共查询到20条相似文献，搜索用时 46 毫秒
1.
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
2.
The hyperbolic Radon transform has a long history of applications in seismic data processing because of its ability to focus/sparsify the data in the transform domain. Recently, deconvolutive Radon transform has also been proposed with an improved time resolution which provides improved processing results. The basis functions of the (deconvolutive) Radon transform, however, are time-variant, making the classical Fourier based algorithms ineffective to carry out the required computations. A direct implementation of the associated summations in the time–space domain is also computationally expensive, thus limiting the application of the transform on large data sets. In this paper, we present a new method for fast computation of the hyperbolic (deconvolutive) Radon transform. The method is based on the recently proposed generalized Fourier slice theorem which establishes an analytic expression between the Fourier transforms associated with the data and Radon plane. This allows very fast computations of the forward and inverse transforms simply using fast Fourier transform and interpolation procedures. These canonical transforms are used within an efficient iterative method for sparse solution of (deconvolutive) Radon transform. Numerical examples from synthetic and field seismic data confirm high performance of the proposed fast algorithm for filling in the large gaps in seismic data, separating primaries from multiple reflections, and performing high-quality stretch-free stacking. 相似文献
3.
Ground roll attenuation using the S and x-f-k transforms 总被引：2，自引：0，他引：2
Ground roll, which is characterized by low frequency and high amplitude, is an old seismic data processing problem in land‐based seismic acquisition. Common techniques for ground roll attenuation are frequency filtering, f‐k or velocity filtering and a type of f‐k filtering based on the time‐offset windowed Fourier transform. These techniques assume that the seismic signal is stationary. In this study we utilized the S, x‐f‐k and t‐f‐k transforms as alternative methods to the Fourier transform. The S transform is a type of time‐frequency transform that provides frequency‐dependent resolution while maintaining a direct relationship with the Fourier spectrum. Application of a filter based on the S transform to land seismic shot records attenuates ground roll in a time‐frequency domain. The t‐f‐k and x‐f‐k transforms are approaches to localize the apparent velocity panel of a seismic record in time and offset domains, respectively. These transforms provide a convenient way to define offset or time‐varying reject zones on the separate f‐k panel at different offsets or times. 相似文献
4.
Planar waves events recorded in a seismic array can be represented as lines in the Fourier domain. However, in the real world, seismic events usually have curvature or amplitude variability, which means that their Fourier transforms are no longer strictly linear but rather occupy conic regions of the Fourier domain that are narrow at low frequencies but broaden at high frequencies where the effect of curvature becomes more pronounced. One can consider these regions as localised “signal cones”. In this work, we consider a space–time variable signal cone to model the seismic data. The variability of the signal cone is obtained through scaling, slanting, and translation of the kernel for cone‐limited (C‐limited) functions (functions whose Fourier transform lives within a cone) or C‐Gaussian function (a multivariate function whose Fourier transform decays exponentially with respect to slowness and frequency), which constitutes our dictionary. We find a discrete number of scaling, slanting, and translation parameters from a continuum by optimally matching the data. This is a non‐linear optimisation problem, which we address by a fixed‐point method that utilises a variable projection method with ?1 constraints on the linear parameters and bound constraints on the non‐linear parameters. We observe that slow decay and oscillatory behaviour of the kernel for C‐limited functions constitute bottlenecks for the optimisation problem, which we partially overcome by the C‐Gaussian function. We demonstrate our method through an interpolation example. We present the interpolation result using the estimated parameters obtained from the proposed method and compare it with those obtained using sparsity‐promoting curvelet decomposition, matching pursuit Fourier interpolation, and sparsity‐promoting plane‐wave decomposition methods. 相似文献
5.
地震信号属于非线性和非平稳信号,传统的分析方法主要包括短时傅立叶变换、小波变换和Cohen类时频分布等等;希尔伯特-黄变换是分析非平稳信号的新方法,该方法的关键部分是信号的经验模态分解,通过经验模态分解,复杂的信号可以分解为有限的数量很少的几个固有模态函数,从而可以得到信号的希尔伯特时频谱;将该方法应用于单个的地震道数据,可以对地震道进行经验模态分解并得到希尔伯特谱,应用于地震剖面,可以得到意义更加明确的瞬时频率和瞬时振幅等地震属性,模型试算和实际应用表明了该方法的有效性. 相似文献
6.
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
7.
KAMAL M. AL-YAHYA 《Geophysical Prospecting》1991,39(1):77-93
The Karhunen-Loève (K–L) transform is an effective technique for suppressing spatially uncorrelated noise, but because of its high computational cost, fast transforms, such as the Fourier transform, have been more favoured. Two techniques that combine to make the K–L transform feasible for seismic data processing are discussed. The first technique filters the data for limited dips. For each dip, linear moveout is applied to the seismic sections so that events with this dip are made flat. By interpolation, we can include dips that are fractions of a sample/trace. After linear moveout, zero-lag K–L filtering is applied followed, by inverse linear moveout; the results from all dips are added to form the final filtered data. The second technique is blocking, in which the seismic section is divided into blocks small enough for each block to be processed using relatively small matrices; the processed blocks are assembled to form the final filtered section. Using a combination of these techniques, seismic sections can be filtered at a reasonable cost using the K-L transform. 相似文献
8.
