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1942年,Hartley在傅立叶变换基础上进行改进,提出Hartley变换,Hartley变换(HT)是一种实数域内的变换,比傅立叶变换(FT)至少减少一半的空间和时间.本文介绍了Hartley变换在地震波研究中的应用,包括强震数据转换、地震动模拟中的变换问题,举例说明了Hartley变换在节约计算空间和提高计算效率上的优越性. 相似文献
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本文采用一种新颖的积分变换Hartley变换,系统推导了其频率域化极方法,提出在实数空间利用Hartley变换进行磁异常化极.结合现有的低纬度化极方法,讨论了低纬度Hartley变换化极特性,实现低纬度化极.理论模型计算表明建立的Hartley变换化极方法准确、可靠,实际资料处理表明该化极方法具有实用性. 相似文献
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《Journal of Applied Geophysics》2010,72(4):157-161
An intimate mathematical relation between Hartley and Hilbert transforms is given here in contrast with the well known Fourier and Hilbert transform relations. It is interesting to note that the Fourier–Hilbert and Hartley–Hilbert transforms while possessing the same magnitude differ in phase by 270°. The inverse Hartley–Hilbert transform returns the original function unlike the Fourier–Hilbert transform which results the negative of the original function. Further, it may be realized that the envelope defined here of the analytic signal in both Fourier–Hilbert and Hartley–Hilbert domains numerically remain the same while differing in polarity. The feasibility of Hartley–Hilbert transform for a straight forward interpretation, total magnetic anomaly due to a thin plate from Tejpur, India and self potential data of the Sulleymonkey anomaly in the Ergani Copper district, Turkey are illustrated in contrast with the Fourier–Hilbert transform. This pair of transforms have innumerable geophysical applications. 相似文献
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Yang Qi-qiang Lin Chan Zhong Cheng Zhang Shulu Wang Changlong 《Journal of Applied Geophysics》2010,70(2):169-180
Numerical methods using the Hartley transform are described for the simulation of 3-D wave phenomena with application to the modeling of seismic data. Four topics are covered. The first deals with the solution of the 3-D acoustic wave equation. The second handles the solution of the 3-D two way nonreflecting wave equation. The third involves modeling with an areal source. The fourth treats wave phenomena whose direction of propagation is restricted within ± 90° from a given axis.The numerical methods developed here are similar to the Fourier methods. Time stepping is performed with a second-order differencing operator. The difference is that expressions including space derivative terms are computed by the Hartley transforms rather than the Fourier transforms. Being a real-valued function and equivalent to the Fourier transform, the Hartley transform avoids computational redundancies in terms of the number of operations and memory requirements and thus is more efficient and economical than the Fourier transform. These features are crucial when dealing with 3-D seismic data. The numerical results agree with the analytical results. The use of areal source in modeling can efficiently provide data for testing some schemes that deal with the areal shot-records. Using the transform methods, we can impose constraints on the direction of the wave propagation most precisely in the wavenumber domain when attempting to restrict propagation to upward moving waves. The implementation of the methods is demonstrated on numerical examples. 相似文献
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The Fourier transform formula for a two-dimensional fault truncating a horizontal bed at an arbitrary angle of inclination is derived. The amplitude spectrum of the Fourier transform is found to give information about the depth to the top of the upper part of the faulted bed and the inclination of the fault-plane. Under suitable conditions the thickness and the displacement of the bed involved can be obtained. With actual field data, these transforms can be obtained at discrete points by a Fourier analysis of the gravity anomaly. A field example from the Logan fault area near Montreal, Que., Canada, is given. 相似文献
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基于反射系数谱理论的薄层多波AVO 总被引：2，自引：0，他引：2
