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.     

Effects of a covering layer in a circular-arc canyon on incident plane SV waves

Introduction The effect of local topographies on seismic wave propagation is one of the most attractive topics in seismology. It may be resolved by either an analytical method or a numerical method. Here, the analytical method is the wave function expansion method; numerical methods include the finite difference, finite element, boundary integration equation, and discrete wave number method, etc. The advantage of these numerical methods is that they can be applied to local inhomogeneity and ir…     

圆弧形凹陷地形表面覆盖层对入射平面SV波的影响

利用Fourier Bessel级数展开法，给出了表面具有覆盖层的圆弧形凹陷地形对入射平面SV波散射问题的一个解析解，并利用该解分析了不同深宽比凹陷地形表面覆盖层刚度和厚度对入射SV波的影响．结果表明，凹陷地形表面覆盖层的存在，即使厚度很薄，也会显著增加对入射SV波的放大作用，该放大作用可达到单一凹陷地形的2.5倍以上．覆盖层刚度和厚度的变化对入射平面SV波也具有很大影响．      

Multiple scattering effects under vertical sounding of equatorial ionosphere

This paper presents a theoretical study of the influence of electron density small-scale irregularities on radio propagation under vertical sounding of the equatorial ionosphere. The sounder is assumed to radiate in the plane perpendicular to geomagnetic field lines. An approximate analytical solution of the equation of radiation energy balance in a plane layer of randomly inhomogeneous plasma has been obtained for this case. Analysis of the results shows that multiple scattering leads to attenuation of signal power and change of the signal arrival angles in the sounder vicinity.     

A New Theory of Love Waves in Multi-layered Media with Irregular Interfaces

In this article, we have derived a new and more general formulation of Love waves in arbitrarily irregular multi-layered media by using the global generalized reflection/transmission (abbreviated to R/T thereafter) matrices method developed earlier by Chen [17~20]. From the basic principle that the modal solutions are the non-trivial solutions of the free elastodynamic equation under appropriate boundary conditions, we naturally derived the characteristic frequencies and the corresponding distorted modes of Love wave in irregular multi-layered media. Moreover, we have derived the corresponding excitation formulation of Love waves in such laterally heterogeneous media by using the general solution of elastodynamic equation [17~20]. Similar to the result for laterally homogeneous layered structure, the Love waves radiated from a point source in irregular multi-layered media can be expressed as a superposition of distorted modes. Since the structure model used here is quite arbitrary, it can be used for so     

Cylindrical-Wave Approach for electromagnetic scattering by subsurface metallic targets in a lossy medium

An analytical solution is developed to the two-dimensional scattering problem of a plane-wave propagating in air, impinging on the interface with a dissipative soil, and interacting with a finite set of subsurface metallic targets. The Cylindrical Wave Approach is applied, the electromagnetic field scattered by the targets is expanded into cylindrical waves and use is made of the plane-wave spectrum to take into account the interaction of such waves with the planar interface between air and soil. The theoretical solution is implemented in a Fortran code. The numerical evaluation of the spectral integral relevant to reflected and transmitted cylindrical wave functions in the presence of lossy media is performed by means of Gaussian adaptive quadrature formulas. The method may return the field values in each point of the space, both in the near and far zones; moreover it may be applied for any polarization, and for arbitrary values of the cylinder sizes and positions.     

Separation of Variables Applied to the Wave Equation in Laterally Inhomogeneous Media

--The new eigenfunction expansion formula based upon the method of separation of variables is derived. The method gives the exact transport equation and the generalized eikonal equation without the need of asymptotic series expansions. The generalized eikonal equation extends the classical eikonal equation to a rapidly varying medium. It governs the wave propagation with dispersive phase velocity depending upon the amplitude. Both equations are separated by making use of conventional phase-ray coordinates. The solution is expressed in terms of the elementary Sturm-Liouville eigenfunctions or modes for the vibrating string. The generalized eikonal equation is solved by employing the modified Hamiltonian formalism. This results in frequency-dependent phase-ray trajectories associated with the energy flux vector field.     

