改进的TTI介质纯P波方程正演模拟与逆时偏移

逆时偏移作为一种高精度偏移方法已成为复杂构造成像的重要技术,描述纵波独立传播的延拓方程是各向异性介质逆时偏移的一个关键问题.在对VTI介质几个经典相速度近似公式回顾的基础上,针对常用于描述纯P波的Harlan近似公式在各向异性参数ε较大情况下近似精度较低的问题,本文对Harlan公式中的非椭圆项进行了修正,在非椭圆项前添加了一个与各向异性参数ε有关的修正系数,得到了三种改进型Harlan公式,并以近似精度最高的改进式为基础,推导了TTI介质纯P波方程.针对该伪微分方程,本文利用伪谱法和有限差分法联合实现波场延拓,对于常密度二阶方程,基于中心网格实现;对于一阶应力-速度方程则基于旋转交错网格实现.通过数值试验分析了TTI介质纯P波一阶应力-速度方程的近似精度,并以一阶纯P波方程为基础进行了TTI介质逆时偏移数值模拟试验.结果表明,本文给出的方法能够较准确地描述TTI介质纯P波波场特征,可以应用至各向异性介质逆时偏移.     

基于二维VTI拟声波程函方程的椭圆各向异性立体层析反演

基于二维VTI介质拟声波程函方程,应用射线扰动理论建立了该方程控制下的数据空间各参数对于模型空间各个参数之间的线性关系,从而获得二维VTI介质拟声波程函方程的各向异性立体层析核函数.考虑到拟声波近似程函方程中η参数与ε和δ存在强烈耦合,本文首先探讨椭圆各向异性情形,为二维拟声波程函方程椭圆各向异性立体层析算法奠定了理论基础.同时也为日后推广到非椭圆各向异性情况提供了一种获得高质量初始模型的可靠途径.理论数据算例证实了Fréchet核函数求取的正确性以及在此基础上设计的工作流程实现两参数反演的可行性.     

各向异性半空间中浅埋孔洞对地表 反平面运动的影响

本文采用复变函数方法研究了稳态水平剪切波(SH波)在各向异性弹性半空间中任意形状孔洞上的散射及其对地面运动的影响.在变换空间中构造出自动满足各向异性半空间水平表面上应力为零的散射波函数,并根据孔洞表面应力为零的边界条件,采用最小二乘法求解散射波函数的系数.用介质的各向异性性质来模拟地质条件,给出了SH波作用下含圆孔、椭圆孔和方孔的各向异性半空间表面位移幅值的数值结果,并分析了介质特性、孔洞的形状、埋深、入射波波数及入射角度等因素对地面运动的影响规律.数值结果表明:介质的各向异性对含有孔洞的半空间表面的地表位移具有显著的影响;沿一定角度的入射波在某一频段内所引起的地表位移幅值比各向同性介质的可能要大,且随着孔洞埋深的增加,地表位移的幅值逐渐减小.      

存在低刚性不均匀体情况下的走滑断裂

在含有椭圆包体的介质中，利用由３型裂纹组成的二维模型分析了不均匀介质中的走滑断裂，以例评估局部或层状不均匀体对断裂发展的影响，表征和控制不均匀介质中断层的主要特征是有效剪切应力的空间变化，有效剪切应力变化范围可解释同一地区的地震事件的各种不同应力降值，在含有低刚性不均匀体的介质中的应力场最明显特征是在不均匀体内有效剪切应力大幅度减少，这个结果可以用来解释沉积层中动态扩展的破裂受到抑制作用，同时它也     

岩石的共轭剪裂角与围压大小关系的探讨

在讨论岩石共轭剪裂角大小及其与围压大小关系的基础上,提出了以椭圆曲线近似代替岩石剪切破裂极限应力莫尔圆包络线;以椭圆短轴位置作为岩石脆性状态和韧性状态的界线,推导一组用共轭剪裂角求应力值的计算公式.通过与佩特森,卡门的岩石力学实验曲线相比较,证实椭圆曲线和有关公式可以半定量到定量地估算岩石发生剪切破裂时的瞬时极限应力值.     

