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1.
Kinematical characteristics of reflected waves in anisotropic elastic media play an important role in the seismic imaging workflow. Considering compressional and converted waves, we derive new, azimuthally dependent, slowness-domain approximations for the kinematical characteristics of reflected waves (radial and transverse offsets, intercept time and traveltime) for layered orthorhombic media with varying azimuth of the vertical symmetry planes. The proposed method can be considered an extension of the well-known ‘generalized moveout approximation’ in the slowness domain, from azimuthally isotropic to azimuthally anisotropic models. For each slowness azimuth, the approximations hold for a wide angle range, combining power series coefficients in the vicinity of both the normal-incidence ray and an additional wide-angle ray. We consider two cases for the wide-angle ray: a ‘critical slowness match’ and a ‘pre-critical slowness match’ studied in Parts I and II of this work, respectively. For the critical slowness match, the approximations are valid within the entire slowness range, up to the critical slowness. For the ‘pre-critical slowness match’, the approximations are valid only within the bounded slowness range; however, the accuracy within the defined range is higher. The critical slowness match is particularly effective when the subsurface model includes a dominant high-velocity layer where, for nearly critical slowness values, the propagation in this layer is almost horizontal. Comparing the approximated kinematical characteristics with those computed by numerical ray tracing, we demonstrate high accuracy. 相似文献
2.
Part II of this paper is a direct continuation of Part I, where we consider the same types of orthorhombic layered media and the same types of pure-mode and converted waves. Like in Part I, the approximations for the slowness-domain kinematical characteristics are obtained by combining power series coefficients in the vicinity of both the normal-incidence ray and an additional wide-angle ray. In Part I, the wide-angle ray was set to be the critical ray (‘critical slowness match’), whereas in Part II we consider a finite long offset associated with a given pre-critical ray (‘pre-critical slowness match’). Unlike the critical slowness match, the approximations in the pre-critical slowness match are valid only within the bounded slowness range; however, the accuracy within the defined range is higher. Moreover, for the pre-critical slowness match, there is no need to distinguish between the high-velocity layer and the other, low-velocity layers. The form of the approximations in both critical and pre-critical slowness matches is the same, where only the wide-angle power series coefficients are different. Comparing the approximated kinematical characteristics with those obtained by exact numerical ray tracing, we demonstrate high accuracy. Furthermore, we show that for all wave types, the accuracy of the pre-critical slowness match is essentially higher than that of the critical slowness match, even for matching slowness values close to the critical slowness. Both approaches can be valuable for implementation, depending on the target offset range and the nature of the subsurface model. The pre-critical slowness match is more accurate for simulating reflection data with conventional offsets. The critical slowness match can be attractive for models with a dominant high-velocity layer, for simulating, for example, refraction events with very long offsets. 相似文献
3.
The existence of‘*-waves’has, in recent years, prompted a renewed interest in these non-geometrical arrivals, which are generated by point sources located adajcent to plane interfaces. It has led to the re-evaluation of seismic data aquisition techniques and to the question of how to use this real phenomena in enhancing existing seismic interpretation methods. This paper considers a non-geometrical SH-arrival which is generated by a point torque source unrealistically buried within a half-space. The method of solution is essentially the same as presented in an earlier paper, with the modification that the limitation placed on the distance of the source from the interface has been removed in the saddle point method used to obtain a high-frequency approximate solution. In the earlier paper, a preliminary assumption forced the saddle point, which corresponded to the *-wave arrival, to be real when it is generally complex. However, for offsets removed from the distinct ray, the imaginary part of this complex quantity is negligible. A problem which arose when comparing exact synthetic traces with those obtained using zero-order saddle point methods, was the inability to match either the amplitude or phase of the geometrical arrival in the range of offsets when the *-wave and this corresponding geometrical ray were well separated. For this range of offsets the geometrical arrival was approaching grazing incidence and another term in the saddle point expansion of the integral was necessary to rectify this error. This method is also being used to validate the results for higher order terms obtained using asymptotic ray theory. Analytical formulae are given for both the *-wave and the higher order expansion of the geometrical event, together with a comparison of synthetic seismograms using the method developed here and a numerical integration algorithm. 相似文献
4.