Moveout approximation for horizontal transversely isotropic and vertical transversely isotropic layered medium. Part I: 1D ray propagation‡

Anisotropy in subsurface geological models is primarily caused by two factors: sedimentation in shale/sand layers and fractures. The sedimentation factor is mainly modelled by vertical transverse isotropy (VTI), whereas the fractures are modelled by a horizontal transversely isotropic medium (HTI). In this paper we study hyperbolic and non‐hyperbolic normal reflection moveout for a package of HTI/VTI layers, considering arbitrary azimuthal orientation of the symmetry axis at each HTI layer. We consider a local 1D medium, whose properties change vertically, with flat interfaces between the layers. In this case, the horizontal slowness is preserved; thus, the azimuth of the phase velocity is the same for all layers of the package. In general, however, the azimuth of the ray velocity differs from the azimuth of the phase velocity. The ray azimuth depends on the layer properties and may be different for each layer. In this case, the use of the Dix equation requires projection of the moveout velocity of each layer on the phase plane. We derive an accurate equation for hyperbolic and high‐order terms of the normal moveout, relating the traveltime to the surface offset, or alternatively, to the subsurface reflection angle. We relate the azimuth of the surface offset to its magnitude (or to the reflection angle), considering short and long offsets. We compare the derived approximations with analytical ray tracing.     

三维层状孔隙介质中弹性波的一种积分表达式II：正确性检验和数值模拟实验

基于前一篇文章中得到的关于三维层状孔隙介质中弹性波场的积分形式半解析解,本文通过离散波数法开展了数值模拟.将全空间均匀孔隙介质中单力点源和爆炸点源作用下弹性波场的解析解和我们的数值模拟结果进行对比,发现两者是完全一致的.而在一个两层半空间模型下的数值模拟,验证了固相位移Green函数的9组空间互易性情况.通过以上两种对比检验,验证了半解析解理论公式、数值模拟方法以及相应程序代码的正确性和可靠性.随后利用敏感度分析研究了不同的介质参数变化对爆炸点源在界面上会产生的反射波场的影响.通过垂直地震剖面模型的数值模拟,发现弹性波场能很好地反映孔隙介质物理性质的变化,同时也讨论了动力协调这一孔隙介质中的特殊现象.我们发展的基于半解析解的数值模拟方法可以为三维层状孔隙介质中弹性波传播特征的研究提供一种可供选择的有效工具和手段.     

Scattering of plane P waves by circular-arc layered alluvial valleys: An analytical solution

IntroductionThe site effect of local inhomogeneity and irregularity on seismic wave propagation is one of the most attractive topics in seismology. The problem may be resolved by either analytical method or numerical method. Here, the analytical method is the wave function expansion method; numerical methods include the finite difference, finite element, boundary integration equation, and discrete wave number method, etc. Although these numerical methods can be applied for sites of arbitrary s…     

A two-dimensional analytical solution of groundwater responses to tidal loading in an estuary and ocean

Previous studies on tidal dynamics of coastal aquifers have focussed on the inland propagation of oceanic tides in the cross-shore direction, a configuration that is essentially one-dimensional. Aquifers at natural coasts can also be influenced by tidal waves in nearby estuaries, resulting in a more complex behaviour of head fluctuations in the aquifers. We present an analytical solution to the two-dimensional depth-averaged groundwater flow equation for a semi-infinite aquifer subject to oscillating head conditions at the boundaries. The solution describes the tidal dynamics of a coastal aquifer that is adjacent to a cross-shore estuary. Both the effects of oceanic and estuarine tides on the aquifer are included in the solution. The analytical prediction of the head fluctuations is verified by comparison with numerical solutions computed using a standard finite-difference method. An essential feature of the present analytical solution is the interaction between the cross- and along-shore tidal waves in the aquifer area near the estuary’s entry. As the distance from the estuary or coastline increases, the wave interaction is weakened and the aquifer response is reduced, respectively, to the one-dimensional solution for oceanic tides or the solution of Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour Res 1997;33:1429–35) for two-dimensional non-interacting tidal waves.     