地热与地震关系的研究(一)——弹性介质中椭圆盘状裂纹尖端附近的热应力分布

近年来,人们越来越多地注意到地震发生前所存在着的地温增高的各种异常现象.本文以这些异常现象为根据,试图探讨地热变化与地震孕育的关系.文章假定,无限弹性介质中含有椭圆盘状断层面,并以此断层面为热通道.考虑在压应力作用下,温度为 x,y 的线性函数分布在此通道内,根据线弹性断裂力学观点,借助断裂力学中三维问题的解法,求出了断层面边缘附近的应力场和应力强度因子.结果表明,热应力有千巴的量级,并较定量地讨论了热应力大小与介质线膨胀系数的关系.最后简要地讨论了介质线膨胀系数的变化对地震孕育的影响.      

双组份裂缝岩石非线性有效应力模型研究

为认识黏土矿物和裂缝对岩石有效应力的影响,提出了双组份裂缝岩石椭圆模型.同时,将双组份裂缝岩石椭圆模型等效为共聚焦的椭圆岩石环与椭圆黏土环的叠加;基于复变函数和保角变换,分别得到了黏土环内椭圆长半轴和短半轴与压力间的关系式.进而结合椭圆孔渗透率计算式和岩石有效应力表达式,计算与分析了岩石孔隙度、黏土矿物含量、硬度比以及椭圆孔截面纵横比等参数对有效应力系数的影响.结果表明,当岩石中不含黏土矿物时,有效应力系数随纵横比的减小而增大,且小于1.0,这与Bernabé的观点一致.当岩石中含有易于压缩的黏土矿物,且纵横比为1.0（孔隙截面为圆形）时,有效应力系数随硬度比和黏土矿物含量的增大而增大,甚至远大于1.0,这与Al-Wardy等的研究结论一致;当纵横比小于1.0时,有效应力系数表现出了明显的非线性特征,随硬度比的增大而增大——甚至远大于1.0,而随黏土矿物含量的增大而减小,纵横比对有效应力系数的影响受黏土矿物含量大小的影响.易于压缩组分和裂缝的存在使得岩石有效应力系数变化特征更为复杂.     

任意倾斜各向异性介质中弹性波波场交错网格高阶有限差分法模拟

给出了任意倾斜各向异性介质中二维三分量一阶应力速度弹性波方程交错网格任意偶数阶精度有限差分格式及其稳定性条件,并推导出了二维任意倾斜各向异性介质完全匹配吸收层法边界条件公式和相应的交错网格任意偶数阶精度差分格式. 数值模拟结果表明,该方法模拟精度高,计算效率高,边界吸收效果好. 各向异性介质中弹性波波前面形态复杂, 且qP波波速不总是比qS波波速快. qS波波前面和同相轴的三分叉现象普遍, 且其同相轴一般不是双曲线型. 当TI介质倾斜时,3个分量上均能够观测到横波分裂现象, 而且各波形的同相轴变得不对称.      

用固体潮观测资料将钻孔应变变化换算为地层的应力变化

利用钻孔应变观测值中潮汐频段部分和钻孔岩芯的弹性系数,将钻孔应变换算为地层应力的格值,用此格值可将钻孔应变的非潮汐变化换算成该地地层的非潮汐应力变化。从潮汐模型研究和潮汐观测结果来看,勒夫数受地球在结构的影响,空间变化不大,据此可用勒夫数的模型值去求定标应力。由钻孔应变观测值求定钻孔应变的面应力系数和差应力系数,而不必知道耦合介质的力学性能。探头周围介质若非各向同性时,应力系数可用椭圆的解析式拟合     

地球介质的非弹性

地球介质并不是一种完全弹性体,从总体来看它是一种粘弹性体,在长时间应力的作用下,介质的行为类似于粘性流体,而在短时间应力的作用下介质呈滞弹性。由于地球的非弹性性质直接与诸多的地球物理现象有关,因此越来越受到广泛的重视。     

Derivation and relative performance of strings of line elements for modeling (un)confined and semi-confined flow