A new method of numerical computation of elastic wavefields in regions containing caustics is tested. The method is an extension of the asymptotic ray theory (ART). The essential features of the method consist of the application of expressions which are well defined at caustics and expressed in terms of ray tracing combined with complex ray tracing in caustic shadows. The method and an outline of the underlying theory are briefly presented, followed by a comparison with finite differences on a test model involving a caustic cusp. The comparison reveals the unexpectedly high degree of accuracy of the new method. 相似文献
5.
Ru-Shan Wu 《Pure and Applied Geophysics》1996,148(1-2):155-173
When reverberations between heterogeneities or resonance scattering can be neglected but accumulated effects of forward scattering are strong, the Born approximation is not valid but the De Wolf approximation can be applied in such cases. In this paper, renormalized MFSB (multiple-forescattering single-backscattering) equations and the dual-domain expression for scalar, acoustic and elastic waves are derived by a unified approach. Two versions of the one-return method (using MFSB approximation) are given: One is the wide-angle dual-domain formulation (thin-slab approximation); the other is the screen approximation. In the screen approximation, which involves a small-angle approximation for the wave-medium interaction, it can be seen clearly that the forward scattered, or transmitted waves are mainly controlled by velocity perturbations; while the backscattered or reflected waves, by impedance perturbations. The validity of the method and the wide-angle capability of the dual-domain implementation are demonstrated by numerical examples. Reflection coefficients of a plane interface derived from numerical simulations by the wide-angle method match the theoretical curves well up to critical angles. For the reflections of a low-velocity slab, the agreement between theory and synthetics only starts to deteriorate for angles greater than 70°. The accuracy of the wide-angle version of the method could be further improved by optimizing the wave-number filtering for the forward propagation and shrinking the step length along the propagation direction. 相似文献
6.
横向各向同性介质是地球内部广泛分布的一种各向异性介质.针对这种介质,我们对各向同性介质的最小走时树走时模拟方法进行了推广,推广后的方法可适用于非均匀、对称轴任意倾斜的横向各向同性介质模型.为保证计算效率,最小走时树的构建采用了一种子波传播区域随地震波传播动态变化的改进算法.对于弱各向异性介质,我们使用了一种新的地震波群速度近似表示方法,该方法基于用射线角近似表示相角的思想,对3种地震波（qP, qSV和qSH）均有较好的精度.应用本文地震波走时模拟方法对均匀介质、横向非均匀介质模型进行了计算,并将后者结果与弹性波方程有限元方法的模拟结果进行了对比,结果表明两者符合得很好.本文方法可用于横向各向同性介质的深度偏移及地震层析成像的深入研究. 相似文献
7.
TTI介质是石油地震勘探领域最常用的各向异性介质,快速计算TTI介质射线路径和走时信息有重要的研究意义.TTI介质传统运动学射线追踪方法一般基于任意弹性介质射线方程,利用Bond变换或者四阶张量变换来处理复杂的21个弹性参数,因而非常耗时.实际野外对称轴统一的TTI介质模型,一般可以看成VTI介质模型旋转一定角度获得.为此,本文推导了三维VTI介质射线追踪方程,提出先在本构坐标系中进行VTI介质射线追踪,再通过坐标旋转将射线路径旋转至观测坐标系中,获得TTI介质射线路径.数值模型计算表明该方法高效和精确,较传统方法效率提高了近4倍.在强各向异性等特殊情况下,体波波前面都与理论群速度面一致. 相似文献
8.
9.
