参考波速线性变化时的声波方程逆散射反演

声波方程的逆散射反演乃是求解双曲型偏微分方程系数项反问题的一种解析方法,一般利用Born近似把这一非线性反问题线性化,并给出了恒参考波速介质中反问题解的解析表达式.由于Born近似假定波速扰动为一级无穷小,因此,在大多数情况下,恒参考波速介质模型的反问题的解无法得以应用.本文研究介质参考波速沿某个方向线性变化时的声散射理论,导出了声波方程逆散射问题解的解析表达式,从而既可使Born近似的假定在大多数情况下能得以满足,又可利用快速Fourier变换快速实现介质波速扰动的反演成象.     

参考波速线性变化时的声波方程逆散射反演

声波方程的逆散射反演乃是求解双曲型偏微分方程系数项反问题的一种解析方法,一般利用Born近似把这一非线性反问题线性化,并给出了恒参考波速介质中反问题解的解析表达式.由于Born近似假定波速扰动为一级无穷小,因此,在大多数情况下,恒参考波速介质模型的反问题的解无法得以应用.本文研究介质参考波速沿某个方向线性变化时的声散射理论,导出了声波方程逆散射问题解的解析表达式,从而既可使Born近似的假定在大多数情况下能得以满足,又可利用快速Fourier变换快速实现介质波速扰动的反演成象.     

THE PERFECTLY REFLECTING WEDGE USED AS A CONTROL MODEL IN SEISMIC DIFFRACTION MODELLING*

The numerical modelling of seismic diffraction, e.g., at faults and other discontinuities, generally requires the use of fast approximate methods. The geophysicist responsible for the development of such numerical methods has a real need of exact solutions to certain ideal geometries to check the accuracy of his calculations. One such exact solution, which is available, is the acoustic wave solution to the perfectly reflecting wedge. The solution is three-dimensional and the source is an explosive point source. This model is ideal for seismic diffraction; the solution has the advantage of being exact, truly three-dimensional and of being in the convenient form of the temporal and spatial impulse response. More complicated sources which are extended in either space or time can, therefore, be modelled exactly by numerical integration. This paper presents some examples of the use of the perfectly reflecting wedge as a control model for an asymptotic high frequency diffraction modelling method. This control model has revealed that certain survey and wedge configurations can yield significant disagreement with, e.g., the Kirchhoff approximation. Such configurations could occur during VSP modelling when the survey lies in the near field or in the shadow zone of a high contrast fault. This control model has also been instructive in demonstrating why the high frequency, asymptotic, approximation is generally very good and has indicated a possible improvement to the Kirchhoff approximation for edge diffraction.     

简谐平面弹性波在楔形域中传播

本文利用自动满足楔形域任一面自由边界条件的纵、横驻波系,满足另一面上的初始应力条件,求得了初始简谐平面P波入射时楔形域中波传播的解析解.     

简谐平面弹性波在楔形域中传播

本文利用自动满足楔形域任一面自由边界条件的纵、横驻波系,满足另一面上的初始应力条件,求得了初始简谐平面P波入射时楔形域中波传播的解析解.     

各向异性双相介质中多极源声波测井理论研究

将各向异性地层模拟为横向各向同性双相介质 ,使其对称主轴与井孔中心轴线相垂直 .本文针对井孔模型下的多极源声波测井问题提出了一种解析的摄动方法 .将各向异性双相介质看作是由对应的各向同性双相介质加上摄动部分而组成 ,并引入 5个关于弹性模量偏离各向同性时的摄动量 ,对对称主轴与井轴垂直的各向异性双相介质的多极源声波测井问题进行了系统的理论研究和分析 ,严格求解了井孔内外的零级和一级近似声波场 .发现在n级多极源激发下 ,井孔中不仅出现n级多极声场 ,而且还能激发出与各向同性地层时不相同的高于和低于n级的多极声波场     

各向异性双相介质中多极源声波测井理论研究

将各向异性地层模拟为横向各向同性双相介质 ,使其对称主轴与井孔中心轴线相垂直 .本文针对井孔模型下的多极源声波测井问题提出了一种解析的摄动方法 .将各向异性双相介质看作是由对应的各向同性双相介质加上摄动部分而组成 ,并引入 5个关于弹性模量偏离各向同性时的摄动量 ,对对称主轴与井轴垂直的各向异性双相介质的多极源声波测井问题进行了系统的理论研究和分析 ,严格求解了井孔内外的零级和一级近似声波场 .发现在n级多极源激发下 ,井孔中不仅出现n级多极声场 ,而且还能激发出与各向同性地层时不相同的高于和低于n级的多极声波场     

