离散点集（地震）空间分布多重分形计算的精度估算

地震是一种非线性现象,因而很多人计算地震分布的分形维数,但具体各种计算方法的误差（或精度）是多少,还没有定量的估计。鉴于地震空间分布具有有限、离散、点集的特点,用双标度Contor 多分形集理论模型数值模拟来估算其精度（误差）,并判定各种方法的优劣。理论模型数值模拟得出如下结论:① 随着样本容量的增大,计算精度会提高;② 固定半径法（RAD） 计算误差偏大,固定质量法（MAS）和最小生成树法（MST）较好;③ 当样本容量达到约200时,MAS法和MST 法计算误差大体可稳定在0.05的范围内。     

The minimal spanning tree method for calculating seismic multi-fractal

IntroductionEarthquake occurrence is resulted from the movement of the Earth's crust and the fr~re ofrock. It is a phenomenon of instability and self-organized criticality. It is possible that the phenomenon only occurs in non-linear syStem. As a pat of non-linear science, the fractal thatfounded by Mandelbrot in 1977 pioneered a new way tO solve inhomogeneous and complex phenomenon and offered a new tool. Some natural or social phenomena seem difficult to deal withbecause they are disordere…     

正则参数控制下的波阻抗约束反演

通过势函数方式将波阻抗反演的病态问题转为良态问题，并且给出了边界保护势函数所具备的条件. 在反演过程中，通过改变正则参数数值以及合理地选择正则参数的初值，改善反演结果，提高反演收敛速度. 同时，在具体反演中使用快速模拟退火算法，可以克服目标函数局部极值的限制，从而获得全局最优解. 通过理论模型试算和实际资料处理，说明本文方法具有精度高、实用性强的特点.     

基于广义正交多项式褶积微分算子的地震波场数值模拟方法

地震波场模拟方法研究对于与波动现象有关的地震学问题的重要性是不言而喻的.就目前现有的各种正演算法来说,精度较高的算法（如有限元法、谱元法、高阶有限差分法等）,其计算速度较慢;计算速度较快的算法（如低阶有限差分法、付氏伪谱法等）计算精度却比较低.为了兼顾地震波场模拟的精度与速度,本文推出了一种快速的、高精度地震波场模拟方法（基于Forsyte广义正交多项式的褶积微分算子法）,该方法是以计算数学中的Forsyte广义正交多项式插值函数为基础,构建一个新的褶积微分算子,并将该算子引入到地震波动方程的一阶速度-应力方程的空间微分运算中去,采用时间交错网格有限差分算子替代普通的差分算子以匹配高精度的褶积微分算子,从而构造一种全新的地震波场数值模拟方法.该方法同时具有广义正交多项式方法的高精度和短算子低阶有限差分算法的高速度.通过对算子长度的调节及算子系数的优化,可同时兼顾波场解的全局信息与局部信息.复杂非均匀介质模型中的波场数值模拟实验证实了该方法的可行性及优越性.     

Fractal analysis of rainfall observed in two different climatic regions

Abstract

The importance of high-resolution rainfall data to understand the intricacies of the dynamics of hydrological processes and describe them in a sophisticated and accurate way has been increasingly realized. The present study investigates the general suitability of fractal (or scaling) theory for understanding the rainfall behaviour and transforming rainfall data from one time scale to another. The study, employing a multi-fractal approach, follows the research undertaken earlier by the author (Sivakumar, 2000) employing a mono-fractal approach in which some preliminary indication as to the possibility of existence of (multi-) fractals was obtained. Rainfall data of three different resolutions, six-hourly, daily, and weekly, observed over a period of 25 years in two different climatic regions: a subtropical climatic region (Leaf River basin, Mississippi, USA); and an equatorial climatic region (Singapore) are analysed. The existence of multi-fractal behaviour in the rainfall data is investigated using (a) the power spectrum method; (b) the empirical probability distribution function (PDF) method; (c) the statistical moment scaling method; and (d) the probability distribution multiple scaling (PDMS) method. The results achieved from all these methods for the six different rainfall data sets considered indicate the existence of multi-fractal behaviour of rainfall observed in Leaf River basin and Singapore, providing further support to the results obtained using the mono-fractal approach (Sivakumar, 2000). The suitability of a multi-fractal framework to characterize the behaviour of rainfall observed in the above two significantly different climatic regions, subtropical and equatorial, seems to suggest the general suitability of the fractal theory for transforming rainfall from one time scale to another. Investigations with rainfall data from several other climatic regions are underway with a view to strengthening the above conclusions.     

