Seismic signals are often irregularly sampled along spatial coordinates, leading to suboptimal processing and imaging results. Least squares estimation of Fourier components is used for the reconstruction of band-limited seismic signals that are irregularly sampled along one spatial coordinate. A simple and efficient diagonal weighting scheme, based on the distance between the samples, takes the properties of the noise (signal outside the bandwidth) into account in an approximate sense. Diagonal stabilization based on the energies of the signal and the noise ensures robust estimation. Reconstruction for each temporal frequency component allows the specification of a varying spatial bandwidth dependent on the minimum apparent velocity. This parameterization improves the reconstruction capability for the lower temporal frequencies. In practical circumstances, the maximum size of the gaps in which the signal can be reconstructed is three times the (temporal frequency dependent) Nyquist interval. Reconstruction in the wavenumber domain allows a very efficient implementation of the algorithm, and takes a total number of operations a few times that of a 2-D fast Fourier transform corresponding to the size of the output data set. Quality control indicators of the reconstruction procedure can be computed which may also serve as decision criteria on in-fill shooting during acquisition. The method can be applied to any subset of seismic data with one varying spatial coordinate. Applied along the cross-line direction, it can be used to compute a 3-D stack with improved anti-alias protection and less distortion of the signal within the bandwidth.

Seismic data regularization, which spatially transforms irregularly sampled acquired data to regularly sampled data, is a long-standing problem in seismic data processing. Data regularization can be implemented using Fourier theory by using a method that estimates the spatial frequency content on an irregularly sampled grid. The data can then be reconstructed on any desired grid. Difficulties arise from the nonorthogonality of the global Fourier basis functions on an irregular grid, which results in the problem of spectral leakage: energy from one Fourier coefficient leaks onto others. We investigate the nonorthogonality of the Fourier basis on an irregularly sampled grid and propose a technique called antileakage Fourier transform to overcome the spectral leakage. In the antileakage Fourier transform, we first solve for the most energetic Fourier coefficient, assuming that it causes the most severe leakage. To attenuate all aliases and the leakage of this component onto other Fourier coefficients, the data component corresponding to this most energetic Fourier coefficient is subtracted from the original input on the irregular grid. We then use this new input to solve for the next Fourier coefficient, repeating the procedure until all Fourier coefficients are estimated. This procedure is equivalent to reorthogonalizing the global Fourier basis on an irregularly sampled grid. We demonstrate the robustness and effectiveness of this technique with successful applications to both synthetic and real data examples.

Simon Spitz（1989）提出的用<em>F-X</em>域预测技术实现道内插的方法,尽管有许多优点,但还是存在计算量大、精度低等一些问题。本文给出了一种新的<em>F-X</em>域实现道内插的方法,该方法是利用<em>F-X</em>域预测算子包含了所有反射波同相轴的倾角信息这一特性来实现道内插。它不必像常规方法那样扫描反射波同相轴的倾角,而且即使存在严重的空间仅频时,也可得到较好的内插效果。理论与实际资料试验的结果表明,该方法具有速度快、精度高、内插出的地震道波形自然、不受空间仅频影响等优点,但前提是要求在作道内播之前道距必须相等。

f-x domain trace interpolation is based on the theory that x-t domain linear events are predictable in f-x domain.f-x domain generalized prediction filter for x-t domain linear events and the existence condition for the filter are described here,and so is the implementation of seismic trace interpolation.We may deem that seismic data(such as stacked data) in a small spatial-temporal gate consist of some linear reflection events,so that the f-x domain trace interpolation technique can be used to achieve seismic trace interpolation and to reduce spatial aliasing.

<FONT face=Verdana>野外采集的地震数据经常存在空道或者坏道的情况，为了满足地震数据处理精度的要求，就必须首先进行插值.本文提出了一种新的地震数据插值方法：F-K偏移和反偏移插值法，该方法是通过F-K偏移和反偏移的串联使用来实现的.与其他的插值方法相比，这种插值方法的优点在于计算速度快，没有经过近似处理，精度高.F-K偏移/反偏移能够实现道插值的原理和Kirchhoff偏移/反偏移插值方法类似，也是由于数据是有限带宽的原因引起的.通过对模型的试算，可以看到F-K偏移和反偏移插值方法有着比较好的插值效果，是一种高效、准确、可行的方法.</FONT>

地震数据重构问题是一个病态的反演问题. 本文基于地震数据在curvelet域的稀疏性, 将地震数据重构变为一个稀疏优化问题, 构造0范数的逼近函数作为目标函数, 提出了一种投影梯度求解算法. 本文还运用最近提出的分段随机采样方式进行采样, 该采样方式能够有效地控制采样间隔并且保持采样的随机性. 地震数值模拟表明, 基于0范数逼近的投影梯度法计算效率有明显的提高; 分段随机采样方式比随机欠采样有更加稳定的重构结果.