MULTI-OFFSET ACOUSTIC INVERSION OF A LATERALLY INVARIANT MEDIUM: APPLICATION TO REAL DATA1

The aim of seismic inversion methods is to obtain quantitative information on the subsurface properties from seismic measurements. However, the potential accuracy of such methods depends strongly on the physical correctness of the mathematical equations used to model the propagation of the seismic waves. In general, the most accurate models involve the full non-linear acoustic or elastic wave equations. Inversion algorithms based on these equations are very CPU intensive. The application of such an algorithm on a real marine CMP gather is demonstrated. The earth model is assumed to be laterally invariant and only acoustic wave phenomena are modelled. A complete acoustic earth model (P-wave velocity and reflectivity as functions of vertical traveltime) is estimated. The inversion algorithm assumes that the seismic waves propagate in 2D. Therefore, an exact method for transforming the real data from 3D to 2D is derived and applied to the data. The time function of the source is estimated from a vertical far-field signature and its applicability is demonstrated by comparing synthetic and real water-bottom reflections. The source scaling factor is chosen such that the false reflection coefficient due to the first water-bottom multiple disappears from the inversion result. In order to speed up the convergence of the algorithm, the following inversion strategy is adopted: an initial smooth velocity model (macromodel) is obtained by applying Dix's equation to the result of a classical velocity analysis, followed by a smoothing operation. The initial reflectivity model is then computed using Gardner's empirical relationship between densities and velocities. In a first inversion step, reflectivity is estimated from small-offset data, keeping the velocity model fixed. In a second step, the initial smooth velocity model, and possibly the reflectivity model, is refined by using larger-offset data. This strategy is very efficient. In the first step, only ten iterations with a quasi-Newton algorithm are necessary in order to obtain an excellent convergence. The data window was 0–2.8 s, the maximum offset was 250 m, and the residual energy after the first inversion step was only 5% of the energy of the observed data. When the earth model estimated in the first inversion step is used to model data at moderate offsets (900 m, time window 0.0–1.1 s), the data fit is very good. In the second step, only a small improvement in the data fit could be obtained, and the convergence was slow. This is probably due to the strong non-linearity of the inversion problem with respect to the velocity model. Nevertheless, the final residual energy for the moderate offsets was only 11%. The estimated model was compared to sonic and density logs obtained from a nearby well. The comparison indicated that the present algorithm can be used to estimate normal incidence reflectivity from real data with good accuracy, provided that absorption phenomena play a minor role in the depth interval considered. If details in the velocity model are required, large offsets and an elastic inversion algorithm should be used.     

圆弧形凹陷饱和土场地对平面P波散射问题的解析解

以Biot 饱和多孔介质动力学理论为基础，利用Fourier Bessel级数展开法, 得到饱和多孔介质半空间中圆弧形凹陷地形对平面P波的散射问题的解析解. 数值计算给出地表位移幅值，分析了入射波波长、入射角、圆弧高宽比对地表位移幅值的影响，并与现存的在单相介质情况下得到的结论进行对比.     

关于弹性体内充流体圆形钻孔的简正模

本文运用声波导的理论讨论钻井声场的共振模式问题,特别注意稳态现象和暂态现象的区别与联系.本文考察了共振模式的存在性及其在声波测井信号中的反映.     

关于弹性体内充流体圆形钻孔的简正模

本文运用声波导的理论讨论钻井声场的共振模式问题,特别注意稳态现象和暂态现象的区别与联系.本文考察了共振模式的存在性及其在声波测井信号中的反映.     