北京地区气候变量的多分形特征研究

在气候系统的变量时间序列中往往存在着不同尺度间的自相似结构,这种自相似结构,又称为分形的特征.本文运用多分形去趋势波动分析方法(MF-DFA),分析北京市近50年来不同气象变量的逐日序列,并用一个扩展的二项式串级模式来分别估计其多分形谱.结果表明,平均气温等变量表现出多重分形的特征,并且多分形谱宽一致.而气温日较差和日照时数则表现出单分形的特征.且这种分形特征与长程记忆性相关,为中长期气候预测提供了理论基础.     

3D multi-fractal analysis of porous media using 3D digital images: considerations for heterogeneity evaluation

Pore structure heterogeneity is a critical parameter controlling mechanical, electrical and flow transport behaviour of rock. Multi-fractal analysis method was used for a heterogeneity comparison of three-dimensional rock samples with different lithology. Six real digital samples, containing three sandstones and three carbonates, were used. Based on the mercury injection capillary pressure test on these samples, we found that the carbonate samples are more heterogeneous than sandstones, but primary results of multi-fractal behaviours for all samples were similar. We show that if multi-fractal is used to evaluate and compare heterogeneity of different samples, one needs to follow some considerations such as (1) all samples must have the same size in pixel, (2) samples volume must be bigger than representative volume element, (3) multi-fractal dimensions should be firstly normalized to a determined porosity value and (4) multi-fractal results should be interpreted based on resolution of the imaging tool (effects of fine scale sub-resolution pores are missed). Results revealed that using normalized fractal dimensions, the real samples were divided to less and high heterogeneous groups. Moreover, the study of scale effect also showed that porous structures of these samples are scale invariant in a wide range of scales (from one to eight times bigger).     

微分求积法在结构动力分析中的应用

微分求积法（DQM）是1种求解微分方程初（边）值问题的数值方法,通常以较小的计算工作量即可获得较高的数值精度。这种方法应用于工程领域时多用来解决梁、板等结构的静力分析或结构特征值分析等问题,即对边值问题的微分方程的求解。结构动力分析属于初值问题,荷载和结构反应都具有特殊性,直接套用DQM求解边值问题并不能获得问题的解。本文尝试利用微分求积原理建立求解结构动力反应的具体方法。借鉴单元法的思想,将荷载持时划分为若干个时步,在每个时步内对动态荷载和结构反应进行离散,然后用DQM对时步逐个进行求解,得到体系在整个时域内的反应过程。通过对3种不同自振周期的线弹性单自由度体系在不同频率简谐激励下反应的计算,阐释了本文方法的可行性以及高精度、高效率的特点,通过数值试验确定了时步内相对较优的节点数,并为时步长度的选取提供了建议。     

基于遗传算法的地震短期综合预报分类系统研究

简要介绍了基于遗传算法的分类器和在此基础上建立的地震预报分类法系的基本原理。设计出基于遗传算法的地震短期综合预报分类系统的研究思路和方法,即以异常持续时间为编码依据。以遗传算法为优选预报规则的工具,以预报3个月地震为目标,综合测震和前兆多手段进行地震预测,对北天山西段进行多参数初步试算后表明该方法具有很高的学习正确率和较高检验和预测能力。     

波前重建法折射成像及应用研究

根据实际工作需要对传统的地震折射资料解释方法的适用范围进行了讨论,指出了传统折射资料解释方法所存在的问题。采用重建波前的方法进行折射成像,通过改进震源函数,并在反演过程中使用有限差分技术解程函方程,进行波场外推,从根本上解决了传统折射资料解释方法存在的问题,计算精度高,速度快。通过理论模型和实际资料的对比计算和验证,效果良好。     

模拟震源动力学破裂过程的数值方法研究

为模拟震源的动力学破裂过程,本文讨论一种求解剪切裂纹动力学扩展问题的有限差分法。在研究二维反平面破裂的基础上,我们把所用方法推广到三维问题。研究了许多简单震源模型,通过对比同一问题的解析解和其它数值解,对方法的正确性和计算精度进行了检验,结果表明我们的数值方法是可行的。最后,作为初步应用的例子,我们研究了非均匀断层的自发破裂问题。     

单程波李代数深度积分的精度分析和算法改进

本文在利用拟微分算子和象征理论研究单程波传播规律的基础上,详细分析了单平方根算子李代数深度积分存在的问题,利用改进的算法对单平方根算子进行大步长延拓,计算其李代数积分和指数映射,得到地震波走时的解析表达式.对方法改进前后李代数积分象征中系数校正情况和线性横向变速介质中走时的计算误差进行了对比,数值算例表明,改进后的方法收敛更快,减少了计算时间且提高了计算精度.     