A fast algorithm is presented for numerical evaluation of forward and inverse Radon transforms. The algorithm does not perform exact one-to-one mapping as the discrete Fourier transform but, due to the use of band-limited basis functions, it is robust and sufficiently accurate for seismic applications. By rewriting the transform as a convolution, a computational speed is obtained similar to the speed of the 2D fast Fourier transform. 相似文献
9.
南方海相地震资料脊波非线性阈值去噪方法 总被引：2，自引：0，他引：2
小波分析方法在数据处理中已得到成功广泛的应用,这主要得益于它的局部时频分析能力,但是小波分析对方向的表征能力有限。脊波变换具备优越的方向选择性能,能更好地处理含有线状变化特征的信号。本文针对低信噪比地震记录,尝试研究利用脊波变换方法对其进行处理,提高剖面资料信噪比,突出同相轴信息。在对南方某油田的实际地震资料的处理中,可以发现处理后的地震剖面同相轴品质及连续性有了明显改善,信噪比增强,分辨率相应提高,体现出了该方法相对常规小波分析方法的优越性。 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
12.
针对工程中常见的非平稳地震动激励,进一步建立了时变功率谱估计的理论框架。首先,在多个样本情形下,采用信号处理中的时频分析方法对非平稳激励的时变谱估计理论进行了讨论。当激励样本数量有限时,对Priestley提出的估计方法进行了介绍。其次,以地震工程中常用的Kanai-Tajimi谱模型为目标,分别对均匀调制与一般调制谱的估计结果以及不同估计方法的精度与收敛性进行评价后,提出了能够方便工程应用的建议。最后,针对SMART-Ⅰ(Strong Motion Array in Taiwan,Phase Ⅰ)密集台阵第45次地震记录的多组三维样本,揭示了EW、NS、UD三个方向时变谱的典型特征以及各方向间的时变相干性。结果表明:与短时Fourier变换相比,复Morlet小波与广义谐和小波估计谱具有较好的精度与收敛性,Priestley方法估计单个样本具有优势;SMART-Ⅰ台阵地震动具有强度和频率的双重非平稳性,三个方向具有弱相干性。研究结论可为拓展谱估计理论的工程应用以及后续大跨结构多维多点非平稳地震响应的分析提供参考。 相似文献
13.
Procedures using cross-correlation functions to analyze telluric and magnetotelluric field data can be designed which, in certain applications, are more efficient than conventional techniques using fast Fourier transforms. One such application, involving the processing ofband-limited data, is presented here. The linear coupling relations between fields in a limited frequency band are estimated from transient time series by minimizing, in a least squares sense, the residuals between observed and predicted values of the frequency coefficients. The resulting normal equations contain integral averages over the continuous auto- and cross-energy spectra which are efficiently evaluated as Fourier transforms of windowed auto- and cross-correlation functions in the time domain. The method is outlined in general terms, then illustrated with a specific example involving the analysis of 30–80 second pulsation data. The procedure involves three stages: Stage I: Data sections approximately 2000 seconds long are digitally sampled at 1 second intervals, filtered at 50 seconds and decimated to 500 point series with 4 second sampling intervals. Stage II: The correlation functions are formed for 16 lags (of 4 secs. each) on either side of zero and multiplied by a Gaussian window. Stage III: These modified correlation functions are Fourier transformed at the single period, 50 seconds; the band-averaged energy spectra which result are used to solve the desired field relations for either the telluric or the magnetotelluric coupling coefficients. Several built-in advantages are demonstrated. Since the window is concentrated around the origin, the correlation functions only need to be calculated out to relatively small lags. Decimation of the data during filtering further improves efficiency by dramatically reducing the number of points summed over. Visual display of intermediate results throughout the analysis not only provides added insight, but improves reliability by pinpointing problems early. For the examples considered here, linear coupling coefficients are shown to be stable within about 5 percent over several data sets. The method gives results within 1 percent of those determined by fast Fourier transform techniques while using half the computer time. 相似文献
14.
Antoine Roueff Jocelyn Chanussot Jerome I. Mars Minh-Quy Nguyen 《Geophysical Prospecting》2004,52(4):287-300
This paper illustrates the use of image processing techniques for separating seismic waves. Because of the non‐stationarity of seismic signals, the continuous wavelet transform is more suitable than the conventional Fourier transforms for the representation, and thus the analysis, of seismic processes. It provides a 2D representation, called a scalogram, of a 1D signal where the seismic events are well localized and isolated. Supervised methods based on this time‐scale representation have already been used to separate seismic events, but they require strong interactions with the geophysicist. This paper focuses on the use of the watershed algorithm to segment time‐scale representations of seismic signals, which leads to an automatic estimation of the wavelet representation of each wave separately. The computation of the inverse wavelet transform then leads to the reconstruction of the different waves. This segmentation, tracked over the different traces of the seismic profile, enables an accurate separation of the different wavefields. This method has been successfully validated on several real data sets. 相似文献
15.
