各向同性介质中射线理论与有限差分地震波场模拟方法比较研究

地震波场数值模拟不仅是研究复杂地区地震资料采集、处理和解释的有效辅助手段,而且是研究地球深部精细构造和地球深部探测的有效工具.射线理论和波动方程理论是地震波场数值模拟的理论基础.射线理论主要刻画地震波在介质中传播的走时场、地震射线等运动学属性;波动方程理论通过求解波动方程来描述地震波在介质中传播的弹性动力学响应(能量衰减、相位特征、偏振属性、以及全波形等).基于波动方程理论的波场数值模拟由于能够引入丰富的波场信息,使得人们对不同介质中地震波的传播过程有了较全面的了解.本文以二维层状均匀介质模型为例,通过射线追踪法和交错网格有限差分法模拟得到的波场快照图、单炮地震记录剖面、合成理论地震图的分析比较,不但对地震波在各向同性层状均匀介质中的传播规律和特点有了深刻的理解和认识,同时又可以相互验证两种不同方法的正确性和有效性.     

固体介质中非线性波的能量初探

本文从能源问题与勘探问题的密切关系出发，提出进行深入的非线性波研究的必要性——进一步提供可靠而详实的地质资料，以解决实际地质问题.说明了非线性科学与非线性波动的关系和特点，非线性波动是非线性科学的一个重要的分支，而地球本身的特点也决定了非线性科学是解决地质问题的重要基础.回顾了波动理论的研究历程及当今国内外非线性研究的进展情况.通过上述认识，提出了非线性波动问题中能量的重要性，然后分别从震源与冲击波的形成，界面处的能量分配，介质中能量的衰减，波的相互作用四个方面讨论了非线性波的能量问题.通过对能量问题的讨论，进一步讨论了影响非线性波能量的因素.从能量的角度出发，探讨了以后进行固体中非线性波研究的重点.最后对非线性波在地学应用中的可能性进行了探讨.     

饱和多孔微极介质的波动方程及其势函数方程

土是由一定尺寸大小颗粒所构成的多孔介质,具有明显的颗粒特性,当土颗粒间的孔隙被流体（如水或油）充满时则成为饱和土.利用微极理论和Biot波动理论的研究成果,把饱和土中多孔固体骨架部分近似地视为微极介质,孔隙中的流体部分视为质点介质,获得饱和多孔微极介质的弹性波动方程.借鉴Greetsma理论,建立了饱和多孔微极介质弹性本构方程力学参数与相应单相介质弹性参数的相互关系,使饱和多孔微极介质弹性波动方程中的物理参数具有明确的物理意义,易于在试验中确定.运用场论理论把饱和多孔微极介质的波动方程简化为势函数方程,建立了饱和多孔微极介质中五种弹性波的弥散方程,数值分析了五种简谐体波在无限饱和多孔微极介质中的传播特性. 结果表明,P1波、P2波和剪切S1波的波速弥散曲线与经典饱和多孔介质基本相同,当频率小于临界频率ω0时旋转纵波θ波和横波S2波不存在,当频率大于临界频率ω0时,θ波和S2波的传播速度随频率增加而减小.     

对流层上传重力波的非线性演化

利用二维全隐欧拉格式对重力波在可压、非等温大气中的非线性传播过程进行了数值模拟和分析.分析结果表明，从对流层顶激发的重力波能稳定地经平流层传到中层顶，从而将能量和动量从一个区域带到另一个区域；在向上传播过程中，重力波经历了发展、位温翻转、对流直至最终破碎的演变；重力波的破碎是对流和小尺度波动的重要的源，对流不稳定和翻转是非线性现象的一个基本特征.计算还显示，扰动源的大小直接影响着重力波的非线性传播过程，当扰动源足够小时，重力波能稳定传播，而大振幅扰动可以加速重力波的破碎.     

基于波动理论的结构损伤识别研究进展

目前人们对于结构的使用安全越来越重视,结构在日常使用或灾后的损伤识别检测也变得尤为重要。近年来国内外对于波在结构中的传播理论进行了深入研究,基于波动理论的结构损伤识别方法也取得了一定进展。文章首先介绍波在介质中的传播以及在各种类型结构中的传播规律和传播特性,其次从基于波传播理论的结构损伤识别、基于Lamb波的结构损伤识别、波动理论和神经网络相结合、波动理论与其他技术或算法的融合4个方面对国内外基于波动理论对结构损伤识别方法的研究成果进行综述。     

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.     