In the analytic element method, strings of line-sinks may be used to model streams and strings of line-doublets may be used to model impermeable walls or boundaries of inhomogeneities. The resulting solutions are analytic, but the boundary conditions are met approximately. Equations for line elements may be derived in two ways: through integration of point elements (the integral solution) and through application of separation of variables in elliptical coordinates (the elliptical solution). Using both approaches, two sets of line elements are presented for four flow problems: line-sinks and line-doublets in (un)confined flow, and line-sinks and line-doublets in semi-confined flow. Elliptical line elements have the advantage that they do not need a far-field expansion for accurate evaluation far away from the element. The derivation of elliptical line elements is new and applicable to both (un)confined flow and semi-confined flow; only the resulting expressions for elliptical line elements for semi-confined flow have not been found in the current groundwater literature. Existing solutions for elliptical line elements for (un)confined flow were intended for the modeling of isolated features. Four examples are presented, one for each flow problem, to demonstrate that strings of elliptical line elements may be used to obtain accurate solutions; elliptical line-doublets for semi-confined flow can only be strung together in combination with two integral line-doublets. For a zigzag canal in (un)confined flow, a string of elliptical line-sinks performed better than a string of integral line-sinks of the same order when the smallest angle between two adjacent segments is less than 130°. Elliptical line-doublets performed better than integral line-doublets for a square inhomogeneity in a uniform, confined flow field; the difference was smaller for an octagonal inhomogeneity. For semi-confined flow, the difference between the integral and elliptical line-sinks was small when modeling a zigzag canal.     

闽台震源机制和区域应力场

本文系统地汇集、修订了1933年至1969年台湾及其东部海域6级以上强震的震源机制资料,并重新测定了1970年至1978年台湾6级以上地震,福建省和台湾海峡部份地震以及1604年泉州海外8级强震的震源机制,分析了闽、台两省震源机制特征,指出:(1)由震源机制求出的断层面解与源深处的现代构造运动紧密相关;(2)大部份主压应力轴方向与主要断裂带垂直;(3)在台湾东部海中,中强地震组成三个互相平行的椭圆形空区,空区周围83%的6.0——6.9级地震的主 P 轴方向近似与空区边线垂直,7级以上强震都发生在空区边缘;(4)以巴士海峡为中心,面向福建大陆,应力场呈现向西北展开的扇形分布.      

Theory of earthquakes. Part III: Inclusion collapse theory of deep earthquakes

A theory of deep earthquakes, termed the inclusion collapse theory, is proposed in this paper. In the inclusion theory of crustal (or shallow) earthquakes, faults were shown to terminate within an inclusion zone. This zone represents a region within the brittle portion of the lithospheric plate that contains open cracks (voids) of varying sizes that, to a first order approximation, are uniformly distributed throughout the inclusion zone. When the lithospheric plate containing these faults and their associated inclusions is subducted into the mantle, the stress normal to the fault planes must increase. A depth is eventually reached where slippage along the fault planes is no longer possible. Earthquakes are postulated to occur at a specified depth within the mantle as a result of processes leading to collapse of these voids.When the long-term modulus of the plate is much greater than the long-term modulus of the mantle, large pressures are shown to develop within the plate during periods of active subduction. These pressures are shown to be sufficient to initiate partial collapse of voids of similar geometry throughout the inclusion zone.The inclusion collapse theory and the concentration of pressure within the plate lead to four results. (1) Earthquakes that are produced by a void collapse mechanism will not occur below a subduction depth calculated to be between 350 and 1000 km (2) The physical process most likely responsible for producing void collapse is the formation of shear, melt zones whose thicknesses are on the order of 1 to 10 cm in the immediate vicinity of the voids. This mechanism, is shown to produce a precursor time on the order of a few hundred seconds during which there is a release of shear strain prior to the earthquake. (3) The maximum energy released by void collapse is independent of the source depth. (4) The number of earthquakes produced by this process will decrease hyperbolically with source depth. Source depth, in the context used in this article, refers to the depth in the mantle to the inclusion zone where voids of similar geometry are undergoing partial collapse. The maximum source depth refers to the depth where all voids have closed.     

Dynamic stress concentration of an elliptical cavity in a semi-elliptical hill under SH-waves

The method of wave-function expansion in elliptical coordinates,elliptical cosine half-range expansion and Mathieu function were applied to obtain an exact analytical solution of the dynamic stress concentration factor(DSCF)around an elliptical cavity in a shallow,semi-elliptical hill.An infinite system of simultaneous linear equations for solving this problem was established by substituting the wave expression obtained by the Mathieu function including the standing wave expression of elliptical lining given herein into the boundary condition obtained by the region-matching method.The finite equations system with unknown coefficients obtained by truncation were solved numerically,and the results in the case of an ellipse degenerating into a circle were compared with previous results to verify the accuracy of the method.The effects of different aspect ratios,incident wave angles and aperture ratios on the dynamic stress concentration around the elliptical cavity were described.Some numerical results,when the elliptical hill was changed into a circular one,were analyzed and compared in detail.In engineering,this model can be regarded as a semi-cylindrical hill with an elliptical cylindrical unlined tunnel under the action of SH waves,and the results are significant in aseismic design.     