AVO分析是目前地震勘探潜在油气储层的一个重要方法。体散射信息包含了层结构、岩性和孔隙流体信息,对地震勘探非常有用。但是基于 Zoeppritz方程的传统AVO分析之只包含了单层信息。薄层厚度定量解释对构造解释、储层描述和储层横向预测都非常重要。本文阐述的基于频率域弹性传播矩阵反射系数谱方法既考虑了层界面引起的振幅变化(Zoeppritz方程),也考虑了层内传播引起的振幅变化。因此该反射系数谱既包括单一层界面信息,也包括层内体散射信息。该反射系数谱是层厚和频率的连续函数,便于分析频率和层厚对反射系数谱的影响。可分析的薄层厚度可以无限小,直至消失。可分析的频率是任意的和连续的。这是对时间域反射系数做傅里叶变换无法实现的。地震波的传播是复杂的,各种波型是同时存在而且相互转换的,该反射系数谱考虑了各种波型在传播过程中的相互转换以及多次波。与比射线方法比更便于正演薄层多波多分量AVO响应。 相似文献
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基于Bregman迭代的复杂地震波场稀疏域插值方法 总被引：2，自引：1，他引：1
在地震勘探中,野外施工条件等因素使观测系统很难记录到完整的地震波场,因此,资料处理中的地震数据插值是一个重要的问题。尤其在复杂构造条件下,缺失的叠前地震数据给后续高精度处理带来严重的影响。压缩感知理论源于解决图像采集问题,主要包含信号的稀疏表征以及数学组合优化问题的求解,它为地震数据插值问题的求解提供了有效的解决方案。在应用压缩感知求解复杂地震波场的插值问题中,如何最佳化表征复杂地震波场以及快速准确的迭代算法是该理论应用的关键问题。Seislet变换是一个特殊针对地震波场表征的稀疏多尺度变换,该方法能有效地压缩地震波同相轴。同时,Bregman迭代算法在以稀疏表征为核心的压缩感知理论中,是一种有效的求解算法,通过选取适当的阈值参数,能够开发地震波动力学预测理论、图像处理变换方法和压缩感知反演算法相结合的地震数据插值方法。本文将地震数据插值问题纳入约束最优化问题,选取能够有效压缩复杂地震波场的OC-seislet稀疏变换,应用Bregman迭代方法求解压缩感知理论框架下的混合范数反问题,提出了Bregman迭代方法中固定阈值选取的H曲线方法,实现地震波场的快速、准确重建。理论模型和实际数据的处理结果验证了基于H曲线准则的Bregman迭代稀疏域插值方法可以有效地恢复复杂波场的缺失信息。 相似文献
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Simulation of induction logging responses in formations with large conductivity contrasts is an important but challenging problem due to the singularity of a linear system caused by large contrasts. Also, three‐dimensional (3D) analysis of complex geophysical structures usually encounters high computational demands. In this paper, a pre‐corrected fast Fourier transform (pFFT)‐accelerated integral equation method is applied to overcome these difficulties. In the approach, the entire formation is included in the solution domain. The volume integral equation is set up in the region based on the fact that the total field is the summation of the excitation field and the secondary field. The emitted field by the transmitter coil (treated as a magnetic dipole) is regarded as the excitation of the system. Then the method of moments (MoM) is used to solve the integral equation. To reduce the high computational requirements of the MoM, the pFFT method is used to speed up the solution of the matrix equation and reduce the memory requirement as well. The resultant method is capable of computing induction logging problems involving large and complex formations. For problems with high conductivity contrasts, the solution of the matrix equation usually converges very slow or even fails to converge due to the large condition number of the coefficient matrix. To overcome this difficulty, an incomplete LU pre‐conditioner is used to significantly speed up the convergence of the matrix equation, thus further reducing the computation time. Numerical results show that the present method is efficient and flexible for 3D simulation of induction logging and is specifically superior for problems with high conductivity contrasts. 相似文献
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利用小波变换方法可以把原始信号分解为一系列载有不同信息的子信号,每种子信号载有储层的特定信息,包括流体、岩性和孔隙结构等。我们开发出了基于小波变换的谱分析方法,利用该方法可以从这些子信号中提取出反映地层流体特性的子信号,通过对该子信号的处理识别出地层所含流体的特性。本文利用该流体识别新方法对某油田的实际测井资料进行了处理,处理结果与试油结果符合得很好,进一步证明了本方法的可靠性和实用性。 相似文献
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借助Walsh变换实现引力位球谐函数的快速Fourier变换导出了球谐函数的Walsh-Fourier变换、转换矩阵的快速Walsh-Hadamard变换算法及其数据压缩方法还讨论了Walsh-Fouriede换的特性及其在球谐分析中的应用研究表明：当序率和频率等同时．Walsh．Fourier变换和Fourier变换的结果完全一致,两者曲线形态相同;按双精度运算,两种方法的计算准确度均可达到±（10－15-10－14）;Walsh－Fourler变换可以用实数变换取代Fourier变换的复数变换;快速Walsh－Hadamard变换速度提高的幅度将随着阶数的增加而递增：Walsh-Fourier变换可以用于序率和频率等同或不等同的情形Walsh-Fourler变换可在计算精度、数据压缩和位场谱表示方面好于Fourier变换 相似文献
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Rumpa Chakraborty 《地球物理与天体物理流体动力学》2013,107(5):481-496
The two-dimensional problem of the generation of water waves due to instantaneous disturbances prescribed at the bed of a beach sloping at an arbitrary angle is studied here. It is formulated in terms of an initial-boundary-value problem for the velocity potential describing the motion in the fluid region assuming the linear theory. Using the Laplace transform in time and the Mellin transform in distance, the problem is reduced to solving a difference equation whose method of solution is of considerable importance in the literature. The form of the free surface is obtained in terms of a multiple infinite integral that is evaluated by the method of steepest-descent. For some prescribed forms of the disturbance at the bed of the beach, the free surface is depicted in a number of figures for different beach angles. It is observed that as the beach angle decreases, the maximum wave height increases, which is plausible. 相似文献