为达到更加有效地表示地震数据的目的,仅仅将地震数据当作普通的图像数据处理是远远不够的,地震数据中蕴含的地震波的运动学特性也应作为重要因素而被考虑到.本文讨论了利用Dreamlet变换方法实现地震数据压缩的方法,并针对地震数据本身所蕴含的频散关系特性进一步提出了多尺度Dreamlet变换压缩方法.Dreamlet变换由2个一维局部谐波变换的张量积构成,它在提供地震波场时间-空间局部化性质的同时可以保留波场的运动学特性.通过对二维SEG/EAGE叠前、叠后数据的算例说明了Dreamlet变换用于地震数据压缩的有效性.利用压缩后的数据进行成像的结果更表明,与Curvelet变换方法相比,Dreamlet与多尺度Dreamlet方法可以提供更高的压缩比;在相同压缩比的条件下,使用Dreamlet与多尺度Dreamlet方法压缩重建后的数据进行成像能更好地保留成像结果中的重要结构.

<p>传统的地震勘探数据采样必须遵循奈奎斯特采样定理,而野外数据采样可能由于地震道缺失或者勘探成本限制,不一定满足采样定理要求,因此存在数据重建问题.本文基于压缩感知理论,利用随机欠采样方法将传统规则欠采样所带来的互相干假频转化成较低幅度的不相干噪声,从而将数据重建问题转为更简单的去噪问题.在数据重建过程中引入凸集投影算法(POCS),提出采用<em>e</em>^{-&radic;<span style="border-top: 1px solid; padding-top: 0px"><em>x</em></span>}(0&le;<em>x</em>&le;1)衰减规律的阈值参数,构建基于曲波变换三维地震数据重建技术.同时针对随机采样的不足,引入jitter采样方式,在保持随机采样优点的同时控制采样间隔.数值试验表明,基于曲波变换的重建效果优于傅里叶变换,jitter欠采样的重建效果优于随机欠采样,最后将该技术应用于实际地震勘探资料,获得较好的应用效果.</p>

研究基于Fourier变换的数据重建方法,既能进行非均匀采样数据重建,又可以去除空间假频. 将不规则采样数据重建问题归结为信息重建的地球物理反演问题，采用最小二乘方法从观测的稀疏或不规则数据反演模型空间完全信息. 在求解信息重建反演问题时，引入DFT加权范数规则化策略，采用预条件共轭梯度法（PCG）求解，保证解的稳定性和收敛速度. 处理线性同相轴假频问题时，根据采样定理，引入线性预测方法，采用YuleWalker方程由带限信号的无假频低频功率谱预测高频功率谱，达到反假频目的. 本文研究了均匀采样数据内插，非均匀采样数据重建，非均匀分布高频信息重建等方面问题，数值试验取得较好效果.

ABSTRACT Presents a general principle underlying reverse-time migration and discusses the various reverse-time migration procedures in light of it.-from Author

为了提高叠前逆时偏移成像精度,开展了针对逆时偏移的地震资料预处理方法研究——叠前插值处理。从Marmousi理论模型出发,对模拟的理论炮集数据进行抽稀,在满足数值频散关系条件下进行叠前逆时偏移处理,计算结果表明,炮集记录道间距增大会引入线性干扰,较大程度影响了逆时偏移结果的精度和横向连续性;从实际三维地震资料数据出发,对比分析了沿检波线方向和沿检波站方向进行叠前频率-空间域三维插值前、后的数据和对应的逆时偏移结果。研究表明,未进行叠前插值处理的逆时偏移剖面存在类似于理论数据抽稀情况下的线性干扰,同相轴的连续性差;而经插值处理后,插值地震道的同相轴过渡自然无畸变,对应的逆时偏移剖面连续性明显增强,线性干扰得到有效压制。因此,叠前插值处理能够有效提高高信噪比地震工区资料的逆时偏移成像精度。

Data acquired with the parallel geornetry can be described as a collection of common-offset gathers. Prestack migration of such data can be conveniently considered as the repeated application of the migration proces to all common-offset gathers.