含有旅行时间的水平反射界面上P-SV转换波转换点坐标的唯一解析解

转换波转换点位置的求取一直是一个引人关注的问题.Schneider（2002）从一个关于转换点的三次方程中推导出了P-SV转换波转换点位置的一种解析解,这种解是偏移距、横纵波速度和P-SV转换波旅行时的函数.我们严格地论证了Schneider（2002）给出的解析解的唯一性.这个解析解可以被看作为水平反射层P-SV转换波叠前偏移的精确算子.     

3D3C陆地反射PS转换波CMP成像影响因素分析

三维三分量(3D3C)陆地反射PS转换波共中心点(CMP)叠加成像方法,虽然抽道集简单,但是对实际资料处理结果往往不理想.尤其当反射界面为三维倾斜界面时,其成像质量较差.本文提出有三个主要因素影响其成像质量:第一,转换点离散.运用实例计算得出,转换点离散度随着纵横波速度比、偏移距和界面倾角的增大而增大.相同界面倾角,不同测线方位的转换点离散度不同,视倾角的绝对值越大离散度也越大;第二,道集内静校正量差异增大.CMP道集中,由于转换点离散使得转换点横向跨度较大,经倾斜界面反射转换的S波出射到近地表地层时的角度差异也较大,导致静校突出;第三,加大动校叠加复杂性.三维倾斜界面PS波CMP道集近炮检距时距方程可表示为双曲形式,但是曲线的顶点位置和动校速度同时随测线方位变化,使得CMP道集同相轴很难校平,动校叠加过程很复杂.     

浅析接收函数共转换点叠加成像方法

回顾了接收函数叠加成像方法的发展过程,发现现在仍被广泛用于接收函数成像的共转换点(CCP)叠加成像方法存在着一定的缺点.通过计算转换波射线路径,得到不同深度、不同震中距转换波射线参数,发现共转换点叠加方法适合于P波接收函数叠加成像,对S波接收函数叠加成像却可能产生错误.结果显示在震中距为60°左右时,真正的转换点位置与共转换点叠加方法追踪到的转换点位置在深度为140km处水平方向偏离约200km,在震中距70°-80°之间时,真正的转换点位置与传统共转换点叠加方法追踪到的转换点位置之间的偏差小于S波接收函数的水平分辨率.利用不同深度产生的转换波射线参数进行反投影,能将转换点归位到更接近于真实的转换点位置上,从而使得通过S波接收函数获取的地球内部结构更加可靠.在岩石圈厚度变化剧烈的地区,建议优先采用震中距在70°-80°之间的远震S波事件进行岩石圈结构的研究.     

自适应转换波炮域偏移方法的研究与应用

抛开常规的转换点位置估计及极性校正,把检波点作为虚拟震源,利用单程波方程实现转换波记录的炮域偏移处理.由于该方法具有无需寻找转换点位置和进行极性校正的自适应特性,尤其适合于复杂构造转换波记录成像,并且在整个偏移处理流程中减少了估算转换点位置这一环节,有利于偏移精度的进一步提高,同时提高了运算效率.理论模型及实际资料的处理效果论证了该方法的正确性和有效性.     

火山岩地震屏蔽层的转换波叠前时间偏移成像

在反射地震转换波资料处理中,准确求取共转换点一直是一个难题,采用叠前时间偏移技术能避免共转换点道集的抽取,而且能够使转换波归位到真正的反射点上,实现准确成像.本文针对火山岩地震屏蔽层的转换波成像问题,通过对转换波共近似转换点道集进行速度分析,建立了转换波叠前时间偏移的初始速度场,通过速度扫描和纵、横波速度比值扫描确定最佳的偏移速度场和纵、横波速度比值,实现了在火山岩高速层覆盖区域的转换波偏移成像.实际资料的成像结果表明,本文采用的近似转换点计算以及转换波叠前时间偏移方法是有效的.     

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.     

VTI介质中P-SV波转换点与各向异性参数关系

对于转换波地震勘探中的转换点位置这个重要问题,提出转换点位置不仅与纵横波速度比,偏移距深度比以及源检距有关,还与地下介质的各向异性的性质有关,计算了忽略地下介质的各向异性影响对转换点的确定带来的严重误差,从而影响地下地质体的精确成像.通过对层状VTI介质中的转换点近似方程的推导过程,引入该方程不同于传统方程的导出是对层状各向同性介质而言,该方程通过引入各向异性参数,使我们对转换波可以有进一步的认识,拓展了转换波处理中各向异性的应用.该方程对于偏移距深度比小于3.0的情况是比较准确的,这对于大偏移距转换波勘探具有实际意义.     