合成三维横向非均匀介质远震体波接收函数的Maslov方法 总被引：5，自引：3，他引：2
三维横向非均匀介质远震体波接收函数的合成算法对于三维介质远震体波接收函数研究至关重要．本文发展了基于Ｍａｓｌｏｖ理论的横向非均匀介质接收函数合成算法,针对远震体波接收函数计算的特点,利用遗传算法完成三维动力学射线追踪,并采用递归算法组织射线的追踪过程,从而在保证追踪精度的同时提高了射线追踪的效率,并可完全避免传统射线追踪过程中的射线编码问题．正演计算结果表明,此法是一种高效、实用的三维横向非均匀介质接收函数计算方法． 相似文献
10.
Identifying the sources of crustal reflections is essential for deriving more geological information from deep crustal reflection profiles. Theoretical and model studies help place constraints on the role of compositional variation in producing deep crustal reflections. Analysis of laboratory-derived velocities and densities of rock types typical for the continental crust indicates that reflection coefficients are generally small, but significantly, 17% of the possible reflection coefficients have magnitudes between 0.1 and 0.2. Comparison between reflection coefficients derived from well logs and reflections observed in associated seismic profiles indicates that constructive interference associated with geological layering is at least as important as the magnitude of the reflection coefficients for producing detectable reflections. Constructive interference can increase reflection amplitude by two to three times but is limited to a relatively narrow range of layer thickness. For a typical 10–40 Hz seismic wavelet and typical crustal velocities of about 6 km/s, constructive interference occurs for layer thickness ranging between about 35 and 80 m. Layers thinner than 35 m interfere destructively. If reflections result from compositional variation, seismic models of hypothetical and observed geologic relations provide analogs for interpreting complex reflection patterns observed in deep crustal reflection profiles. Such models show reflection patterns similar to those observed in the reflection profiles. The models indicate that the reflections could originate in the complexly deformed and intruded terranes that are common in the crystalline crust and it may not be necessary to appeal to unobserved phenomena such as special lamellae or fluid-filled fractures to explain the reflections. 相似文献
11.
３ＤｓｔｒｕｃｔｕｒａｌｒｅｃｏｎｓｔｒｕｃｔｉｏｎｏｆＭｏｈｏｉｎｔｈｅＴａｎｇｓｈａｎｅａｒｔｈｑｕａｋｅａｒｅａｂｙｕｓｉｎｇｉｎｖｅｒｓｉｏｎｏｆｃｕｒｖｅｄｉｎｔｅｒｆａｃｅＸＩＡＯＬＩＮＧＬＡＩ（赖晓玲）ＸＩＡＮＫＡＮＧＺＨＡＮＧ... 相似文献
12.
Common-ray tracing and dynamic ray tracing for S waves in a smooth elastic anisotropic medium 总被引：1，自引：0，他引：1
L. Klimeš 《Studia Geophysica et Geodaetica》2006,50(3):449-461
Anisotropic common S-wave rays are traced using the averaged Hamiltonian of both S-wave polarizations. They represent very
practical reference rays for calculating S waves by means of the coupling ray theory. They eliminate problems with anisotropic-ray-theory
ray tracing through some S-wave slowness-surface singularities and also considerably simplify the numerical algorithm of the
coupling ray theory for S waves.
The equations required for anisotropic-common-ray tracing for S waves in a smooth elastic anisotropic medium, and for corresponding
dynamic ray tracing in Cartesian or ray-centred coordinates, are presented. The equations, for the most part generally known,
are summarized in a form which represents a complete algorithm suitable for coding and numerical applications. 相似文献
13.
