量分析入手,研究利用高阶累积量计算高阶谱的方法.在分析高阶累积量及高阶谱提取分离具有非高斯分布信号时,详细讨论了产生非高斯分布的地震记录的特征规律.阐明了用地震资料的低频高阶谱预测砂体含油气性的机理.从理论模型和实际资料论证了研究方法的正确性.最后利用该方法计算的高阶谱结果和实际产油气井资料进行符合率验证分析.在此基础上,利用该方法进行有利含油气层预测.     

压制空间非平稳地震勘探随机噪声的ROAD径向时频峰值滤波算法

径向时频峰值滤波算法是一种有效保持低信噪比地震勘探记录中反射同相轴的随机噪声压制方法,但该算法对空间非平稳地震勘探随机噪声压制效果不理想.本文研究空间非平稳地震勘探随机噪声,即各道噪声功率不同的地震勘探随机噪声,其在径向滤波轨线上表征近似脉冲噪声,在径向时频峰值滤波过程中干扰相邻道滤波结果.为了减小空间非平稳随机噪声的影响,本文提出一种基于绝对级差统计量(ROAD)的径向时频峰值滤波随机噪声压制方法.该方法首先根据径向轨线上信号的绝对级差统计量检测空间非平稳地震勘探随机噪声,然后结合局部时频峰值滤波和径向时频峰值滤波压制地震勘探记录中的随机噪声.将ROAD径向时频峰值滤波方法应用于合成记录和实际共炮点地震记录,结果表明ROAD径向时频峰值滤波方法可以压制空间非平稳地震勘探随机噪声且不损害有效信号,有效抑制随机噪声空间非平稳对滤波结果的影响.与径向时频峰值滤波相比,ROAD径向时频峰值滤波方法更适用于空间非平稳地震勘探随机噪声压制.     

灰色关联度在地震预报中的应用

根据灰色系统理论中的关联度统计量,使用计算机,计算了河北北部和南部地下水观测资料,对关联度在地震预报中的应用进行了分析和研究。     

基于独立分量分析的南极半岛GNSS网区域滤波

高精度GNSS速度场是研究地壳垂向运动及板块运动的基础,能够为冰川均衡调整（Glacial Isostatic Adjustment,GIA）的建模提供外部检核和新的约束.共性误差（Common Mode Error,CME）是区域连续GNSS时间序列中存在的一种与时空相关的主要误差源,通过空间滤波可有效的降低共性误差的影响,提高坐标时间序列的精度.目前广泛采用的主分量分析法（Principal Component Analysis,PCA）,基于二阶统计量（方差和协方差）进行处理,没有充分利用CME高阶统计信息.而独立分量分析ICA （Independent Component Analysis）,引入高阶统计量,能够分离出统计独立的非高斯信号.以南极半岛地区的15个GNSS站点为例,由于某些站点存在强烈的局部效应,因此引入了因子分析法首先对异常站进行剔除,然后对比分析了PCA和ICA方法在南极半岛地区区域滤波结果.结果显示,ICA的滤波效果要优于PCA,ICA滤波前后E、N、U三个方向RMS平均降低44.69%、26.94%、34.87%,不确定度分别降低37.43%,44.58%,55.86%,有效的降低了GNSS残差序列的发散性和速度的不确定度.     

Random vibration of hysteretic systems under bi-directional ground motions

A random vibration method is developed for the response analysis of hysteretic structural systems under stochastic two-dimensional earthquake excitations. The biaxial hysteretic restoring force is modelled by coupled non-linear differential equations; the response statistics are obtained using the equivalent linearization technique. The validity of the proposed model is appraised using available biaxial loading tests of reinforced concrete columns. A parametric study was performed to examine the significance of the effects of biaxial interaction under earthquake excitations. A practical method to evaluate the extreme response statistics is also presented.     

Stochastic seismic response analysis of hysteretic multi-degree-of-freedom structures

Analytical study of random vibration of non-linear mutli-degree-of-freedom (MDF) systems is generally difficult. This is particularly true for MDF inelastic systems due to the highly non-linear and hereditary behaviour of the restoring force. On the other hand, to obtain the response statistics using a step-by-step Monte Carlo simulation requires a large sample, and it could be very costly. The purpose of this paper is to present a practical analytical-empirical method for an MDF yielding system. The method is based on a substitute structure (SS) concept in which the SS parameters are determined from empirical results of single-degree-of-freedom systems, i.e. each element in the system is replaced by a linear counterpart with ductility-dependent stiffness and damping. Based on a linear random vibration response analysis, the statistics of the maximum response (ductility) of each element are obtained by iteration. Numerical examples are given for multi-storey buildings with deteriorating (reinforced concrete frame) or non-deteriorating (steel frame) restoring forces. Comparisons with empirical results are satisfactory qualitatively. The main advantage of this method is that it requires relatively insignificant computation time, e.g. 1 s of execution time on the IBM 360–75 system for an eight-storey steel frame.     

大气（气候）系统可预报性问题的讨论

讨论了大气（气候）系统可预报性问题,并指出:1.线性系统、一维自治动力系统、二维自治动力系统和部分可化为二维自治动力系统的一维非自治动力系统是可以进行数值预报的,其预测结果要比统计方法更为科学。而对浑沌动力系统的预报,统计方法则比动力方法更为严谨。2.非浑沌动力系统或浑沌动力系统在非浑沌区的演化行为客观上存在着可预报期限。     

Seismic response statistics of SDOF system to exponentially modulated coloured input: An explicit solution

For single-degree-of-freedom systems, this paper presents an explicit solution of response statistics to earthquake excitation modelled by modulated filtered white noise. The modulation is described by the sum of exponentially decaying functions, accounting for non-stationarity of strong ground motion. The solution was obtained by analysis in the time domain using the state-space approach and impulse responses. This solution is reducible to several known solutions for simpler cases. Also, it may be used to develop probabilistic seismic response spectra for design and retrofit of structures, such as highway bridges.     

