弹性波在离散介质中传播的贝塞尔函数解Ⅰ

对弹性波在离散介质中的传播问题进行了新的探索研究,本文用贝塞尔函数的线性组合构造了弹性波在非均匀离散介质中传播解。借助于贝塞尔函数的良好性质,其研究结果可用于地震波传播问题的研究。     

含裂隙双相各向异性介质中的地震波传播

基于各向异性介质和含裂隙双相介质中的地震波传播理论,导出了具有四阶对称轴的含裂隙双相各向异性介质的本构关系与波传播的运动方程．指出在含裂隙双相各向异性介质中可能传播６种类型的准纵横波,即快纵波ＱＰ１,慢纵波ＱＰ２,两个分裂的快横波ＱＳＶ１,ＱＳＨ１和两个分裂的慢横波ＱＳＶ２,ＱＳＨ２．并以平面波传播为例作了进一步分析     

Wave-propagation in uniaxially-stressed elastic media

Summary The propagation of waves of small amplitude in an elastic medium, with a particular form of strain-energy function, and subjected to a large homogeneous uniaxial stress, is considered in detail. The main characteristics, including speed and polarisation, of these waves in an unbounded medium are calculated numerically, and the existence and general properties of Rayleigh waves on the surface of a semi-infinite medium are investigated.     

在初始应力作用下磁热粘弹波的传播

本文研究在初始应力作用下导热导电粘弹体内平面波的传播.首先导出有初始应力存在时电磁场、位移场、温度场所满足的基本方程然后用它研究了流体静压力或张力及单轴压或张的初始应力条件下,磁——热——粘弹平面波的传播特性.讨论了弱耦合情况下,热效应磁场对波传播特性的影响.在无初始应力存在并略去热、磁耦合效应时,所得结果变成经典的粘弹波结果.      

Seismic waves in cracked two-phase anisotropic medium with fourfold rotation symmetry

IntroductionBasedontheresearchresultSofmanyintemalandextemalseismologiSts,mediuminseis-mogeniczonemaybethecrackedinordermediumsaturatedwithfluid(airorwater),namely,two-phaseanisotropicmedium.Inseismicprospecting,oilorgasreservoirrockmayaPproachtothecrackedtwo-phaseanisotropicmediumtoo.Therefore,thefiJrtherstudyonpropagaiontheoryofseismicwavesintWo-phaseanisotropicmediumpossessestheoreticalsignificanceandaPPlicationprospects-Inthispaper,onthebasisofthetheoryofseismicwavesinanuid-sbedporousso…     

四重旋转对称含裂隙双相各向异性介质中的地震波

基于各向异性介质和含裂隙双相介质中的地震波传播理论,导出了四重旋转对称含裂隙双相各向异性介质的本构关系与地震波传播的运动方程,并以平面波为例,进行了初步的分析研究．      

Surface and plate waves in biaxially-stressed elastic media

Summary The propagation of waves of small amplitude in an incompressible elastic medium subjected to a large homogeneous equibiaxial stress is investigated. The dispersion equation for surface waves on a semi-infinite medium is obtained explicitly, and the dispersion equation for waves in a slab of finite depth. In the latter case, approximate values, valid for waves whose lengths are much greater than the slab thickness, are determined for the phase-velocities of the different modes.     

热弹性介质中波传播特征

深层-超深层油气地震勘探涉及高温介质地震波传播问题,热弹介质参数对地震波传播有重要影响.含弛豫时间修正项的Lord-Shulman双曲型耦合热弹波动方程从理论上预测了热弹性介质中存在快纵波、慢纵波(一种准静态慢纵波,简称热波)和横波的传播,两个纵波为热耗散衰减波而横波不受介质热特性的影响.本文结合平面波频散分析和格林函数法数值模拟,详细研究两个热耗散衰减波的频散和衰减特征,着重分析热导率、热膨胀系数及比热的变化对波速和衰减的影响.研究表明热导率作为主要参数决定了波速与衰减的临界变化,热膨胀系数对波速和衰减的幅度有明显影响,比热则兼顾了前两个热弹系数的影响特征.最后,利用热弹性动力学频率域的二阶格林函数进行波场快照数值模拟,展示热弹性介质中纵波、横波和热波的传播行为.     

Wave-propagation in biaxially-stressed elastic media

Summary The propagation of small-amplitude plane waves through a homogeneous, isotropic elastic medium, with a particular form of strain-energy function and subjected to a large primary deformation, produced by a homogeneous biaxial stress, is considered in detail. The properties of such waves in an unbounded medium, the conditions for their existence, their speeds and their polarisations are investigated and similar results are also obtained for Rayleigh surface waves.     