人工地震数据总是受到随机噪声的干扰,地震数据时-空变的特性使得常规去噪方法处理效果并不理想,容易导致有效信号的损失.目前广泛应用的预测滤波类方法存在处理时变数据能力不足的问题.随着压缩感知理论的不断完善,稀疏变换阈值算法能够解决时变地震数据噪声压制问题,但是常规的稀疏变换方法,如傅里叶变换,小波变换等,并不是特殊针对地震数据设计的,很难提供地震数据最佳的压缩特征,同时,常规阈值算法容易导致去噪结果过于平滑.因此开发更加有效的时-空变地震数据信噪分离方法具有重要的工业价值.本文将地震数据信噪分离问题归纳为数学基追踪问题,在压缩感知理论框架下,利用特殊针对地震数据设计的VD-seislet稀疏变换方法,结合全变差(TV)算法,构建seislet-TV双正则化条件,并利用分裂Bregman迭代算法求解约束最优化问题,实现地震数据的有效信噪分离.通过理论模型和实际数据测试本文方法,并且与工业标准FXdecon方法进行比较,结果表明基于seislet-TV双正则化约束条件的迭代方法能够更加有效地保护时-空变地震信号,压制地震数据中的强随机噪声. 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
18.
地震数据规则化是地震信号处理中一个重要步骤,近年来受到广泛关注的压缩感知技术已经被应用到地震数据规则化中。压缩感知技术突破了传统的Shannon-Nyqiust采样定理的限制,可以用采集的少量地震数据重构完整数据。基于压缩感知技术的地震数据规则化质量主要受三个因素影响,除了受地震信号在不同变换域的稀疏表达和11范数重构算法的影响外,极大地取决于地震道随机稀疏采样方式。尽管已有学者开展了2D地震数据离散均匀分布随机采样方式研究,但设计新的稀疏采样方案仍然很有必要。在本文中,我们提出满足Bernoulli分布规律的Bernoulli随机稀疏采样方式和它的抖动形式。对2D数值模拟数据进行四种随机稀疏采样方案和两种变换（Fourier变换和Curvelet变换）实验,对获取的不完整数据应用11范数谱投影梯度算法（SPGL1）进行重构。考虑到不同随机种子点产生不同约束矩阵R会有不同的规则化质量,对每种方案和每个稀疏采样因子进行10次规则化实验,并计算出相应信噪比（SNR）的平均值和标准偏差。实验结果表明,我们提出的新方案好于或等于已有的离散均匀分布采样方案。 相似文献
19.
Hilbert-Huang变换在提取地震信号动力特性中的应用 总被引：1，自引：0，他引：1
H ilbert-Huang变换(HHT)是一种处理非线性、非平稳信号的新方法。它通过经验模态分解将信号分解为有限个固有模态函数,并对每个固有模态函数进行H ilbert变换得到H ilbert谱。本文将这种方法应用于地震信号动力特性的提取,有效地获得了信号能量的时频分布,量化提取了中心频率、瞬时相位、瞬时能量、H ilbert能量、最大振幅对应的时频分布等动力特性,并与Fourier变换、小波变换等进行了比较,显示了HHT的优势以及对于进一步实现结构分析和控制的重要意义。 相似文献
20.
ZHOU YUNXUAN 《Geophysical Prospecting》1993,41(4):459-494
The Radon transform is applied to airborne geophysical data, which consist of parallel profiles, analogous to a seismic record. The plane-wave decomposition (PWD) thus becomes the strike-direction decomposition (SDD) since the observed spatially distributed information is represented by its strike directions in a domain achieved by the transformation. It is important that, after the SDD, we can identify anomalies and work on them according to their strikes. In particular, for gridding purposes, we may guide the second interpolation of the bi-directional gridding approach along the strike directions. In principle, the proposed Radon transform gridding method (RTGM) transforms the observed parallel profiles into a domain where information is mapped as its strike-direction ‘traces’ against its wavelengths. The number of strike directions into which the data are decomposed is equal to the number of lines to be interpolated. The Fourier spectrum of the grid is reconstructed from the strike-wavenumber domain by using the projection-slice theorem and the final square grid is obtained by performing an inverse Fourier transformation on the spectrum. The SDD is restricted to the Nyquist wavenumber bandwidth imposed by the survey line-spacing, so that there is no addition of ambiguous short wavelengths in the gridded data. A tapering window is employed to prevent any Gibb's oscillation in the final grid because of the sharp Nyquist cut-off in the reconstructed spectrum due to the survey line-spacing. The RTGM is first tested on a set of synthetic line-based data. It is also applied to aeromagnetic profile data from northern Botswana as a practical example. 相似文献