Models of interacting pairs of thin,quasi-geostrophic vortices: steady-state solutions and nonlinear stability

We study pairwise interactions of elliptical quasi-geostrophic (QG) vortices as the limiting case of vanishingly thin uniform potential vorticity ellipsoids. In this limit, the product of the vertical extent of the ellipsoid and the potential vorticity within it is held fixed to a finite non-zero constant. Such elliptical “lenses” inherit the property that, in isolation, they steadily rotate without changing shape. Here, we use this property to extend both standard moment models and Hamiltonian ellipsoidal models to approximate the dynamical interaction of such elliptical lenses. By neglecting non-elliptical deformations, the simplified models reduce the dynamics to just four degrees of freedom per vortex. For simplicity, we focus on pairwise interactions between identical elliptical vortices initially separated in both the horizontal and vertical directions. The dynamics of the simplified models are compared with the full QG dynamics of the system, and show good agreement as expected for sufficiently distant lenses. The results reveal the existence of families of steadily rotating equilibria in the initial horizontal and vertical separation parameter space. For sufficiently large vertical separations, equilibria with varying shape exist for all horizontal separations. Below a critical vertical separation (stretched by the constant ratio of buoyancy to Coriolis frequencies N / f), comparable to the mean radius of either vortex, a gap opens in horizontal separation where no equilibria are possible. Solutions near the edge of this gap are unstable. In the full QG system, equilibria at the edge of the gap exhibit corners (infinite curvature) along their boundaries. Comparisons of the model results with the full nonlinear QG evolution show that the early stages of the instability are captured by the Hamiltonian elliptical model but not by the moment model that inaccurately estimates shorter-range interactions.     

The relationship between the deep-level structure in crust and brewing of strong earthquakes in Xingtai area

IntroductionWiththefurtherstudyonthefinestructureofcrustandapplicationoftheCTtechnologytotheresearchonthecontinentaldeepstructureinNorthChina,thenon-heterogeneityofcrustanduppermantleintheseareashasbeenclearlyacknowledged.Zeng,etal(1991)gavethefocalmodeloflargeearthquakeinNorthChina,inwhichthemostimportanttraitisthetransversenonuniformoftemperaturedistributiononthetopofthemantle.Liu,etal(1986)studiedtheseismictomographyofNorthChinaregion,andindicatedthattherearemanydifferentlowervelocityare…     

中国强震前兆地震活动图像机理的三维数值模拟研究

建立了含有母体岩石、硬包体和随机分布的小裂纹的三维有限元模型，计算了包体和各层实体中的应力分布. 利用最高应力破裂准则、释放破裂单元刚度生与死的方法，模拟强震前岩石的破裂和小震的空间分布特征. 结果表明，文中三种模型都显示出强震前在孕震体即包体附近出现了高应力集中单元. 它们是形成小震空区、条带和地震空间丛集图像的基础. 随机裂纹的存在，有利于在孕震体（包体）外的裂纹端部应力集中，先发生小震，形成包围孕震包体的前兆地震活动图像，而包体中的应力逐渐增加，为发生强震提供了条件. 包体的形状和几何位置是影响强震前兆地震活动图像形态的重要因素. 引入材料的黏弹性，导致了其中应力随时间迅速减小和弹性层某些部位应力随时间的增加. 但在本文设定的构造模型框架和介质参数下，下层黏弹性的存在对上层母体的应力随时间的增加影响不大.     

新疆南天山环境应力场特征

基于新疆强震固定台和流动观测记录的主要和余震加速度资料，选用了三个分向记录都完整的３７次地震。震级范围为１．８－６．８级，震中距为几至几十公里。根据用位错理论二维断裂力学模式推导的震源峰值、加速度与环境剪应力场关系式计算了新疆南天山环境剪应力值。计算结果表明，新疆南天山环境应力平均值偏高，这与新疆处于特殊构造环境条件有关。