Scattering of Plane P Waves by Circular-arc Canyon Topography:High-frequency Solution

Through the Fourier-Bessel series expansion of wave functions,the analytical solution to the two-dimensional scattering problem of incidental plane P waves by circular-arc canyon topography with different depth-to-width ratio is deduced.Unlike other existing analytical solutions,in order to ensure that the analytical solution is valid for higher frequency incident waves,the asymptotic properties of cylindrical functions are in this paper introduced to directly determine the unknown coefficients of scattering waves,avoiding the solution of linear equation systems and corresponding numerical issues,which in turn expand the frequency band in which the analytical solution is valid.Comparison with other existing analytical solutions demonstrates that the proposed analytical solution is correct.Furthermore,the scattering effects of a circular-arc canyon on the incident plane P wave are analyzed in a comparatively broad frequency band.     

Modified ray-mode (phase) theory: Understanding counter-wind propagation effects from atmospheric explosions

We have incorporated horizontal winds into ray-mode theory including the full spectrum of acoustic–gravity waves for a perfectly stratified, range-independent, steady-state model atmosphere for frequencies from 10^?4 to ～10 Hz. This approach has also been applied to a specific atmospheric propagation problem that has long defied a solution, namely counter-wind propagation arrivals at a location ～300 km up-wind of the source. Our modified ray-mode theory predicts reliable up-wind solutions, but only if small-scale sound speed fluctuations were added to the mean seasonal sound speed profiles. Since full-waveguide theory and modified ray-mode mode theory incorporate diffraction and scattering propagation effects, we have performed additional analyses to determine the mechanism through which these fluctuations produce the up-wind signals. We have concluded that the dominant mechanism is through diffraction due to the presence of semi-permanent turbulence and internal gravity waves located near the stratopause.     

断层衍射波及其应用ht

本文从衍射波的物理定义出发,简化了Trorey提出的断层上Kirchhoff-Helmholtz衍射方程的解法;计算了不同深度、不同测线方向下的断层衍射波理论地震图;计算了衍射波振幅谱与相位谱,给出了利用衍射波求断层位置的公式;得出了一些新的结论,通过人工地震测深与地震勘探的实例,对断层衍射波的特性有了更明确的认识。 本文的结果表明:断层衍射波发生在地球介质剧烈变化处;衍射点两侧的衍射波走时曲线呈双曲线状;波初动清晰且半周期小;其优势频率振幅谱与反射波的相同,在衍射波与反射波走时曲线相切处附近,记录图中出现衍射波最大振幅,且波反相;视断点与真实断点一般不重合。上述特点可能为判定衍射波并确定断层位置提供判据。      

Propagation of radio waves reflected from the ionosphere during a solar eclipse

Summary The article first describes in chronological order the observations on the propagation of radio waves during the solar eclipses, and the development of the conflicting results on the similar transmissions of radio signals. The general theory of the absorption of radio waves in the ionosphere is briefly described and therefrom a method is derived to estimate the variation of the absorption of obliquely incident radio waves during a solar eclipse.The variation of field-strength can be studied in terms of the relationship between the vertical incident equivalent frequency of the signals and the critical frequencies of the ionospheric layers at the regions of reflection. The total absorption of radio waves consists of the non-deviative absorption in theD region and the deviative absorption in the higher layers of the ionosphere. During the eclipse, theD region absorption decreases in phase with the progress of the eclipse, but the variation of deviative absorption may differ in each observation. The deviative absorption is large when the equivalent frequency is close to the critical frequency of the layer reflecting the waves or of the layer just penetrated by the waves. The changes in the deviative absorption during an eclipse can be estimated on the basis of the variation of the critical frequencies of the ionospheric layers. The resultant changes in the total absorption during a solar eclipse may thus be estimated. The different types of field strength variation expected during an eclipse are given.The observations of the vertical incident absorption of radio waves and the field strength variations of obliquely incident continuous wave radio signals during the solar eclipse are described and the changes are explained on the basis of the above theory.     

