A note on dynamic ray tracing in ray-centered coordinates in anisotropic inhomogeneous media

Dynamic ray tracing plays an important role in paraxial ray methods. In this paper, dynamic ray tracing systems for inhomogeneous anisotropic media, consisting of four linear ordinary differential equations of the first order along the reference ray, are studied. The main attention is devoted to systems expressed in a particularly simple choice of ray-centered coordinates, here referred to as the standard ray-centered coordinates, and in wavefront orthonormal coordinates. These two systems, known from the literature, were derived independently and were given in different forms. In this paper it is proved that both systems are fully equivalent. Consequently, the dynamic ray tracing system, consisting of four equations in wavefront orthonormal coordinates, can also be used if we work in ray-centered coordinates, and vice versa. vcerveny@seis.karlov.mff.cuni.cz     

基于耦合标势与矢势的有限体积法模拟非均匀各向异性地层中多分量感应测井三维响应

为快速有效地研究、考察各向异性地层条件下多分量感应测井的响应特征,本文利用电场标势与矢势的有限体积法研制出三维频率域电磁场响应的数值模拟算法,克服由低频发射或高阻地层产生的低感应数问题,有效提高了三维电磁数值模拟算法的应用范围和计算效率.首先利用电场的标势与矢势将Maxwell方程转化为满足库仑规范条件的耦合势Helmholtz方程,以Yee氏交错非均匀网格中不同位置上的节点为中心建立四种控制体积单元,通过对控制体积单元中电磁场与电导率的积分平均实现耦合势方程和磁偶极子旋度的离散,并得到一个对角占优的大型稀疏复线性代数方程组,然后,通过不完全LU分解预处理和稳定双共轭梯度法快速求解离散方程.数值结果证明了该算法的有效性,并进一步考查了仪器偏心、倾斜井、垂直裂缝等复杂条件下多分量感应的响应特征.     

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.     

Modelling S-wave radiation for SP-waves in isotropic and anisotropic media

Utilizing shear-wave (S-wave) data acquired with compressional waves (P-waves) is becoming more common as joint imaging and inversion techniques improve. Interest in S-waves radiated from vertical sources and buried explosives exploits conversion to P-waves as primary reflections (SP-waves) for reducing acquisition costs and for application to legacy data. However, recent investigations overstate the extent of SP-wave illumination and show isotropic processing results with narrow bandwidth frequency and wavenumber data. I demonstrate that illumination with SP-waves is limited in general to near vertical polar angles up to around 30° or 35° for V_P/V_S of 2 or 3, respectively. At greater angles, S-waves are typically in the P-wave evanescent range and cannot excite SP-wave reflections. Contrary to recent claims, these sources for P-wave do not radiate S_H-waves polarized in horizontal planes in all azimuths. I show these properties for isotropic media with radiation expressions for amplitude derived in vector slowness coordinates. Also, I extend these expressions to transversely isotropic media with a vertical symmetry axis to show agreement with synthetic seismic data that only quasi S_V-waves are radiated and become more narrowly focused towards 45°. Furthermore, in orthorhombic media, synthetic data show that fast S₁- and slow S₂-waves polarized parallel and perpendicular to fractures may appear as S_V- and S_H-waves. For the partially saturated fracture model studied here, S₁-wave radiation has broader azimuthal illumination than slow S₂-waves, which are more narrowly focused in azimuth. These produce SP-wave splitting signatures on vertical component reflection data that are nearly identical to PS-wave signatures on radial horizontal component data. Separating these fast and slow SP-waves is an additional processing challenge.     

移动线源的Green函数求解及辐射能量分析:高铁地震信号简化建模

在基于人工主动源的勘探地震学中,往往采用固定位置和激发时间的点源数学模型来描述爆炸型震源或可控震源,因此就有了描述单点力源作用下的弹性全空间或半空间中弹性波传播的Green函数,成为了勘探地震学的重要理论基础.而如今,行进中的高速列车（高铁）是一种全新的主动源,其接近匀速的运行速度、确定的长度和荷载使其可以被重复利用.本文将行进中的高铁在数学上简化建模为一个移动线源来进行研究,给出了这一震源作用下的弹性半空间和全空间中Green函数的计算方法,并分别讨论了全空间中远场Green函数的频谱特征和空间辐射能量的方向性特点,以及半空间中Green函数与近场观测数据的对比结果,为高铁震源下的地震波传播规律和振动信号的研究与利用提供帮助.

     

Radiation patterns of point sources situated close to structural interfaces and to the earth's surface

The seismic wave field is considerably influenced by local structures close to the source and to the receiver. This applies to sources and receivers situated close to localized inhomogeneities, to structural interfaces, to the earth's surface, etc. In this paper we concentrate our attention mainly to the ray-theoretical radiation patterns of point sources situated close to the structural interfaces and to the earth's surface. In numerical modeling of high-frequency seismic wave fields by the ray method, the interaction of the source with the earth's surface has not usually been taken into account.The proposed procedure of the computation of the radiation patterns of point sources situated directly on structural interfaces and on the earth's surface is based on the zero-order approximation of the ray method, assuming that the length of the ray between the source and the receiver is long. The derived equations are extended to point sources located close to structural interface, to the earth's surface and to thin transition layers using the hybrid ray-reflectivity method, seeervený (1989). The thin layer need not be homogeneous; it may include an arbitrary inner layering (transition layers, laminas, etc.) The only requirement is for the layer to be thin. Roughly speaking, we require its thickness to be less than one quarter of the prevailing wavelength. The hybrid ray-reflectivity method describes well even certain non-ray effects (tunneling.S ^* waves, etc.). Explicit analytical expressions for radiation patterns for all above listed point sources are found. These expression have a local character and may be easily implemented into computer codes designed for the routine computation of ray amplitudes and synthetic ray seismograms in 2-D and 3-D, laterally varying isotropic layered and block structures by the ray method.Numerical examples of radiation patterns ofP andS waves of point sources situated close to the earth's surface and to a thin low-velocity surface layer are presented and discussed. The explosive point source (center of dilatation) and the vertical and horizontal single force point sources are considered. It has been ascertained that the radiation patterns of point sources depend drastically on the depth of the source below the surface even if the depths vary within one quarter of the prevailing wavelength.