固体中非线性纵波一维数值模拟

分别采用四阶精度和六阶精度的中心差分格式，限定扰动（振幅）的取值在10-3m以内，进行了一维固体中非线性纵波传播的数值模拟，并通过两种格式对比性研究来保证差分格式的稳定性和收敛性．讨论了边界所输入正弦波的振幅、频率及介质非线性系数对非线性波的影响．模拟结果与位于生存周期之内近似解析解相符，并证实非线性波在传播过程中会发生波形畸变、产生倍频效应及谐波能量积累，而且这些非线性波动特征随输入振幅、频率和介质非线性系数（绝对值）的增大而增强．      

横向各向同性(VTI)介质中非线性地震波场模拟

数值计算方法是考察非线性弹性波在介质中（如岩石）传播特征的重要手段.非线性弹性波的数值模拟存在陡峭间断面（点）、数值振荡以及误差的指数级增长等现象而破坏数值解的稳定性、收敛性，能否消减上述现象的不利影响成为制约数值方法有效与否的重要因素.文中同时引入了FCT算子和幅值限制器，采用中心差分格式对具有垂直对称轴的横向各向同性（VTI）介质中的二维非线性弹性波进行数值模拟，从而克服了上述困难；介绍了适用于非线性弹性波的吸收边界条件，给出了差分方程的稳定性条件.在验证了方法的有效性后成功地获取了二维VTI介质中非线性弹性波的三分量地震正演记录，表明非线性波在传播过程中会发生波形畸变等现象.     

双相各向异性介质中弹性波方程的有限元解法及波场模拟

基于双相各向异性介质模型,首先推导了双相各向异性介质中弹性波传播的动力学方程及其Galerkin变分方程和有限元运动方程,然后给出了孔隙弹性波方程的有限元数值解法以及二维双相PTL介质中波场模拟的人为吸收边界条件. 最后,利用本文给出的有限元方法对双相PTL介质和双相各向同性介质中的弹性波传播进行了数值模拟. 结果表明:有限元方法和吸收边界条件有效、可行,在理想相界条件下,不论是从固体位移,还是从流体位移的波场快照都能看到明显的慢速拟P波;在黏滞相界情况下,能否观察到慢速拟P波,与含流体地层介质的耗散性质有关.对实际含流体介质,从流体位移分量的波场快照比从固体位移波场快照更容易观察到慢速拟P波.     

具有离散裂缝空间分布的二维固体中地震波传播的有限差分模拟

结合有限差分方法和等效介质理论,模拟了离散分布裂缝介质中地震波的传播. 基于等效介质理论,利用二维有限差分实现封闭裂缝的离散分布;裂缝可以处理成固体岩石中的高度柔性界面,并可以用线性滑动或者位移间断模型进行裂缝的物理描述. 对于含有多组裂隙的破裂固体,其有效柔度可以认为是固体骨架背景柔度和裂缝附加柔度之和. 在一阶近似条件下,固体骨架和裂缝参数可以通过有效各向异性系数联系起来,有效各向异性系数决定了各向异性（裂缝效应）对于地震波传播的影响. 通过与射线理论方法的对比检验,说明本文提出的模拟方法的有效性,并通过几个数值算例说明本方法可有效模拟不同的裂缝分布效应. 结果表明,即使在裂缝密度很小的情况下,具有相同裂缝密度的不同的空间分布可以产生不同的波场特征. 同时,也验证了不同裂缝尺度对波长的不同影响,以及裂缝尺度具有幂率分布（分形）时,尺度对波场的影响. 最后得出结论：在运用建立在等效介质理论基础上的地震各向异性概念来描述裂缝固体的特征时,要倍加小心,等效介质理论中尚未合理处理的裂缝尺度和空间分布对波的传播特征具有重要的影响.     

非线性波动理论在地震勘探中的应用综述

从非线性科学入手,详细地分析了非线性波动场产生的物理机制及国内科学者对非线性波动理论的研究现状,对非线性波动问题的求解技术进行详细概述,并分析了各种算法的特点,最后对非线性波动现场今研究的一些物理现象进行了综合分析,并探讨了非线性波动理论在地震勘探中的应用前景。     

线性粘弹体中地震波场伪谱法模拟技术

以积分本构方程为基础,应用对应原理建立线性粘弹体中的波动方程,采用伪谱法进行数值模拟.实际计算结果表明该方法能有效模拟标准线性粘弹体中地震波的传播.     

Nonlinear wave Packets of Equatorial Kelvin Waves

The weakly nonlinear dynamics of packets of equatorial Kelvin waves is studied using singular perturbation theory applied to the shallow water wave equations. Within the limits of the perturbation theory, which is formally restricted to weak mean shear and weak nonlinearity, we derive a Nonlinear Schroedinger equation to describe the envelope of the wave packet. We find that nonlinearity has a defocusing effect so that coherent wave packets must owe their existence entirely to the generation mechanism rather than to nonlinear focusing of a broad initial disturbance.     

再论地震数据偏移成像

利用地震波正向传播方程对属于波形线性反演问题近似求解方法的地震数据偏移成像进行重新推导,得到了适合散射地震数据的散射偏移成像方法和适合反射地震数据的反射偏移成像方法.以地震波传播的散射理论为出发点,首先根据描述一次散射波正向传播的线性方程研究建立散射地震数据的偏移成像方法理论;利用高频近似对产生散射波场的地下速度扰动函数的空间变化进行近似,推导出地下反射率函数,再由散射波传播方程推导出基于反射率函数的反射波传播方程,然后根据描述一次反射波正向传播的线性方程研究建立反射地震数据的偏移成像方法理论.本文指出和修正了Claerbout偏移成像方法中的不足,提出的地震数据偏移成像方法是对当前偏移成像方法理论的完善,使反射地震数据偏移成像具有了更坚实的数学物理理论基础,得到的偏移成像结果相位正确、位置准确、分辨率提高.     

