基于Zoeppritz偏导方程精确解的地层密度多角度反演

基于Zoeppritz方程对介质密度偏导数所建立的偏导方程的精确解,构造了多角度反演地层介质密度的反演方程,在偏导数求解过程中考虑了介质密度对波速度的影响因素,并由此实现了利用反射系数梯度精确解计算地层密度的多角度联合反演.通过数值算例考察了计算方法,结果显示:反演方法对层状地层模型不论反射波是否存在相干现象均获得了较好的反演结果,反演迭代10次后计算结果的最大相对误差能够收敛到1%之内;随着反演角度的增加地层介质密度反演的精度逐步提高,反演具有自动校正能力,有快的计算速度.本方法克服了传统AVO(Amplitude Versus Offset)基于Zoeppritz方程近似所遇到的困难,不受反演角度大小及反射界面对波反射强弱的限制,为地层介质密度的多角度包括大角度反演提供了一种新的快速有效的计算方法.     

介质密度反演偏导矩阵的精确计算方法

实现反演偏导矩阵的计算是基于导数最优化反演方法的关键,然而目前的地震反演几乎都是基于Zoeppritz方程近似实现的,使计算精度和适应范围受到限制.本文利用Zoeppritz方程建立了反射系数对地层介质密度比偏导方程,导出了Zoeppritz方程矩阵元对介质密度比的导数.通过求解偏导方程获得了反射系数对介质密度比偏导数的精确计算(考虑了速度中含介质密度的问题).利用数值算例分析了反射系数对介质密度比偏导数的变化特点.本文采用直接解法求解偏导矩阵方程组,获得了快的计算速度和高的计算精度,为实现地层介质密度反演(包括大角度反演)提供了偏导矩阵的计算方法.     

Multi-angle inversion of formation densities based on the accurate solutions of Zoeppritz's partial derivative equations

基于Zoeppritz方程对介质密度偏导数所建立的偏导方程的精确解,构造了多角度反演地层介质密度的反演方程,在偏导数求解过程中考虑了介质密度对波速度的影响因素,并由此实现了利用反射系数梯度精确解计算地层密度的多角度联合反演.通过数值算例考察了计算方法,结果显示:反演方法对层状地层模型不论反射波是否存在相干现象均获得了较好的反演结果,反演迭代10次后计算结果的最大相对误差能够收敛到1％之内;随着反演角度的增加地层介质密度反演的精度逐步提高,反演具有自动校正能力,有快的计算速度.本方法克服了传统AVO(Amplitude Versus Offset)基于Zoeppritz方程近似所遇到的困难,不受反演角度大小及反射界面对波反射强弱的限制,为地层介质密度的多角度包括大角度反演提供了一种新的快速有效的计算方法.     

地震波的场方程矩阵和能量的正定二次型及其意义

场方程是能够表述半空间地震波场的整体特征.波动方程、速度方程和能量方程.通过分析可知每个场方程都具有各自的“场方程矩阵”.能量方程能够对所有场方程矩阵进行综合和贯通,给出了能量方程以“弹性矩阵”为核心的普适性表达形式.最后,运用矩阵的正定二次型理论阐述了“能量矩阵与弹性矩阵”之间一致的对称性和正定性.能量矩阵蕴含的动态力的平衡关系、速度的时间_空间分布和能量的传播及变化的物理意义,能够从能量矩阵的正定二次型特性表述出来.本文研究分析问题的方法完全适用于复杂介质模型,相关的认识和结论可以拓展到均匀黏弹性各向同性介质、均匀弹性各向异性介质、均匀黏弹性各向异性介质以及比奥饱和流体介质.     