EQUIVALENT LINEARIZATION OF GENERALLY PINCHING HYSTERETIC,DEGRADING SYSTEMS

Many types of structural systems that undergo cycles of inelastic deformation under severe natural hazard loadings exhibit ‘pinching’ of hysteresis loops. In this paper, a generally pinching hysteretic restoring force model—an extension of the Bouc–Wen differential hysteresis model—is used in stochastic equivalent linearization of single-degree-of-freedom structural systems. The severity and rate of pinching are controlled by the hysteretic energy dissipation and the pinching level can be specified to match experimental data. Under white noise excitations, estimates of reponse statistics from linearization are shown to compare favourably with those from Monte Carlo simulation. Numerical studies on the sensitivity of the accuracy of response statistics obtained by linearization to changes in the hysteresis parameters showed that, for a range of practical cases, the linearization method can be used in lieu of simulation and that, in low-frequency systems, some hysteresis parameters may be set to a constant value a priori to reduce the number of model parameters that needs to be estimated or identified, and to simplify further random vibration analysis and/or performance evaluation studies.     

Computing Earthquake Probabilities on Global Scales

Large devastating events in systems such as earthquakes, typhoons, market crashes, electricity grid blackouts, floods, droughts, wars and conflicts, and landslides can be unexpected and devastating. Events in many of these systems display frequency-size statistics that are power laws. Previously, we presented a new method for calculating probabilities for large events in systems such as these. This method counts the number of small events since the last large event and then converts this count into a probability by using a Weibull probability law. We applied this method to the calculation of large earthquake probabilities in California-Nevada, USA. In that study, we considered a fixed geographic region and assumed that all earthquakes within that region, large magnitudes as well as small, were perfectly correlated. In the present article, we extend this model to systems in which the events have a finite correlation length. We modify our previous results by employing the correlation function for near mean field systems having long-range interactions, an example of which is earthquakes and elastic interactions. We then construct an application of the method and show examples of computed earthquake probabilities.     

Site-dependent models of earthquake ground motion

Random vibration analyses of structural systems subjected to seismic loading are dependent upon the characterization of earthquake ground motion as a stochastic process. The response of structural systems to earthquakes is dependent strongly on the local geological conditions, which should be incorporated into seismological models of ground motion. In the study presented herein, three previously developed ground-motion models are adapted to incorporate site-dependent characteristics. Records obtained from two recording stations in California are used as a basis for the ground-motion models. Single-degree-of-freedom (SDOF) oscillators are subjected to ensembles of accelerograms generated from these models, and both elastic and inelastic response are considered. Response statistics are compared to those generated by the analysis of structural response to ensembles of recorded motion from the two sites. The important features of the ground motion for effective reproduction of response statistics are identified, and observations are made on the sensitivity of specific response parameters to site-dependent characteristics of the ground motion.     

Geomagnetically induced currents in the Finnish high-voltage power system

We consider geomagnetically induced currents (GICs) in power systems from the viewpoint of a geophysicist. Special attention is paid to the Finnish high-voltage power system, in which exact theoretical model calculations together with recordings have been performed for several years. We present several examples of theoretically computed GICs using different geophysical models for estimating the geoelectric field driving GICs. Statistical prediction of GICs is outlined referring to studies made in Finland. We show that a combination of GIC recordings at few sites with theoretical modelling of ionospheric currents and the earth's conductivity, and data of geomagnetic activity makes it possible to derive GIC statistics of the entire power system. Finally, we discuss requirements for a long-range prediction of GICs, which will obviously be a widely-studied topic in future.     

Statistics of long-crested extreme waves in single and mixed sea states

Ocean Dynamics - Most of the studies on extreme waves are focused on the systems with single-peak wave spectra. However, according to the statistics of occurrence, the bimodal spectral system is...     

Statistical Variability and Tokunaga Branching of Aftershock Sequences Utilizing BASS Model Simulations

Aftershock statistics provide a wealth of data that can be used to better understand earthquake physics. Aftershocks satisfy scale-invariant Gutenberg–Richter (GR) frequency–magnitude statistics. They also satisfy Omori’s law for power-law seismicity rate decay and Båth’s law for maximum-magnitude scaling. The branching aftershock sequence (BASS) model, which is the scale-invariant limit of the epidemic-type aftershock sequence model (ETAS), uses these scaling laws to generate synthetic aftershock sequences. One objective of this paper is to show that the branching process in these models satisfies Tokunaga branching statistics. Tokunaga branching statistics were originally developed for drainage networks and have been subsequently shown to be valid in many other applications associated with complex phenomena. Specifically, these are characteristic of a universality class in statistical physics associated with diffusion-limited aggregation. We first present a deterministic version of the BASS model and show that it satisfies the Tokunaga side-branching statistics. We then show that a fully stochastic BASS simulation gives similar results. We also study foreshock statistics using our BASS simulations. We show that the frequency–magnitude statistics in BASS simulations scale as the exponential of the magnitude difference between the mainshock and the foreshock, inverse GR scaling. We also show that the rate of foreshock occurrence in BASS simulations decays inversely with the time difference between foreshock and mainshock, an inverse Omori scaling. Both inverse scaling laws have been previously introduced empirically to explain observed foreshock statistics. Observations have demonstrated both of these scaling relations to be valid, consistent with our simulations. ETAS simulations, in general, do not generate Båth’s law and do not generate inverse GR scaling.