高分辨率P-SV波速度分析

本文在常规转换波速度分析算法基础上,引入两个速度检测因子,提出了两种高分辨率的转换波速度分析方法,称之为转换波协方差速度分析法和转换波ECM（Enhanced Complex Matched Filter Method）速度分析法,同时对转换点计算公式、共转换点道集选排进行了研究,选取了最佳的转换点精确解计算公式,应用到基于时窗的CCP道集分选方法中,并与高分辨率速度分析同时进行,实现了转换波的高分辨率速度分析的算法,理论模型的计算结果表明,二者在时间及速度上都具有较高的分辨率.     

起伏地表下P-SV转换波动校正

P-SV转换波勘探是一种行之有效的地震勘探技术。基于地表一致性假设,P-SV转换波动校正过程中将地表假设为平坦地形。而随着地震勘探向复杂地区的深入,地表起伏大、高速老地层出露的问题,使得地震数据难以满足地表一致性假设。因此,现行的基于地表一致性的P-SV转换波动校正处理方法不能很好地对P-SV转换波进行动校正,影响转换波勘探的准确性。为此,本文从转换波的运动学特征出发,建立了起伏地表下P-SV转换波动校正方程,并构建了起伏地表条件下转换波动校正方法。通过理论模型模拟计算了起伏地表下P-SV转换波动校正方法,结果表明采用起伏地表下的转换波动校正方程能够取得较好的动校正效果,为P-SV转换波速度分析提供了一种行之有效的方法技术。     

垂向非均匀介质中转换波转换点计算

转换点位置的计算是转换波资料处理中的一个关键问题. 本文提出了分别基于速度随深度线性变化、速度随垂直走时线性变化、慢度随深度线性变化和慢度随垂直走时线性变化四种等效垂向非均匀介质情况下转换点位置的计算方法. 研究了通过速度拟合、走时近似和相似系数谱三种方式选择合适的等效速度方法. 结合理论模型对非均匀介质转换点计算方法、渐进转换点计算方法、Thomsen近似公式和均匀介质解析计算方法的误差进行了分析,结果表明非均匀介质转换点计算方法能更准确地计算转换点位置.     

Application of the edge wave superposition method

Numerical examples of high-frequency synthetic seismograms of body waves in a 2-D layered medium with complex interfaces (faults, wedges, curvilinear, corrugated) are presented. The wave field modeling algorithm combines the possibilities of the ray method and the edge wave superposition method. This approach preserves all advantages of the ray method and eliminates restrictions related to diffraction by boundary edges and to caustic effects in singular regions. The method does not require two-point ray tracing (source-to-receiver), and the position of the source, as well as the type of source, and the position of receivers can be chosen arbitrarily. The memory and the time required for synthetic seismogram computation are similar to ray synthetic seismograms. The computation of the volume of the medium (the Fresnel volume or Fresnel zones), which gives the essential contribution to the wave field, is included in the modeling program package. In the case of complicated irregular interface (or a layered medium with a regular ray field at the last interface), the method displays a high accuracy of wave field computation. Otherwise, the method can be considered a modification of the ray method with regularization by the superposition of edge waves.     

3D description and inversion of reflection moveout of PS‐waves in anisotropic media

Common‐midpoint moveout of converted waves is generally asymmetric with respect to zero offset and cannot be described by the traveltime series t²(x²) conventionally used for pure modes. Here, we present concise parametric expressions for both common‐midpoint (CMP) and common‐conversion‐point (CCP) gathers of PS‐waves for arbitrary anisotropic, horizontally layered media above a plane dipping reflector. This analytic representation can be used to model 3D (multi‐azimuth) CMP gathers without time‐consuming two‐point ray tracing and to compute attributes of PS moveout such as the slope of the traveltime surface at zero offset and the coordinates of the moveout minimum. In addition to providing an efficient tool for forward modelling, our formalism helps to carry out joint inversion of P and PS data for transverse isotropy with a vertical symmetry axis (VTI media). If the medium above the reflector is laterally homogeneous, P‐wave reflection moveout cannot constrain the depth scale of the model needed for depth migration. Extending our previous results for a single VTI layer, we show that the interval vertical velocities of the P‐ and S‐waves (V_P0 and V_S0) and the Thomsen parameters ε and δ can be found from surface data alone by combining P‐wave moveout with the traveltimes of the converted PS(PSV)‐wave. If the data are acquired only on the dip line (i.e. in 2D), stable parameter estimation requires including the moveout of P‐ and PS‐waves from both a horizontal and a dipping interface. At the first stage of the velocity‐analysis procedure, we build an initial anisotropic model by applying a layer‐stripping algorithm to CMP moveout of P‐ and PS‐waves. To overcome the distorting influence of conversion‐point dispersal on CMP gathers, the interval VTI parameters are refined by collecting the PS data into CCP gathers and repeating the inversion. For 3D surveys with a sufficiently wide range of source–receiver azimuths, it is possible to estimate all four relevant parameters (V_P0, V_S0, ε and δ) using reflections from a single mildly dipping interface. In this case, the P‐wave NMO ellipse determined by 3D (azimuthal) velocity analysis is combined with azimuthally dependent traveltimes of the PS‐wave. On the whole, the joint inversion of P and PS data yields a VTI model suitable for depth migration of P‐waves, as well as processing (e.g. transformation to zero offset) of converted waves.     