上海地震台阵的F-K分析

频率－波数（F－K）谱分析是地震台阵数据处理基本方法之一。采用该分析方法，可以从地脉动背景中提取有用的地震信号，提高地震的定位精度。本文列举了F－K功率谱的不同计算方法，并将该方法应用于上海地震台阵所记录的地震事件。对地震和地脉动的F－K分析结果得出，地震的方位角和慢度值分别对记录长度的分布呈线性特征，而地脉动的方位角和慢度值则呈不规则分布。     

有序波前重建法的射线追踪

建立了一种新的计算最小走时和射线路径的方法——有序波前重建法. 文中算法按照波前面的实际扩展顺序外推计算走时，采用以计算点为中心的走时计算策略，直接记录计算点获取最小走时的前一节点坐标，同步计算最小走时和射线路径，得到一种全局算法. 该方法具有原理简单、易于实现、不受介质速度差异大小限制、计算速度快等优点. 数值实验表明有序波前重建法具有较高的计算精度和运行效率.     

一种基于蒙特卡罗模拟的发震概率计算方法

针对大震发生概率计算过程中的不确定性, 本文分别对不确定性及其处理方法进行了探讨． 考虑到不确定构成的复杂性, 提出了一种基于蒙特卡罗模拟的大震发生概率计算方法, 并以东昆仑断裂带塔藏段为计算实例, 利用蒙特卡罗法处理发震概率计算过程中的各种不确定性. 结果表明, 古地震数据的不完整性对计算结果的影响很大. 本文采用逻辑树法考虑古地震数据的不完整性, 得到塔藏段未来100年的大震发生概率为0.12．      

Study of the anomaly of seismic fractal spectrum before strong earthquakes

3 Conclusions The research of some theoretical Contor models of multi-scale and the numerical model of seismic spatial distribution show that the physical property of anomalies in seismic fractal spectrums is due to an increment of nonuniformity in the point set (earthquakes), in another word, the complexity increases. It is exactly the general precursory that the distribution pattern becomes complex from simple or nonuiform from uniform. So seismic multi-fractal spectrums is one of the best methods or tools for describing the complexity of seismic temporal-spatial distribution patterns. According to this view of point, taking the anomalies of the seismic multi-fractal spectrum as the earthquake prediction criterion is very valuable and worth while further studying. This project is supported by Chinese Joint Seismological Science Foundation.     

震后短期和长期形变模拟——以1960年智利Mw9.5地震为例

以1960年5月智利瓦尔迪维亚(Valdivia)Mw9.5地震为例分析震后不同时期的形变,实现了以Burgers体为粘弹介质模型来模拟震后粘弹松弛效应有限元数值模拟.计算结果表明,该粘弹介质模型可以模拟地震引起的瞬时同震弹性响应及震后粘弹松弛的短期和长期响应.由1960智利Mw9.5地震震后模拟的应变率显示以Burgers体为粘弹介质模型可以解决Maxwell体在模拟震后短期和长期形变不协调问题.     

Global precision analysis of carrier phase relative positioning in BeiDou navigation satellite system and United States global positioning system

In this paper, we derived a high-efficiency formula for calculating the precision of carrier phase relative positioning,analyzed the various factors that affect the positioning accuracy using the carrier phase, and proposed the concept of using a frequency dilution of precision to describe the quantitative effect of different frequency combinations on the positioning precision. To this end, we computed and plotted the global spatial distribution map of the relative positioning dilution of precision for single-day solution, half-hour solution, and single-epoch solution of the global positioning system(GPS), regional Beidou navigation satellite system(BDS2), future global Beidou navigation satellite system(BDS3), and their fusion systems.Using processing software with autonomous intellectual property rights(GCN and VENUS/ARSNet), we solved the measurement data and examined the positioning precision of the single-day solution and single-epoch solution of GPS and BDS2.The analysis demonstrated that the B1/B2 frequency positioning precision of BDS2 was better than that of L1/L2 frequency positioning of GPS, but the positioning precision of the BDS2 is worse than that of GPS over most of the service region of the BDS2. Further, the positioning precision of BDS3 is better than that of GPS in the Asia-Pacific region, while it is the opposite in other regions. Based on these conclusions, we put forth some optimization recommendations regarding the signal frequency of the navigation system and GPS measurement standards to serve as references for optimizing the system performance and formulating standards.