声波测井中首波与次首波的理论研究

本文讨论了裸眼井中由点状声源激发的首波与次首波问题,认为:首波与次首波分别是以地层纵波速度V_c和地层横波速度V_s传播的几何衰减波。同时给出了泄漏波的解析式,而泄漏纵波和泄漏横波的截止频率分别为远场处的首波与次首波的传播特征频率。     

有薄疏松复盖层的弹性半空间中地震波的传播问题

本文将地表疏松风化层看作是附在弹性介貭上的一种有慣性而无弹性的薄层,当扰动在弹性介貭中传播吋,风化薄层跟随振动;討論了弹性半空間內点震源产生的地震波和疏松薄层对地震波反射的影响。     

声波测井中首波与次首波的理论研究

本文讨论了裸眼井中由点状声源激发的首波与次首波问题,认为:首波与次首波分别是以地层纵波速度Vc和地层横波速度Vs传播的几何衰减波。同时给出了泄漏波的解析式,而泄漏纵波和泄漏横波的截止频率分别为远场处的首波与次首波的传播特征频率。     

有薄疏松复盖层的弹性半空间中地震波的传播问题

本文将地表疏松风化层看作是附在弹性介貭上的一种有慣性而无弹性的薄层,当扰动在弹性介貭中传播吋,风化薄层跟随振动;討論了弹性半空間內点震源产生的地震波和疏松薄层对地震波反射的影响。     

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.     

射线法在粘-弹性介質中的推广

一、引言在完全弹性介貭中,弹性波的传播問題已經研究得比較深入,尤其用射綫法来解决波的传播強度問題,有了一套完善的方法。实际上,大地岩层近于粘-弹性介貭,地震波在传播过程中要受到內摩擦的作用,振幅随距离逐漸衰減。衰減規律,現在均根据經驗公式来确定。在理論上,虽然可以通过解波动方程的方法解决这問题,但所得結果,即使极簡单的問題也是十分复杂的。在完全弹性介貭中,也存在同样的情形,但如应用射线法,則变得較为方便。     

射线法在粘—弹性介質中的推广

一、引言在完全弹性介貭中,弹性波的传播問題已經研究得比較深入,尤其用射綫法来解决波的传播強度問題,有了一套完善的方法。实际上,大地岩层近于粘—弹性介貭,地震波在传播过程中要受到內摩擦的作用,振幅随距离逐漸衰減。衰減規律,現在均根据經驗公式来确定。在理論上,虽然可以通过解波动方程的方法解决这問题,但所得結果,即使极簡单的問題也是十分复杂的。在完全弹性介貭中,也存在同样的情形,但如应用射线法,則变得較为方便。     

THE INSENSITIVITY OF REFLECTED SH WAVES TO ANISOTROPY IN AN UNDERLYING LAYERED MEDIUM1

Propagation in the plane of mirror symmetry of a monoclinic medium, with displacement normal to the plane, is the most general circumstance in anisotropic media for which pure shear-wave propagation can occur at all angles. Because the pure shear mode is uncoupled from the other two modes, its slowness surface in the plane is an ellipse. When the mirror symmetry plane is vertical the pure shear waves in this plane are SH waves and the elliptical SH sheet of the slowness surface is, in general, tilted with respect to the vertical axis. Consider a half-space of such a monoclinic medium, called medium M, overlain by a half-space of isotropic medium I with plane SH waves incident on medium M propagating in the vertical symmetry plane of M. Contrary to the appearance of a lack of symmetry about the vertical axis due to the tilt of the SH-wave slowness ellipse, the reflection and transmission coefficients are symmetrical functions of the angle of incidence, and further, there exists an isotropic medium E with uniquely determined density and shear speed which gives exactly the same reflection and transmission coefficients underlying medium J as does monoclinic medium M. This means that the underlying monoclinic medium M can be replaced by isotropic medium E without changing the reflection and transmission coefficients for all values of the angle of incidence. Thus no set of SH seismic experiments performed in the isotropic medium in the symmetry plane of the underlying half-space can reveal anything about the monoclinic anisotropy of that underlying half-space. Moreover, even when the underlying monoclinic half-space is stratified, there exists a stratified isotropic half-space that gives the identical reflection coefficient as the stratified monoclinic half-space for all angles of incidence and all frequencies.     

时空变化风场中声重波波包的演变

本文从可压缩情况下的流体力学方程出发,采用多重尺度方法和W.K.B.方法,研究时空变化风场中声重波波包的演变过程。文中导出了声重波波长、相速、传播方向以及振幅的演变方程。结果表明,沿群路径上波长、相速和传播方向的变化取决于风场的时空变化以及风场与波的相对方位。此外,波振幅的演变方程还表明:在时空慢变风场中,声重波的波作用量具有守恒性,声重波波包能量增加伴随波频率增高,声重波波包能量减小伴随频率降低。能量变化的实质是,风场的时变性引起了波流相互作用。