Nonlinear waves on a coupled density front

Abstract

It is shown that the inclusion of the nonlinear terms in the equations of motion of a coupled density front of zero potential vorticity results in wave solutions which merely propagate with time. The linear theory, on the other hand, predicts an exponential temporal growth. The nonlinear equation admits steady solutions representing standing waves whereas if the nonlinear terms are omitted no steady solutions exist. The general initial value problem is difficult to solve numerically since the linear problem is ill posed.

In addition we prove that the general similarity solution of the nonlinear equation tends to zero for large times, at any point in space, regardless of the initial condition.     

The Effect of Fluid Thermal Expansivity on Thermo-mechanical Solitary Shock Waves in the Underground of Volcanic Domains

—This work is a further development of the modern thermo-poro-elasticity theory which has recently been applied to understand how fluid-rock coupling dynamics related to unrest episodes in volcanic domains can both determine, and occur with, ground deformation and rock fracturing processes. In particular by reformulating the energy equation, one of the two nonlinear heat-like equations upon which the thermo-poroelasticity theory is based, it is shown here how fluid thermal expansivity may influence fluid migration during its movement through subsurface volcanic porous-per meable horizons. With these new considerations it is found that a recent theory in which fluid-rock coupling dynamics is interpreted in terms of thermal and mechanical solitary shock wave propagation remains valid. However, the natural time scale of the propagating wave is reduced and consequently Darcy’s velocity is increased as a result of fluid thermal expansivity.     

A numerical study of 1-D nonlinear P-wave propagation in solid

IntroductionBecauseoftheextensivedistributionofruptures,micro-cracksandcrystalfracturesintheearth,therelationshipsbetweenthestressandstrainarenolongerlinear,infact,theyarenonlinear.Inordertoinvestigateandusethenonlinearcharacteristicsofsolidmediumintheearth,weshouldconsidertheinfluenceofnonlinearresponseduringthecourseofseismicmodelingandinversion.Thisisoneoftheimportantstudyfieldsthathavebeenpaidgreatattentionsinthere-centyearsintheworld(Minster,etal,1991;ZHANG,TENG,1993).Thenonlinearchar…     

Fission of a weakly nonlinear interfacial solitary wave at a step

The transformation of a weakly nonlinear interfacial solitary wave in an ideal two-layer flow over a step is studied. In the vicinity of the step the wave transformation is described in the framework of the linear theory of long interfacial waves, and the coefficients of wave reflection and transmission are calculated. A strong transformation arises for propagation into shallower water, but a weak transformation for propagation into deeper water. Far from the step, the wave dynamics is described by the Korteweg-de Vries equation which is fully integrable. In the vicinity of the step, the reflected and transmitted waves have soliton-like shapes, but their parameters do not satisfy the steady-state soliton solutions. Using the inverse scattering technique it is shown that the reflected wave evolves into a single soliton and dispersing radiation if the wave propagates from deep to shallow water, and only dispersing radiation if the wave propagates from shallow to deep water. The dynamics of the transmitted wave is more complicated. In particular, if the coefficient of the nonlinear quadratic term in the Korteweg-de Vries equation is not changed in sign in the region after the step, the transmitted wave evolves into a group of solitons and radiation, a process similar to soliton fission for surface gravity waves at a step. But if the coefficient of the nonlinear term changes sign, the soliton is destroyed completely and transforms into radiation. The effects of cubic nonlinearity are studied in the framework of the extended Korteweg-de Vries (Gardner) equation which is also integrable. The higher-order nonlinear effects influence the amplitudes of the generated solitons if the amplitude of the transformed wave is comparable with the thickness of lower layer, but otherwise the process of soliton fission is qualitatively the same as in the framework of the Korteweg-de Vries equation.     

Acoustic wave propagation in saturated porous media: reformulation of the Biot/Squirt flow theory

A model of wave propagation in fluid-saturated porous media is developed where the principal fluid/solid interaction mode affecting the propagation of the acoustic wave results from the conjunction of the Biot and the Squirt flow mechanism. The difference between the original Biot/Squirt (BISQ) flow theory and the new theory, which we call the reformulated BISQ, is that the average fluid pressure term appearing in the dynamic equation for a two component solid/fluid continuum is independent of squirt flow length. P-velocity and attenuation relate to measurable rock physical parameters: the Biot's poroelastic constants, porosity, permeability, pore fluid compressibility and viscosity. Modelling shows that velocity and attenuation dispersion obtained using the reformulated BISQ theory are of the same order of magnitude as those obtained using the original BISQ theory. Investigation on permeability effect on velocity and attenuation dispersion indicate that the transition zone in velocity and attenuation peak, occurring both at the relaxation frequency, shifts toward high frequency when permeability decreases. This behaviour agrees with Biot's theory prediction.