Weak-contrast approximation of the elastic scattering matrix in anisotropic media     

Bjørn Ursin  Geir U. Haugen 《Pure and Applied Geophysics》1996,148(3-4):685-714

The plane-wave reflection and transmission coefficients at a plane interface between two anisotropic media constitute the elements of the elastic scattering matrix. For a 1-D anisotropic medium the eigenvector decomposition of the system matrix of the transformed elasto-dynamic equations is used to derive a general expression for the scattering matrix. Depending on the normalization of the eigenvectors, the expressions give scattering coefficients for amplitudes or for vertical energy flux.Computing the vertical slownesses and the corresponding polarizations, the eigenvector matrix and its inverse can be found. We give a simple formula for the inverse, regardless of the normalization of the eigenvectors. When the eigenvectors are normalized with respect to amplitudes of displacement (or velocity), the calculation of the scattering matrix for amplitudes is simplified.When the relative changes in all parameters are small, a weak-contrast approximation of the scattering matrix, based on the exactly determined polarization vectors in an average medium, is obtained. The same approximation is also derived directly from the transformed elasto-dynamic equations for a smooth vertically inhomogeneous medium, proving the consistency of the approximation.For monoclinic media, with the mirror symmetry plane parallel to the interface, the approximative scattering matrix is given in terms of analytic expressions for the non-normalized eigenvectors and vertical slownesses. For transversely isotropic media with a vertical axis of symmetry (VTI) and isotropic media, explicit solutions for the weak-contrast approximations of the scattering matrices have been obtained. The scattering matrix for amplitudes for isotropic media is well known. The scattering matrix for vertical energy flux may have applications in AVO analysis and inversion due to the reciprocity of the reflection coefficients for converted waves.Numerical examples for monoclinic and VTI media provide good agreement between the approximative and the exact reflection matrices. It is, however, expected that the approximations cannot be used when the symmetry properties of the two media are very different. This is because the approximation relies on a small relative contrast between the eigenvectors in the two media.Presented at the Workshop Meeting on Seismic Waves in Laterally Inhomogeneous Media, Castle of Trest, Czech Republic, May 22–27, 1995.  相似文献   

Fast computation of Hankel Transform using orthonormal exponential approximation of complex kernel function     

Pravin K. Gupta  Sri Niwas  Neeta Chaudhary 《Journal of Earth System Science》2006,115(3):267-276

The computation of electromagnetic (EM) fields, for 1-D layered earth model, requires evaluation of Hankel Transform (HT) of the EM kernel function. The digital filtering is the most widely used technique to evaluate HT integrals. However, it has some obvious shortcomings. We present an alternative scheme, based on an orthonormal exponential approximation of the kernel function, for evaluating HT integrals. This approximation of the kernel function was chosen because the analytical solution of HT of an exponential function is readily available in literature. This expansion reduces the integral to a simple algebraic sum. The implementation of such a scheme requires that the weights and the exponents of the exponential function be estimated. The exponents were estimated through a guided search algorithm while the weights were obtained using Marquardt matrix inversion method. The algorithm was tested on analytical HT pairs available in literature. The results are compared with those obtained using the digital filtering technique with Anderson filters. The field curves for four types (A-, K-, H-and Q-type) of 3-layer earth models are generated using the present scheme and compared with the corresponding curves obtained using the Anderson sc heme. It is concluded that the present scheme is more accurate than the Anderson scheme  相似文献   

Ekman动量近似下中间边界层模式中的风场结构   总被引：2，自引：0，他引：2  

Tan Zhemin  Wang Yuan 《大气科学进展》2002,19(2):266-278

发展了一个准三维的、中等复杂的边界层动力学模式，该模式包含了EKman动量近似下的惯性加速度和Blackadar的非线性湍流粘性系数，它进一步改进了Tan和Wu(1993）提出的边界层理论模型。该模型在数值计算复杂性上与经典Ekman模式相类似，但由于包含了Ekman动量近似下的惯性项，使得该模式比传统Ekman模式更近于实际过程。中详细地比较了该模式与其他简化边界层模式在动力学上的差异，结果表明：在经典的Ekman模式中，由于忽略了流动的惯性项作用，导致在气旋性切变气流（反气旋性切变气流）中风速和边界层顶部的垂直速度的高估（低估），而在半地转边界层模式中，由于高估了流动惯性项的作用，结果与经典Ekman模式相反。同样，该模式可以应用于斜压边界层，对于Ekman动量下的斜压边界层风场同时具有经典斜压边界层和Ekman动量近似边界层的特征。  相似文献   

Probing mid-mantle heterogeneity using PKP coda waves     

Michael A. H. Hedlin  Peter M. Shearer   《Physics of the Earth and Planetary Interiors》2002,130(3-4):195-208