水井含水层导水系数及其对地震波的响应

利用弹性理论和渗流理论研究了井水位振荡试验,给出了一种计算水井含水层渗流特性参数的新方法。该方法不是用井水位的恢复曲线,而是用井水位的振荡曲线计算出水井含水层的导水系数。对５ 口水井的导水系数及其对地震波的响应进行了统计,结果表明：水井含水层的导水系数越大,井水位对地震波响应的幅度越大,响应的次数越多。     

三维层状场地的精确动力刚度矩阵及格林函数

本文对Wolf二维层状场地精确动力刚度矩阵进行推广,给出了三维层状场地的精确动力刚度矩阵。刚度矩阵具有对称的特点,且因刚度矩阵是精确的,计算结果不受土层单元厚度的影响,可以大大提高计算效率。文中对刚度矩阵进行了数值验证。利用三维层状场地动力刚度矩阵,计算分析了基岩上单一土层场地的动力响应。最后作为动力刚度矩阵的另一重要应用,给出了表面或埋置矩形均布荷载或集中荷载的动力格林函数计算方法。     

有限元三角网格中波动的频散分析及数值仿真

波动问题有限元离散后会引起数值误差, 数值频散的本质就是数值误差传播引起的非物理解. 数值频散不仅没有实际意义, 而且还会影响对真实波动现象的认识. 为厘清有限元三角网格中波动数值频散的影响因素, 本文推导了集中质量矩阵和一致质量矩阵的频散函数, 同时给出了组合质量矩阵的频散函数, 并对不同质量矩阵的数值频散进行了对比研究. 理论分析和数值计算结果表明: 有限元三角网格中波动的数值频散受网格布局、 波传播方向、 单元网格纵横比以及质量矩阵的影响; 一致质量矩阵的数值频散比集中质量矩阵更易受到波传播方向的影响; 不合理的三角网格单元会对数值相速度(数值频散)产生不良影响; 正三角网格中波动的数值频散几乎不受波传播方向的影响; 一致质量矩阵与集中质量矩阵的线性组合能够有效地压制数值频散.      

电极类型及深埋对地电场观测精度的影响分析

精度的高低是考量地电场观测的一项重要指标,通过对阳原地震台近10年的观测精度进行分析(主要针对背景场项目改造后的观测数据),并对目前使用的JH-020型不极化电极观测及深埋处理进行研究,得出使用JH-020型不极化电极观测及电极深埋处理是有效提高观测精度的可行方法。同时,也为全省乃至全国台站提供地电场观测的有益借鉴。     

Ambiguous reflection coefficients for anelastic media

The calculation of reflection and transmission coefficients of plane waves at a plane interface between two homogeneous anelastic media may become ambiguous because it is not always obvious how to determine the sign of the vertical component of the slowness vector of the scattered waves. For elastic media, the sign is determined by applying so-called radiation condition when the slowness vector is complex-valued, but it has long been known that this approach does not work satisfactorily for anelastic media. Other approaches have been suggested, e.g., by requiring that the reflection and transmission coefficients should vary continuously with increasing incident angles, or by relating the sign to the direction of the energy flux. In the present paper, it is shown that these approaches may give different results, and that the results can be inconsistent with the elastic case even for weak attenuation. Instead, it is demonstrated that the ambiguity in the reflection coefficient can be resolved by expressing the seismic response of a point source over an interface as a superposition of plane waves and their reflection coefficients, and solving the resulting integral by the saddle point approximation. Although the saddle point itself (point of stationary phase) does not provide new insight, the ambiguity is removed by considering the steepest descent path through the point. Ray synthetic seismograms computed by this method compare well with synthetics computed by the reflectivity method, which does not suffer from the above-mentioned ambiguity since the integration path is taken along the real axis. This paper concentrates on the isotropic case, but it is discussed how the result may be extended to layered transversely isotropic media. The suggested approach, derived for a point source and plane layers, does not directly apply to 2-D or 3-D laterally inhomogeneous media, or to media of general anisotropy. A generalization of the result found is that the sign of the vertical slowness components should be chosen according to the energy flux direction for subcritical incidence and according to the radiation condition for supercritical incidence, even if this creates a discontinuity in the coefficients at the critical incidence angle. Such a discontinuity is sometimes necessary to get results which are consistent with the elastic case. It is discussed how the generalized result can be obtained by applying certain continuity criteria for the sub-and supercritical angle intervals, but the validity of this approach for general models remains to be proved.     