完全匹配层吸收边界在孔隙介质弹性波模拟中的应用

模拟弹性波在孔隙介质中传播,需要稳定有效的吸收边界来消除或尽可能的减小由人工边界引起的虚假反射. 本文在前人工作基础上,首次建立了弹性孔隙介质情况下完全匹配层吸收边界的高阶速度-应力交错网格有限差分算法,并详细讨论了完全匹配层的构建及其有限差分算法实现. 首先,本文通过均匀孔隙模型的数值解与解析解的对比,验证所提出的数值方法的正确性;然后,本文考察了完全匹配层对不同入射角度入射波和自由表面上的瑞利波的吸收性能,将完全匹配层与廖氏和阻尼吸收边界进行了对比,研究了这三种吸收边界在不同吸收厚度情况下对弹性波吸收能力. 数值结果表明,在孔隙介质中,完全匹配层作为吸收边界能十分有效地吸收衰减外行波,无论对体波还是面波,是一种高效边界吸收算法.     

双变参数标量纵波方程正演模拟方法

常见弹性波动理论的建立是基于介质均匀这一基本假设,实际介质的非均匀性非常普遍.为研究连续介质中波的传播特征,本文从弹性力学中建立弹性波动方程的三个基本方程出发,考虑连续介质弹性参数的空变特征,建立非均匀介质的弹性波动方程,利用Alkhalifah声学近似思想建立位移表征的纵波波动方程,利用本征值问题求解方法建立标量波频率-波数域传播算子,从而建立描述纵波传播的标量波方程,其中波函数为纵波位移的散度,不同于均匀介质标量波方程的波函数为位移势.随后推导含PML边界波动方程差分格式并建立不同模型数值模拟进行数值试算,与均匀假设标量波方程和变密度方程对比证明本方法的准确性和稳定性.     

六分量弹性波场数值模拟与分析

地震波传播过程中,质点的振动不仅包括三个独立的平移部分,还包括三个独立的旋转部分.本文基于一阶速度-应力弹性波方程,采用分裂完全匹配层(SPML)的吸收边界条件,推导了时间导数二阶精度和空间导数高阶精度的交错网格有限差分格式的弹性波速度与应力各分量计算公式,模拟了各向同性介质中均匀模型和层状模型下的六分量波场,并对二维各向同性层状模型下的三个分量地震记录做高分辨率线性拉东变换得到各自的频散能谱.数值模拟分析结果表明:(1)旋转分量的能量要比平动分量弱的多;(2)在平动分量上,面波能量强,频率低,反射P波能量较强,反射S波能量稍弱;在旋转分量上,反射P波能量很弱,S波能量强;(3)与平动分量相比,旋转分量的频散能谱效果更好,能看到基阶和完整的高阶面波,即旋转分量能反映更多的地下介质信息.     

A note on wave propagation in granular medium

Summary The body wave propagation in granular medium is discussed in two sections. In Section I, the solutions of general equations of granular medium involving displacement vector and rotation vector are shown to be dependent on the solutions of four different equations. In Section II, the plane wave propagation is studied, showing the dispersion and dissipation of body waves in the granular medium.     

长周期形变波及其所反应的短期和临震地震前兆

本文应用断裂力学和流变介质中波的传播理论来研究震前长周期形变波的波动源以及这类波传播的一些主要特征,在理论研究结果的基础上,对我国多次较大地震前观测到的短临地震前兆进行了剖析,并从中识别出一些可能与长周期形变波有关的短临地震前兆.首先,从粘滑与破裂这两类主要地震机制出发,提出了粘滑前的预滑与破裂前断裂的预扩展(亚稳态扩展)可能是产生震前长周期波的两类波动源的看法,并着重从理论上讨论了后一类波动源.其次,以地壳流变介质模型为基础,对长周期形变波的传播特性进行了理论研究.选用地壳的广义流变介质模型,求解了所述的两类波动源在这种流变地壳介质中引起的长周期形变波传播的动力学问题,从理论上得出了长周期形变波在地壳内传播的某些一般特征.然后,专门分析了我国多次大地震前实际观测到的短期和临震地震前兆资料,并着重讨论了唐山地震的短临前兆.在这些不同类型的短临地震前兆中,我们得出地下水位、地倾斜及潮位自动记录曲线等的某些振动式及阶跃式短临地震前兆与长周期形变波的理论探讨结果基本相符,因而可以认为它们属于由长周期形变波所反映的地震前兆.在理论研究与实际资料分析的基础上,本文归纳了由长周期形变波所引起的短临地震前兆的一些基本特征,包括传播速度、衰      