3-D simultaneous inversion for velocity and reflector geometry using multiple classes of arrivals in a spherical coordinate frame 总被引：1，自引：0，他引：1
Guo-jiao Huang Chao-ying Bai Xing-wang Li Stewart Greenhalgh 《Journal of Seismology》2014,18(1):123-135
The two key requirements in conducting 3-D simultaneous traveltime tomography on real data at the regional and global scale with multiple classes of arrival time information are (1) it needs an efficient and accurate arrival tracking algorithm for multiply transmitted, reflected (or refracted) and converted waves in a 3-D variable velocity model with embedded velocity discontinuities (or subsurface interfaces), and (2) a subdimensional inversion solver is required which can easily search for different types of model parameters to balance the trade-off between the different types of model parameter updated in the simultaneous inversion process. For these purposes, we first extend a popular grid/cell-based wavefront expanding ray tracing algorithm (the multistage irregular shortest-path ray tracing method), which previously worked only in Cartesian coordinate at the local scale, to spherical coordinates appropriate to the regional or global scale. We then incorporated a fashionable inversion solver (the subspace method) to formulate a simultaneous inversion algorithm, in which the multiple classes of arrivals (including direct and reflected arrivals from different velocity discontinuities) can be used to simultaneously update both the velocity fields and the reflector geometries. Numerical tests indicate that the new inversion method is both applicable and flexible in terms of computational efficiency and solution accuracy, and is not sensitive to a modest level of noise in the traveltime data. It offers several potential benefits over existing schemes for real data seismic imaging. 相似文献
14.
S. N. DOMENICO 《Geophysical Prospecting》1979,27(3):539-563
Inferior reflection quality in the Gulf of Suez at the target depth interval is attributable in part to surficial multiple reflections. An excellent example of the latter is observed on a typical seismic line in the northern portion of the Gulf. An increase in prominence of the multiple reflections appears associated with decreasing depth to a dipping highvelocity layer. Inversion of a second-order polynomial time-distance function, fitted to the observed refraction onset time-distance values, gives the velocity-depth function for sediments between the water bottom and a high-velocity layer. Velocities thus determined increase non-linearly with depth from a value near water velocity at the water bottom. Depths to the high-velocity layer are obtained from the associated head-wave linear time-distance function and by ray tracing in the overlying sediments. As the high-velocity layer approaches the water bottom from sub-water depths exceeding 0.6 km to a depth of 56 m, intensity of the multiple reflections increases to the extent of completely dominating individual records to a time of at least 3 s. The estimated plane-wave normal-incident reflection coefficient at the top of the high-velocity layer increases with decreasing depth to this layer, approaching 0.5 at the shallowest depth. This strong reflection coefficient further substantiates the existence of multiple reflections between the high-velocity layer and water layer. However, existence of water-layer multiples cannot be ruled out. The estimated water-bottom reflection coefficient is approximately 0.3, a substantial value. Multiple reflections of considerably less intensity are apparent where the high-velocity layer is deepest, and it is likely that such are waterlayer multiple reflections. Unfortunately, water-layer multiple reflections and multiple reflections between the water surface and high-velocity layer cannot be separated by their coincidence with time-distance (normal moveout) curves, the configuration of each visibly matching the curves equally well. 相似文献
15.
研究具有弯曲介面、各向同性、完全弹性的二维非均匀介质中波的传播问题, 在一定条件下, 弹性动力学方程的射线级数逼近法的高频渐近解可以对波场作近似计算。采用标准数字程序(龙克-库塔法)求解具有初始条件的两点射线追踪, 用改进了的Euler法求解两个一阶线性微分方程计算几何扩散因子。整个计算过程由Seis83程序包实现。本文利用Seis83程序包, 对通过唐山地震区相互交叉的柏各庄——丰南——丰宁——正兰旗剖面和沧州——天津——喀左剖面的实测资料进行解释, 进一步获得唐山地震区地壳上地幔的构造特征, 以及与地震活动较为关系密切的壳内低速度层的速度分布规律。 相似文献
16.
A closed-form analytical solution is presented for the dynamic response of a SDOF oscillator, supported by a flexible composite foundation embedded in an elastic half-space, and excited by plane SH waves. The solution is obtained by the wave function expansion method. The solution is verified for the two limiting cases of a rigid–flexible composite foundation and a homogeneous flexible foundation by comparison with published results. The model is used to investigate the effect of the foundation flexibility variation on the system response. The results show that the effect is significant for both foundation response and structural relative response. For a system with larger foundation flexibility variation, the peak of the foundation effective input motion is smaller, while the amplitude of structural relative response less changes. When foundation flexibility variation decreases, system frequency will shift to lower frequency, and the shift value is also highly dependent on the foundation flexibility variation. 相似文献
17.