We investigate the utility of PKP coda waves for studying weak scattering from small-scale heterogeneity in the mid-mantle. Coda waves are potentially a useful probe of heterogeneity in the mid-mantle because they are not preferentially scattered near the CMB, as PKP precursors are, but are sensitive to scattering at all depths. PKP coda waves have not been used for this purpose historically because of interference with other late-arriving energy due to near-surface resonance and scattering. Any study of deep mantle scattering using coda waves requires the removal of near-surface effects from the data. We have analyzed 3624 recordings of PKP precursors and coda made by stations in the Incorporated Research Institutions for Seismology (IRIS) Global Seismographic Network (GSN). To study the range and time dependence of the scattered waves, we binned and stacked envelopes of the recordings. We have considered precursors that arrive within a 20 s window before PKP and coda waves in a 60 s window after PKP. The PKP scattered waves increase in amplitude rapidly with range as predicted by scattering theory. At ranges below 125°, we predict and observe essentially no scattered energy preceding PKP. Coda amplitudes at these ranges are independent of range and provide an estimate of energy due to near-surface effects that we can expect at all ranges. We use the average coda amplitude at ranges from 120 to 125° to correct coda amplitudes at other ranges. PKP coda waves show a strong dependence on time and range and are clearly influenced by scattering in the lower mantle. PKP coda waves, however, do not provide a tighter constraint on the vertical distribution of mantle heterogeneity than is provided by precursors. This is due, in part, to relatively large scatter in coda amplitudes as revealed by a resampling analysis. Modeling using Rayleigh–Born scattering theory and an exponential autocorrelation function shows that PKP coda amplitudes are not highly sensitive to the vertical distribution of heterogeneity in the mantle. To illustrate this we consider single-scattering in two extreme models of mantle heterogeneity. One allows heterogeneity just at the CMB; the other includes heterogeneity throughout the mantle. The amplitudes of precursors are tightly constrained by our stack and support our earlier conclusion that small-scale heterogeneity is uniformly distributed throughout the lower mantle. The best-fit model includes 8 km scale length heterogeneity with an rms velocity contrast throughout the mantle of 1%.  相似文献   

The effect of scattering in surface wave tomography   总被引：6，自引：1，他引：6  

Jesper Spetzler  Jeannot Trampert  Roel Snieder 《Geophysical Journal International》2002,149(3):755-767

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变参考慢度Born近似傅氏偏移   总被引：1，自引：0，他引：1  

杜正聪  贺振华  王志  黄德济 《吉林大学学报(地球科学版)》2003,33(4):555-558

针对常规Born近似傅氏偏移方法对于剧烈横向变速介质不能精确成像的状况而提出了变参考慢度Born近似傅氏偏移，理论上解决了任意速度变化地质模型的偏移成像问题。此外，为进一步提高复杂地层的成像精度和波场延拓算子的稳定性，对散射波场的计算公式作了改进。将改进的方法运用于盐丘模型的正演和偏移试验，并与常规Born近似偏移方法相比较，可明显看出变参考慢度Born近似傅氏偏移方法在效果上要优于后者，其处理速度横向变化的能力大大增强。  相似文献   

Spectral and Multiscale Signal-to-Noise Thresholding of Spherical Vector Fields   总被引：1，自引：0，他引：1  

W. Freeden  T. Maier 《Computational Geosciences》2003,7(3):215-250

The basic concepts of spectral and multiscale selective reconstruction of (geophysically relevant) vector fields on the sphere from error-affected data is outlined in detail. The reconstruction mechanism is formulated under the assumption that spectral as well as multiscale approximation is well-representable in terms of only a certain number of expansion coefficients at the various resolution levels. It is shown that spectral denoising by means of orthogonal expansions in terms of vector spherical harmonics reflects global a priori information of the noise (e.g., in form of a covariance tensor field), whereas multiscale signal-to-noise thresholding can be performed under locally dependent noise information within a multiresolution analysis in terms of spherical vector wavelets. An application of the multiscale formalism to Earth's magnetic field determination is presented.  相似文献   

非线性模型线性近似的容许曲率     

王新洲 《武汉大学学报(信息科学版)》1997,(2)

由于不同的非线性模型具有不同的非线性强度，使得一些非线性模型可以线性近似，而另一些则不能。本文介绍度量非线性强度的方法，提出判断非线性模型能否线性近似的数值标准——容许曲率  相似文献   

Resolution limits for crosswell migration and traveltime tomography   总被引：2，自引：1，他引：2  

Gerard T. Schuster 《Geophysical Journal International》1996,127(2):427-440

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松辽盆地白垩系浅水湖泊三角洲沉积微相研究——以大庆杏树岗油田杏三区东部葡Ⅰ1-3小层为例   总被引：1，自引：1，他引：0       下载免费PDF全文

冯旭东  张东  林春明  张霞  刘威  于进  李葳 《沉积与特提斯地质》2016,36(2):1-10

根据密井网测井、录井以及其它分析化验资料,结合区域地质背景,对松辽盆地杏树岗油田杏三区东部白垩系姚家组一段葡萄花Ⅰ组油层1-3小层(葡Ⅰ1-3小层)沉积微相类型、特征、组合模式和不同地质时期沉积微相平面展布特征及其演化规律进行系统的研究。结果表明,葡Ⅰ1-3小层为浅水湖泊三角洲沉积,主要发育三角洲分流平原和三角洲内前缘2种沉积亚相,含11种沉积微相,具有不同的沉积特征和测井相模式;利用自然电位曲线幅变值和砂体厚度,有效识别天然堤、水上决口沉积、溢岸薄层砂3种有成因联系、测井曲线形态类似的沉积微相;进一步根据各沉积微相的测井曲线形态组合、沉积成因及沉积作用的不同,总结出7种沉积微相组合模式。葡Ⅰ1-3小层沉积演化经历了早期湖退、中期稳定、晚期湖侵3个阶段,不同时期的沉积特征、沉积微相展布各异,总体表现出湖盆发育规模由大变小,再变大,骨架砂体厚度和理想钻遇率逐渐减小的特点。  相似文献