水平单轴应力与横波反射系数

地球物理勘探中,地下应力的估测是非常重要的.本文利用应力诱导的弱各向异性的各向异性参数, 借助已有的具有水平对称轴横向各向同性介质顾及高阶小量的横波反射系数近似公式,针对下介质为各向同性受单轴应力作用情况随应力的增加求取应力精度降低的问题,从横波反射系数近似公式的推导出发,联合SH波与SV 波反射系数给出新的改进的单轴应力与横波反射系数的直观表达式;计算并对比了受单轴应力作用的各向同性介质的横波近似和严格的反射系数,并利用理论得到的横波反射系数对应力进行了估值.结果表明,利用改进后横波反射系数与应力的直观表达式, 当应力增加时,应力估值精度有了明显的改善,这为利用横波反射数据直观估测应力提供理论依据.     

长偏移距P波AVO反射系数的一种近似

近年来,长偏移距排列逐渐被大量应用到海上勘探。传统AVO分析都是小入射角,对于长偏移距数据来说有很大不足。为了探讨拓宽AVO分析的研究范围,本文推导了长偏移距时P波反射系数的一种近似公式,并讨论了其精确性。本文的结果和广泛应用的Shuey公式相类似,Shuey公式可以看作本文结果在小入射角情况的简化。     

New imaging method for seismic reflection wave and its theoretical basis

Some new imaging formulas for seismic reflection wave and their theoretical basis are given. Phenomena of wave propagation should be characterized by instantaneous spectrum and expressed by complex function of three variables (time, space and frequency) in mathematics. Various physical parameters of medium are also complex functions of two variables (space and frequency). The relationship between reflection coefficient of medium and spectrum of reflected wave is given. Multi-reflection and filter of formations are considered in inversion formulas. Problems in classical convolution model and wave equation are illustrated. All these inversion formulas can be used to image underground medium by wavelet transform and method of “3-basic colors”. Different colors mean different media.     

Calculation of reflection and transmission coefficients for qP waves incident on a planar interface between isotropic and triclinic media

In the paper by Chattopadhyay and Rajneesh (2006, “Reflection and refraction of waves at the interface of an isotropic medium over a highly anisotropic medium’, Acta Geophysica, vol. 54, no. 3, pp. 239–249), the authors proposed a process to calculate R/T (reflection and transmission) coefficients at the interface between isotropic and triclinic half-spaces, with incident qP waves in triclinic media. Unfortunately, besides several misprints, the authors made a fatal assumption that there is no transmitted SH wave generated in isotropic media, which led the successive analytical derivations and numerical calculations thoroughly wrong. In this paper, the errors are analyzed at length and corrections are given. Then an alternative approach to solve the problem is proposed and numerical results are shown and discussed.     

An approximation to the P-wave reflection coefficient for amplitude variation with long-offset seismic data

近年来,长偏移距排列逐渐被大量应用到海上勘探。传统AVO分析都是小入射角,对于长偏移距数据来说有很大不足。为了探讨拓宽AVO分析的研究范围,本文推导了长偏移距时P波反射系数的一种近似公式,并讨论了其精确性。本文的结果和广泛应用的Shuey公式相类似,Shuey公式可以看作本文结果在小入射角情况的简化。     

地震数据的反射波动方程最小二乘偏移

基于反射波动方程,本文提出了一种估计地下反射率分布的地震数据最小二乘偏移方法.高频近似下,非齐次的一次反射波动方程的源项是由反射率与入射波场的时间一阶导数相互作用产生的.根据反射波动方程,利用线性最小二乘反演方法由地震反射数据重建出地下产生反射波的反射源,再结合波场正演计算出的地下入射波场,得到地下反射率分布的估计.在地下反射源的线性最小二乘反演重建中,我们采用迭代求解方法,并以地震波的检波器单向地下照明强度作为最小二乘优化问题中Hessian矩阵的近似.

     

关于VTI介质中多分量转换波地震数据采集的最佳接收时窗

以P_P波时窗和P_SV波时窗的交叉部分作为VTI介质中P_P波、P_SV波联合采集的最佳时窗,在有效时窗内通过基于VTI介质的射线追踪法确定每个反射点的P_P波、P_SV波射线路径和相角,求解Zoeppritz方程得出P_SV波与P_P波反射系数(或透射系数)的比值,并将该比值的绝对值定义为控制因子G. 以G值作为控制VTI介质中P_P波、P_SV波联合采集观测系统设计的主要参数,通过分析G值确定检波器位置的最佳接收时窗,得出优化VTI介质中多分量转换波地震数据采集的接收时窗的方法.