利用全元素矩张量反演方法识别地下核爆炸

将震源矩张量中的各分量作为权重因子,利用基本Green函数的线性组合可以对地震波场进行描述,本文利用水平分层模型下的广义反射-透射系数方法的地震波场正演公式,反演了苏联东哈萨克斯坦地下核试验场的7次地下核爆炸、3次震中位置相近的天然地震的震源矩张量,反演结果表明地下核爆炸震源明显含有爆炸源成分,同时包含双力偶成分（DC）和线性偶极补偿源成分（CLVD）,且CLVD成分比重大,CLVD的存在可用层裂机制来解释;天然地震震源矩张量的反演结果表明,DC源为主要成分,符合剪切位错震源模式。

     

应用地运动数据反演地下爆炸震源函数

应用近场（震中距为几公里至几十公里）的地表地运动测试数据来研究爆炸震源特性,将近场地震波传播介质近似为均匀半空间模型,通过去除地表响应,反演了硬岩介质中的地下爆炸震源函数折合速度势RVP（reduced velocity potential）,得到了描述地下爆炸震源的折合速度势RVP振幅谱及其参数稳态值、特征频率、过冲特征量,通过回归分析,得到稳态值和特征频率与爆炸当量的关系。     

黏弹性固体中地下爆炸辐射地震波能量的演化

地下爆炸与介质的能量耦合和介质中的波传播机制是理解地下爆炸源物理的重要基础。为研究地下爆炸辐射地震波能量的传播衰减规律,分析了黏弹性介质中地下爆炸地震波能量的组成。基于无限介质中黏弹性球面波理论,给出了速度、位移、应力、应变等物理量Laplace域的理论解。利用Laplace数值逆求解方法,建立了黏弹性介质中地下爆炸辐射地震波场的计算方法。以干黄土作为典型黏弹性材料,计算给出了地震波能量的传播特征,分析了地下爆炸辐射能量的传播衰减规律。结果表明:（1）在黏弹性介质中,某球面处流入的能量随半径增加而逐渐降低。在理想弹性介质中,某球面处流入的能量在几倍弹性半径外即可稳定到某一定值;（2）在某一固定的有限观测区域内,当观测时间足够长时,势能和耗散能均趋于某一定值,辐射动能趋于零;（3）当有限的观测区域能容纳一个完整波长的地震波时,地震波辐射动能的稳态值随波传播距离的增大而减小,总体上可以用指数函数和幂函数进行分段拟合。     

地下强爆炸诱发地表塌陷的试验模拟与应用

地下核爆炸后会在地表产生下陷弹坑、塌陷带等不可逆变形爆炸后效应,利用地表形变信息对地下核试验进行有效监控和评估具有十分重要的意义。基于考虑重力影响的地下强爆炸塌陷成坑相似理论,利用陆军工程大学自主研制的地下爆炸效应真空室模拟试验装置,对2017年9月3日朝鲜地下核试验诱发的地表不可逆变形进行了模型试验。试验结果表明,地表塌陷带半径为257 m,下陷弹坑的半径为154 m,与美国、前苏联等国家已有的地下核试验经验公式的数据结果基本相当,并且符合天基雷达TS-InSar卫星监测数据的估算结果,验证了地下爆炸真空室模型试验在地下强爆炸诱发地表不可逆变形区域模拟和评估的可行性,成为有效补充地震波和卫星监测地下强爆炸的一种研究手段。     

轴向分布式药包激发地震波场模型

炸药震源激发地震波场幅频特性直接影响地震勘探精度,本文通过计算研究轴向分布式药包激发地震波场幅频特征规律:以球形空腔震源模型为基础,采用叠加方法获得轴向分布式药包激发地震波场计算方法,并与数值模拟结果进行对比。研究表明:该方法误差在7%以内;在爆心距大于药柱总长度9.8倍时轴向分布式药包所激发地震波速度场与球形药包基本一致,但地震波的频率更高。     