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.     

SH Wave Propagation in Viscoelastic Media

When comparing solutions for the propagation of SH waves in plane parallel layered elastic and viscoelastic (anelastic) media, one of the first things that becomes apparent is that in the elastic case the location of the saddle points required to obtain a high frequency approximation are located on the real p axis. This is true of the branch points also. In a viscoelastic medium this is not typical. The saddle point corresponding to an arrival lies in the first quadrant of the complex p-plane as do the branch points. Additionally, in the elastic case the saddle point and branch points lie on a straight line drawn through the origin (the positive real axis in the complex p-plane), while in the viscoelastic case this is generally not the case and the saddle point and branch points lie in such a manner as to indicate the degree of their complex values.In this paper simple SH reflected and transmitted particle displacement arrivals due to a point torque source at the surface in a viscoelastic medium composed of a layer over a half space will be considered. The path of steepest descent defining the saddle point in the first quadrant will be parameterized in terms of a real variable and the high frequency solutions and intermediate analytic results obtained will be used to formulate more specific constraints and observations regarding saddle point location relative to branch point locations in the complex p-plane.As saddle point determination for an arrival is, in general, the solution of a non-linear equation in two unknowns (the real and imaginary parts of the complex saddle point p ₀), which must be solved numerically, the use of analytical methods for investigating this problem type is somewhat limited.Numerical experimentation using well documented solution methods, such as Newton's method, was undertaken and some observations were made. Although fairly basic, they did provide for the design of algorithms for the computation of synthetic traces that displayed more efficient convergence and accuracy than those previously employed. This was the primary motivation for this work and the results from the SH problem may be used with minimal modifications to address the more complicated subject of coupled P-SV wave propagation in viscoelastic media.Another reason for revisiting a problem that has received some attention in the literature was to approach it in a fairly comprehensive manner so that a number of specific observations may be made regarding the location of the saddle point in the complex p-plane and to incorporate these into computer software. These have been found to result in more efficient algorithms for the SH wave propagation and a significant enhancement of the comparable software in the P-SV problem.     

CONVERSION POINTS AND TRAVELTIMES OF CONVERTED WAVES IN PARALLEL DIPPING LAYERS1

For converted waves, stacking as well as AVO analysis requires a true common reflection point gather which, in this case, is also a common conversion point (CCP) gather. The coordinates of the conversion points for PS or SP waves, in a single homogeneous layer can be calculated exactly as a function of the offset, the reflector depth and the ratio v_p/v_s. An approximation of the conversion point on a dipping interface as well as for a stack of parallel dipping layers is given. Numerical tests show that the approximation can be used for offsets smaller than the depth of the reflector under consideration. The traveltime of converted waves in horizontal layers can be expanded into a power series. For small offsets a two-term truncation of the series yields a good approximation. This approximation can also be used in the case of dipping reflectors if a correction is applied to the traveltimes. This correction can be calculated from the approximated conversion point coordinates.     

过渡层中地震P-SV波广义反射系数的两种近似算式

本文导出计算过渡层介质中P-SV波广义反射系数的两种近似算式:一种以层状介质作为过渡层的近似模型;另一种是直接由过渡层模型用数值近似方法计算。文中对比分析了数值试验结果。     

Transient scattering of elastic waves by dipping layers of arbitrary shape. Part 2: Plane strain model

Scattering of elastic waves by dipping layers of arbitrary shape embedded within an elastic half-space is investigated for a plane strain model by using a boundary method. Unknown scattered waves are expressed in the frequency domain in terms of wave functions which satisfy the equations of motion and appropriate radiation conditions at infinity. The steady state displacement field is evaluated throughout the elastic medium for different incident waves so that the continuity conditions along the interfaces between the layers and the traction-free conditions along the surface of the half-space are satisfied in the least-squares sense. Transient response is constructed from the steady state one through the Fourier synthesis. The results presented show that scattering of waves by dipping layers may cause locally very large amplification of surface ground motion. This amplification depends upon the type and frequency of the incident wave, impedance contrast between the layers, component of displacement which is being observed, location of the observation station and the geometry of the subsurface irregularity. These results are in agreement with recent experimental observations.     

地壳的Q结构与观测结果的解释

本文分析了地壳Q结构对于实测Q值结果的影响。对已发表的大部分实测数据进行分析,结果表明地震波射线路径与Q值显著相关。因此,在对实测的Q值空间分布状况进行解释的时候,不仅要考虑地震波频率的影响,还应对射线路径—距离效应进行分析和校正。本文还按照现有中国大陆地壳速度模型计算了地震射线在水平层状介质中的传播路径及震中距与射线最低点深度的函数关系,给出了华北及西南部分地区地壳Q结构。