COMPUTATION OF ZERO-OFFSET VERTICAL SEISMIC PROFILES INCLUDING GEOMETRICAL SPREADING AND ABSORPTION*

Synthetic vertical seismic profiles (VSP) provide a useful tool in the interpretation of VSP data, allowing the interpreter to analyze the propagation of seismic waves in the different layers. A zero-offset VSP modeling program can also be used as part of an inversion program for estimating the parameters in a layered model of the subsurface. Proposed methods for computing synthetic VSP are mostly based on plane waves in a horizontally layered elastic or anelastic medium. In order to compare these synthetic VSP with real data a common method is to scale the data with the spherical spreading factor of the primary reflections. This will in most cases lead to artificial enhancement of multiple reflections. We apply the ray series method to the equations of motion for a linear viscoelastic medium after having done a Fourier transformation with respect to the time variable. This results in a complex eikonal equation which, in general, appears to be difficult to solve. For vertically traveling waves in a horizontally layered viscoelastic medium the solution is easily found to be the integral along the ray of the inverse of the complex propagation velocity. The spherical spreading due to a point source is also complex, and it is equal to the integral along the ray of the complex propagation velocity. Synthetic data examples illustrate the differences between spherical, cylindrical, and plane waves in elastic and viscoelastic layered media.     

Propagation characteristics of converted refracted wave and its application in static correction of converted wave

Three-component seismic exploration through P-wave source and three-component geophone is an effective technique used in complicated reservoir exploration. In three-component seismic exploration data processing,one of the difficulties is static correction of converted wave. This paper analyzes propagation characteristics of non-converted and converted refracted waves,and discovers a favor-able condition for the formation of converted refracted wave,i.e. the velocity of overlaying medium S wave is much lower than that of underlying medium S wave. In addition,the paper proposes the static correction method of converted wave based on PPS converted refracted wave,and processes the real three-component seismic data with better results of static correction of converted wave.     

复杂地表边界元-体积元波动方程数值模拟

复杂近地表引起来自深部构造的地震反射信号振幅和相位的异常变化,是影响复杂近地表地区地震资料品质的主要原因.本文采用边界元-体积元方法,通过求解含复杂地表的波动积分方程,来模拟地震波在复杂近地表构造中的传播.其中,边界元法模拟地形起伏和表层地质结构对地震波传播的影响;体积元法模拟起伏地表下非均质低降速层的影响.与其他数值...     

Reflection and transmission of attenuated waves at the boundary between two dissimilar poroelastic solids saturated with two immiscible viscous fluids

The phenomenon of reflection and transmission of plane harmonic waves at the plane interface between two dissimilar poroelastic solids saturated with two immiscible viscous fluids is investigated. Both porous media are considered dissipative due to the presence of viscosity in pore‐fluids. Four attenuated (three dilatational and one shear) waves propagate in such a dissipative porous medium. A finite non‐dimensional parameter is used to define the effective connections between the surface‐pores of two media at their common interface. Another finite parameter represents the gas‐share in the saturation of pores. An attenuated wave in a dissipative medium is described through the specification of directions of propagation and maximum attenuation. A general representation of an attenuated wave is defined through its inhomogeneous propagation, i.e., different directions for propagation and attenuation. Incidence of an inhomogeneous wave is considered at the interface between two dissipative porous solids. This results in four reflected and four transmitted inhomogeneous waves. Expressions are derived for the partition of incident energy among the reflected and transmitted waves. Numerical examples are studied to determine the effects of saturating pore fluid, frequency, surface‐pore connections and wave inhomogeneity on the strengths of reflected and transmitted waves. Interaction energy due to the interference of different (inhomogeneous) waves is calculated in both the dissipative porous media to verify the conservation of incident energy.     

伴随地震波动的一种磁扰

本文应用磁弹性波理论,提出伴随地震波传播的同时,地磁场将产生一个扰动。在电导率σ→∞的理想情况下,震源附近的磁场变化约几个伽玛的量级。对于有限电导率情况,这种磁扰仍然存在。     

耗散大气中水平不均匀风场对内重力波传播的影响

采用包括耗散的射线跟踪方法，计算了在水平不均匀风场作用下，不同尺度重力波从对流层直至220km观测高度的传播，结果表明，垂直于重力波传播方向的风以及风剪切能够引起波射线的折射，从而导致重力波明显偏离初始传播方向.在强顺风场作用下，由于风场引起的捕获，大量重力波不能传播到观测高度.由于风场引起的多普勒频移，小周期的重力波在弱顺风条件下能够传播到观测高度.由于反射作用，强逆风场不支持周期低于约18min的较高频重力波的传播.而在弱逆风作用下，大部分中尺度范围重力波都能够传播到观测高度.本文统计了武汉电离层观象台的TID观测数据随热层风场的分布，统计结果与模拟结果符合较好.