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本文提出一种空间波数混合域磁异常场三维数值模拟方法.该方法利用磁位三维空间域积分为卷积的特点,沿水平方向进行二维傅里叶变换,把空间域磁位满足的三维积分问题转化为不同波数之间相互独立的垂向一维积分问题.保留垂向为空间域,优势之一在于便于浅层单元剖分可适当加密,随着深度增加,单元剖分适当稀疏,可以准确模拟任意复杂地形和磁性体的磁异常,兼顾了计算精度与计算效率;优势之二在于一维积分垂向可离散为多个单元积分之和,每个单元采用二次形函数表征磁化强度,可得出单元积分的解析表达式,计算精度高、效率高.该方法充分利用一维形函数积分的高效和高精度、快速傅里叶变换的高效性及算法高度并行性,实现了磁异常场高效、高精度的数值模拟.设计棱柱体模型,将模型解析解与空间波数混合域法的数值解对比,结果表明该方法计算精度高、效率高.设计了组合棱柱体复杂模型,对比分析了标准FFT扩边法与Gauss-FFT法的计算精度与计算效率,总结了标准FFT的扩边系数选取策略.针对任意复杂地形条件下的磁异常模拟问题,本文提出一种适用于起伏地形条件下的磁异常场快速计算方法,并对其有效性进行了验证. 相似文献
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测井约束地震反演综述 总被引：18，自引：7，他引：18
阐述了测井约束地震反演研究的必要性、技术内涵及研究思路，回顾了测井约束地震反演技术的发晨历程，比较了三种非线性测井约束地震反演方法的优缺点。小波变换以其独特的变时窗特性，在测井约束地震反演技术发展中潜力较大，值得深入研究。同时对测井约束地震反演技术的研究现状做了小结，指出当前的研究对象已转向了复杂地质体。特别是海相碳酸盐岩复杂地质体，由于海相和陆相油气田存在许多不同之处，所以测井约束地震反演技术将面临巨大的机遇和挑战。最后，指出了测井约束地震反演技术的发展方向。 相似文献
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We conducted a study on the numerical calculation and response analysis of a transient electromagnetic field generated by a ground source in geological media. One solution method, the traditional discrete image method, involves complex operation, and its digital filtering algorithm requires a large number of calculations. To solve these problems, we proposed an improved discrete image method, where the following are realized: the real number of the electromagnetic field solution based on the Gaver–Stehfest algorithm for approximate inversion, the exponential approximation of the objective kernel function using the Prony method, the transient electromagnetic field according to discrete image theory, and closed-form solution of the approximate coefficients. To verify the method, we tentatively calculated the transient electromagnetic field in a homogeneous model and compared it with the results obtained from the Hankel transform digital filtering method. The results show that the method has considerable accuracy and good applicability. We then used this method to calculate the transient electromagnetic field generated by a ground magnetic dipole source in a typical geoelectric model and analyzed the horizontal component response of the induced magnetic field obtained from the “ground excitation–stratum measurement” method. We reached the conclusion that the horizontal component response of a transient field is related to the geoelectric structure, observation time, spatial location, and others. The horizontal component response of the induced magnetic field reflects the eddy current field distribution and its vertical gradient variation. During the detection of abnormal objects, positions with a zero or comparatively large offset were selected for the drillhole measurements or a comparatively long observation delay was adopted to reduce the influence of the ambient field on the survey results. The discrete image method and forward calculation results in this paper can be used as references for relevant research. 相似文献
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Prabhakar S. Naidu 《Pure and Applied Geophysics》1970,81(1):17-25
Summary
Cooley andTukey's fast Fourier transform algorithm for two dimensional complex data has been modified so as to reduce the storage space and computation time to half. The modified version has enabled us to Fourier transform aeromagnetic field over twice the area that could be covered by the original method. From the Fourier transform we computed radial spectrum, which could be approximated by three straight line segments whose slopes are related to the depths of the various magnetic layers. The computed depths are: 1090', 2600', and 7200'. 相似文献
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提出直接在序率域内用Walsh变换实现引力场球谐综合的问题。给出球谐函数展开式的Walsh变换及快速算法,讨论了Walsh变换和Walsh-Fourier变换、Fourier变换之间的差异,分析了用地球重力场模型OSU81的位系数作出的Walsh变换和Fourier变换的结果。研究表明:Walsh变换与Walsh-Fourier变换、Fourier变换对应向量在数量方面的差值通常都小于士10~(-5);对于给定的阶数和飞行高度,3种方法求得的球谐综合值总是完全一致的;1°×1°等网格数据和Walsh函数形状相近。在重力场研究中Walsh级数会比Fourier级数收敛得更快;Walsh变换在计算速度、计算准确度、数据储存、收敛速度和方法简单方面都好于Fourier变换。 相似文献