Density fluctuations measured by ISEE 1–2 in the Earth’s magnetosheath and the resultant scattering of radio waves

Radio waves undergo angular scattering when they propagate through a plasma with fluctuating density. We show how the angular scattering coefficient can be calculated as a function of the frequency spectrum of the local density fluctuations. In the Earths magnetosheath, the ISEE 1–2 propagation experiment measured the spectral power of the density fluctuations for periods in the range 300 to 1 s, which produce most of the scattering. The resultant local angular scattering coefficient can then be calculated for the first time with realistic density fluctuation spectra, which are neither Gaussian nor power laws. We present results on the variation of the local angular scattering coefficient during two crossings of the dayside magnetosheath, from the quasi-perpendicular bow shock to the magnetopause. For a radio wave at twice the local electron plasma frequency, the scattering coefficient in the major part of the magnetosheath is b(2f_p) 0.5–4 × 10^–9 rad²/m. The scattering coefficient is about ten times stronger in a thin sheet (0.1 to IR_E) just downstream of the shock ramp, and close to the magnetopause.     

大功率电波加热电离层中热自聚焦不稳定性的理论研究和数值模拟

本文首先从电子密度及电子温度的输运方程和考虑自作用时的电磁波波动方程出发,利用简正模展开的方法推导出泵波在反射区域激发出热自聚焦不稳定性(thermal self-focusing instabilities,TSFI)所需电场阈值以及其增长率的完整数学表达式,并估算了TSFI激发阈值及所对应的有效辐射功率(ERP)的量级.随后利用三维垂直加热的理论模型,结合国际参考电离层(IRI-2012)和中性大气模型(MSIS-E-00)给出的背景参数,数值模拟了大功率高频泵波加热电离层时泵波反射区域电子密度及电子温度因TSFI而产生的变化及发展的过程,并对比分析了不同背景参数对较热效果的影响.结果表明:当高频泵波的加热阈值达到或超过百毫伏每米的量级时,即可激发TSFI,发展出大尺度电子密度及温度不均匀体,这些不均匀体内的密度耗空约为4%~10%,而电子温度剧烈增长,到达背景温度值的1.6~2.1倍;且在相当的加热条件下,背景电子温度越低、电子密度越小,加热效果越显著;电子密度及电子温度的扰动幅度随着加热时间的推移而逐渐减小,即扰动逐渐趋于饱和,且电子温度要快于电子密度达到饱和状态.本文还对泵波反射高度处的电子密度及电子温度变化率进行采样并求得其功率谱密度,分析结果表明:TSFI发展出的大尺度不均匀体满足幂律谱结构,谱指数随着加热的进行逐渐趋于稳定,白天与夜间的幂律谱指数区别不大,但电子密度与电子温度的幂律谱有所区别.     

圆弧形层状沉积谷地对入射平面P波的散射解析解

利用Fourier-Bessel级数展开法，给出了圆弧形层状沉积谷地对入射平面P波散射的一个解析解，并利用该解分析了谷中层状沉积排列顺序及相对刚度等因素对入射波散射的影响．      

Intrinsic attenuation and scattering of shear waves in the lithosphere of Kamchatka

Records of small local Kamchatka earthquakes were processed using Multiple Lapse Time Window Analysis (MLTWA). The method makes use of normalized integrals of 3D seismic energy density in several windows applied to an earthquake record that has been put through a bandpass filter. The intrinsic attenuation and scattering properties of the earth were estimated by choosing parameters that provide the best agreement between experimental and theoretical integrals as functions of hypocentral distance. The theoretical normalized integrals as functions of distance were computed using an analytical solution to the equation of seismic energy transport based on a simple model of isotropic scattering for scalar seismic waves excited by an impulse point source in an earth that is uniform as to scattering and intrinsic attenuation. The resulting estimates of attenuation and scattering parameters are similar to those derived in other studies of Kamchatka, as well as of other continents: America (California, US), Europe (the Canary Is., Spain, and Italy), and Asia (Japan).     

水平界面上P-SV转换波转换点的精确解

转换波共转换点的叠加和道集选取都需要准确地计算转换点的位置.Tessmer和Behle、Taylor分别给出了水平单层介质中P SV转换波转换点坐标的解析解,由于其表达式的复杂性,在应用中几乎不被采用.在本文中,运用Snell定律重新建立了在水平反射界面上反射的P SV转换波的转换点坐标的四次方程,并严格地推导出与纵波速度、横波速度、炮检距和反射深度有关的转换点坐标的解析解,确定了惟一的解析表达式.将这一结果应用于P SV转换波的速度分析和叠加处理中.简化的公式有较好的应用价值.