二维介质参数的大扰动反演方法

对非均匀介质参数反演问题进行了研究，并提出了用于反演二维介质参数的广义射线近似方法．利用参考场量和扰动变量对声波方程中的介质参数进行处理，并利用Ｇｒｅｅｎ函数理论得到扰动参数比的积分方程．基于非均匀介质中波函数的局部理论和射线理论，引入了全波场的广义射线近似形式，通过定义介质参数函数，把反演目标归结为其第一类Ｆｒｅｄｈｏｌｍ积分方程．利用积分变换方法得到二维介质的介质参数函数，从而得到介质参数，在Ｂｏｒｎ近似方法中，反演的介质参数扰动不能超过２０％，但是在本文中介绍的方法能够有效地反演其扰动比不超过５０％的变化情况     

地下核爆诱发工程性地震实测数据分析与不可逆变形范围计算

地下核试验瞬间释放的巨大能量引起地壳能量的连锁反应,产生诱发地震等地球物理现象。本文对20世纪前苏联与美国进行的地下核试验数据进行整理与归纳,给出地下核爆炸试验诱发工程地震的范围以及激活岩块大小等。根据实测数据,指出地下核爆炸诱发工程性地震的力学本质,利用理论公式计算了地下核爆炸产生不可逆位移的临界能量因子范围,为相关研究提供理论基础和场地效应试验数据。     

地下爆炸地震波的数值模拟及震源函数的研究

利用广义反射、透射系数矩阵和离散波数方法 ,计算了水平分层花岗岩介质中近场 (十几公里 )范围内三次地下爆炸的地表粒子速度垂直分量波形 ,并通过对实测波形的拟合 ,得到了地下爆炸激发的地震震源函数。     

覆水饱和双相介质圆弧场地P波激励下散射问题的理论解

采用波函数展开法对平面P波入射复杂水域地形的空间变异性地震动场进行研究,该水域地形具有覆水层、饱和双相介质、场地非平坦以及第二类分层(场地跨越分层界面)等属性.首先,依据地震波反射和透射特性推导直角坐标系下的自由波场分布;然后,根据场地属性并引入大圆弧法分析极坐标系下的含有待定系数的散射波场;进而,结合土-水分界面和饱和土层分界面边界条件,求解散射波场中的待定系数;最后,通过自由波场和散射波场得到覆水饱和双相介质圆弧场地波函数理论解.基于理论解,通过算例验证了理论推导的合理性及可靠性,分析了地表位移在不同入射条件下的差异性.结果 表明,相对于均匀介质,饱和双相介质会显著影响地表位移分布.此外,入射波频率和角度对地震地面运动特性也有较大的影响.     

舰船海底地震波形成机理的理论分析

航行舰船是一个很大的振动和噪声源,其振动和噪声引起的压力波经由流体介质传播到海底,引起海底岩层振动,产生弹性波并向远处传播,这种航行舰船在海底引起的弹性波称为舰船海底地震波。舰船海底地震波可用于识别舰船目标,作为水中武器的目标探测信号。基于波动理论,得到了舰船引起海底地震波的波动方程和有限元数值计算模型。利用该模型,对二维半无限空间层状海洋环境在水压场和极低频点声源作用下的海底地震波信号进行了数值模拟,得到了远场海底表面处加速度和水压的时域频域信号。结果表明,在二维半无限空间层状海洋环境条件下,舰船远场海底地震波主要由舰船极低频的噪声辐射引起,主要频率范围在1-7Hz。     

Areal moments of inertia revisited: on the distinction between the principal directions

Three commonly used methods to determine the principal moments of inertia of a plane area and their directions are based on: (i) the stationarity condition for the axial moment of inertia, (ii) the eigenvalue analysis, and (iii) Mohr’s circle. In this paper we provide two new derivations, which are based on: (a) the matrix diagonalization and the invariant tensor properties, and (b) the conjugacy property of the moment of inertia vectors. A new general expression is derived which specifies the principal directions of inertia, as well as the directions of the maximum and minimum product of inertia. A comparative study of the five presented approaches is given, which is of interest from both conceptual and methodological points of view. The connection between the deviatoric part of the moment of inertia tensor and Land’s circle of inertia is also given. The presented analysis applies to any two-by-two symmetric second order tensor.     