GUY G. DRIJKONINGEN 《Geophysical Prospecting》1991,39(6):757-781
The contributions of the tunnelled constituents to a seismic wave are analysed in two different configurations pertaining to homogeneous acoustic media: a thin high-velocity layer, present in a plane-layered configuration, and a thin layer in media separated by dipping interfaces. The generalized ray method in the far-field is used to determine them. We expand around the relevant ray parameters in order to determine the characteristics of the tunnelling ray and find that the most important feature of this type of ray is a phase (in terms of asymptotic ray theory) which has a real and an imaginary part. Numerical results illustrate this. 相似文献
18.
电磁波走时层析可用于空洞和孤石等离散块体异常的探测中.在传统电磁波走时层析中,通常采用一个低阶差分泛函来稳定反演过程,而这类泛函都具有光滑约束的性质,在成像结果中难以对此类离散块体异常进行准确的解释.本文基于Tikhonov正则化思想,提出了一种反余切泛函,该泛函具有紧凑约束的性质且无需选择一个聚焦因子.结合弯曲胖射线层析理论和重加权正则化共轭梯度反演算法,对两个理论模型进行了成像效果研究.与低阶差分泛函和最小支撑泛函的成像结果相比,该方法能够更好地突出异常的边界,成像结果中的虚假异常也要更少.同时,还分析讨论了激发电磁波的中心频率以及数据噪音对成像结果的影响.此外,针对一个地下连续墙墙体内部缺陷的现场模型,利用该方法取得了理想的成像结果,良好地揭示了缺陷的形态和位置. 相似文献
19.
Alexey P. Kiselev 《Pure and Applied Geophysics》1993,140(4):629-640
Ray theory based upon real rays is presented for high frequencyP andS waves in continuously inhomogeneous isotropic linear media. Simple explicit formulae for the polarization anomalies described by higher order terms of the ray asymptotic expansions are considered. 相似文献
20.
This paper is the second in a sequel of two papers and dedicated to the computation of paraxial rays and dynamic characteristics along the stationary rays obtained in the first paper. We start by formulating the linear, second‐order, Jacobi dynamic ray tracing equation. We then apply a similar finite‐element solver, as used for the kinematic ray tracing, to compute the dynamic characteristics between the source and any point along the ray. The dynamic characteristics in our study include the relative geometric spreading and the phase correction due to caustics (i.e. the amplitude and the phase of the asymptotic form of the Green's function for waves propagating in 3D heterogeneous general anisotropic elastic media). The basic solution of the Jacobi equation is a shift vector of a paraxial ray in the plane normal to the ray direction at each point along the central ray. A general paraxial ray is defined by a linear combination of up to four basic vector solutions, each corresponds to specific initial conditions related to the ray coordinates at the source. We define the four basic solutions with two pairs of initial condition sets: point–source and plane‐wave. For the proposed point–source ray coordinates and initial conditions, we derive the ray Jacobian and relate it to the relative geometric spreading for general anisotropy. Finally, we introduce a new dynamic parameter, similar to the endpoint complexity factor, presented in the first paper, used to define the measure of complexity of the propagated wave/ray phenomena. The new weighted propagation complexity accounts for the normalized relative geometric spreading not only at the receiver point, but along the whole stationary ray path. We propose a criterion based on this parameter as a qualifying factor associated with the given ray solution. To demonstrate the implementation of the proposed method, we use several isotropic and anisotropic benchmark models. For all the examples, we first compute the stationary ray paths, and then compute the geometric spreading and analyse these trajectories for possible caustics. Our primary aim is to emphasize the advantages, transparency and simplicity of the proposed approach. 相似文献