A lattice Boltzmann model for two‐dimensional sound wave in the small perturbation compressible flows

A multi‐entropy‐level lattice Boltzmann model for two‐dimensional sound wave equation in the small perturbation flows is presented. In this model, we used higher‐order moment method, multi‐scale technique and the Chapman–Enskog expansion, and multi‐entropy‐level to obtain sound wave equation with isentropic equation. As numerical examples, the Doppler effects in the sound wave propagation, the sound scattering from circular cylinder are simulated. The numerical results show that this model can be used to simulate sound wave propagation. Copyright © 2010 John Wiley & Sons, Ltd.     

A multi‐energy‐level lattice Boltzmann model for two‐dimensional wave equation

A lattice Boltzmann model for two‐dimensional wave equation is presented. In this model, we used higher‐order moment method, multi‐scale technique and Chapman–Enskog expansion, and multi‐energy‐level to obtain wave equation and energy conservation equation. As numerical examples, the interference and diffraction of wave are simulated. The numerical results show this model can be used to simulate two‐dimensional wave propagation. Copyright © 2009 John Wiley & Sons, Ltd.     

IMPROVEMENT OF EXPLICIT ALGORITHMS STABILITY WITH VISCO-ELASTIC ARTIFICIAL BOUNDARY ELEMENTS 1)

黏弹性人工边界单元是目前常用的处理半无限空间波动问题的数值模拟方法,可有效吸收计算区域内产生的外行波动.黏弹性人工边界单元具有与内部介质不同的质量密度、刚度和阻尼,受其影响,对整体模型进行显式时域逐步积分时,在边界区域易发生失稳现象,影响整体系统显式积分的计算效率. 针对该问题目前尚无行之有效的解决方法.本文针对二维黏弹性人工边界单元,建立可代表整体系统典型特征的侧边子系统和角点子系统,利用传递矩阵谱半径分析方法,基于传统中心差分格式,推导得到局部子系统稳定性条件的解析解.在此基础上通过研究解析解中各物理参数对稳定性条件的影响,给出通过增加人工边界单元的质量密度,以改善采用黏弹性人工边界单元时显式算法稳定性的方法.均匀和成层半空间波动问题算例分析表明,将内部单元质量密度设置为人工边界单元质量密度的上限,可以在保证黏弹性人工边界计算精度的前提下,有效改善整体系统显式时域逐步积分的数值稳定性,大幅提高计算效率.     

Complex frequency shifted convolution PML for FDTD modelling of elastic waves

The perfectly matched layer (PML) is nowadays considered as the best optimum absorbing boundary condition available. However, the PML with the classical stretching tensor has certain limitations. Strangely, these limitations have rarely been addressed in elastic wave modelling. For example, substantial reflections occur when strong evanescent waves are propagating parallel to the interface. To circumvent problems like this, the complex frequency shifted stretching tensor has been introduced in electromagnetic modelling. In this paper we show that the convolution PML with this stretching tensor as used in electromagnetic modelling can be adapted for elastic wave modelling. Numerical results of a model where the presence of evanescent waves is predominant show that the PML based on the complex frequency shifted stretching tensor can improve the performance of the absorbing boundary layer considerably.     

Magnetic dipole moment produced by an explosion of one kiloton of TNT

The paper reports results obtained in numerical simulation of the formation of a magnetic dipole moment by displacement of the geomagnetic field in an underground camouflet. The cases of chemical and nuclear explosions equivalent to an explosion of 1 kiloton of TNT are considered. From the calculation results it is concluded that electromagnetic measurement results can be used for monitoring of nuclear test.     

基于细观混凝土模型的时间逆转损伤成像方法

提出了一种针对混凝土结构损伤检测的时间逆转损伤成像方法.以检测混凝土结构中与骨料尺寸相近的微小损伤为目的,引入细观混凝土随机骨料模型,该模型将混凝土结构视为由水泥浆基底、骨料及粘接层组成的三相复合材料,基于Monte Carlo随机样本原理并结合真实试件的骨料级配曲线建立.在数值模拟分析中,将生成含损伤的细观模型导入有限元分析软件进行超声波场模拟,同时采用自适应性强的时间逆转模型(time reversed model,TRM)进行损伤定位.TRM分为正向检测和逆时成像两个部分:正向检测过程得到包含损伤的一系列散射回波信号,从数值角度进行时间反演并作为逆时过程的输入信号;逆时成像过程选用等效弹性参数模型,几何尺寸与随机骨料模型相同,时反信号在相应几何位置同时加载形成时反波场,时反波场在损伤位置会发生干涉叠加从而导致能量峰值的出现,通过确定干涉峰值时刻,并获取该时刻对应原始波场以及小波变换能量场完成成像.与原始数据波场图相比,小波变换处理成像结果消除了杂波干扰,成像结果更加清晰.进一步对等效弹性参数的取值进行讨论,并且在骨料尺寸范围内调整损伤大小,结果显示成像结果匹配度高,对于非均质混凝土结构的损伤检测能很好满足损伤定位需求.由此证明,时间逆转成像方法对于具有复杂结构的混凝土材料的损伤检测具有较好的适用性.     

Theory of the elastic moduli of a heterogeneous medium

It is shown that the theory of random functions permits the expansion of the effective tensor X~jkl for the elastic moduli with respect to correlation functions and that it leads in the second approximation in the Voigt-Reuss scheme to values that lie to one side of the Xijkl, while in the third approximation it brackets the latter. The analysis is used to refine the Hashin limits to the elastic moduli for a mechanical mixture of isotrcpic components and polycrystalline aggregates of cubic structure.There are two methods for calculating the effective elastic moduli of heterogeneous solids: virial expansion [2] (as a power series in the concentration of one of the components) and the method of correlation functions [2] (expansion with respect to relative fluctuation of the elastic moduli). Identical results should be obtained in the two cases if all terms are incorporated, but great mathematical difficulties restrict one to the lowest approximations. The first approximation in the virial method gives better results when the concentration of one component is low, while the method of correlation functions gives better results when the fluctuations in the elastic moduli are small and the concentrations are similar.Methods have been developed for determining the upper and lower bounds in both approaches, and various schemes of averaging are used for this purpose in the correlation-function method. The upper bound is established by renormalizing the equation of equilibrium, while the lower one is found by renormalizing the equation of incompatibility. The range of the bracketing can be reduced by means of higher approximations. The range can be reduced in the limit to zero, which implies passing from an approximate effective tensor to the true one, which relates the means in stress and strain over the material. Here we show that the two methods of renormalization give identical results when all terms of the series are summed.If the tensor has a Gaussian distribution, the moment functions of odd order are zero, while the even ones are expressed via combinations of the binary functions [3]. However, a mechanical mixture of several components is not Gaussian, and the odd moments are not zero. Splitting of the higher-order correlation functions is possible also for mechanical mixtures having determinate phase interfaces, but this involves various simplifying assumptions. A derivation is given for a moment of arbitrary order, which allows one to formulate the conditions under which such splitting is possible. The results are used in calculating the exact value of the effective bulk modulus for a medium with a homogeneous shear modulus.We are indebted to V. V. Bolotin for a discussion.     

鳗鲡模式游动的鱼体变形曲率波的传播特性研究

将鳗鲡模式游动的七鳃鳗简化成材料性质均匀的变截面黏 弹性梁,通过数值方法求解鱼体在主动弯矩波(作为激励的驱动波)的驱动下匀速游动时身体变形曲率波的传播特性. 结果表明,当主动弯矩 的驱动频率高于鱼体结构基频时,可以观察到曲率波相对于驱动波存在相位滞后,且越靠近尾部滞后现象越明显,这意味着曲率波的波速 小于驱动波的波速,也间接地验证了前人的实验结果. 通过参数研究发现,鱼体变形曲率波与驱动波的波速比与表征流体黏性作用的雷诺数无关,而与表征驱动波和鱼体材料属性的 无量纲激励频率、激励波长及鱼体黏性系数有关. 对于鳗鲡模式游动的鱼类,曲率波与驱动波的波速比随着无量纲激励频率和波长的增大而降低,随着鱼体黏性系数的增大而增大. 进一步研究发现,通过小扰动分析得到的组合相似性参数$\varPi$可以统一描述波速比与激励参数、材料参数之间的关系.