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1.
地震数据的随机噪声去除是地震数据处理中的一项重要步骤,双稀疏字典提供了两层稀疏模型,比单层稀疏模型可以更好地去除噪声.该方法首先利用contourlet变换对地震数据进行稀疏表示,然后在contourlet域中使用快速迭代收缩阈值算法（fast iterative shrinkage-thresholding algorithm,FISTA）对初始字典系数进行更新,接着采用数据驱动紧标架（data-driven tight frame,DDTF）在contourlet域中得到DDTF字典并通过FISTA得到更新后的字典系数,最后通过DDTF字典和更新后的字典系数获得新的contourlet系数,并对新的contourlet系数进行硬阈值和contourlet反变换得到去噪后的数据.通过模拟数据和实际数据的实验证明：与固定基变换去噪方法相比,该方法可以自适应地对地震数据进行稀疏表示,在地震数据较为复杂时得到更高的信噪比;与字典学习去噪方法相比,该方法不仅拥有较快的去噪速度,而且克服了字典学习因为缺少先验约束造成瑕疵的缺点. 相似文献
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多震源混合地震采集技术,即将多个震源以一定编码方式连续地激发,得到多炮混合的地震数据.该技术能减少地震采集时间,节约采集成本,但是混合数据的直接偏移会在成像剖面中引入严重的串扰噪声,影响成像效果.从数学上看,地震成像属于典型的数学物理反问题,可以采用线性反演方法求解一个正则化约束的最小二乘(LS)优化问题,获得更高质量的成像结果.全变分(TV)正则化方法是图像去噪和复原领域中广泛应用的热点技术,其能在去除噪声的过程中保留图像的边缘信息和不连续性.在对TV图像去噪复原方法原理分析的基础上,本文将多震源混合数据直接偏移成像问题转换成图像复原的极小化能量泛函问题,用TV正则化代替传统最小二乘偏移(LSM)中的L2范数正则化,提出基于全变分原理的混合数据直接偏移方法.该方法使用基于梯度的快速迭代收缩阈值与快速梯度投影组合算法——FISTA/FGP求解最优化问题,能有效压制串扰噪声,增强同相轴连续性,提高成像分辨率.理论模型测试结果表明:将本方法应用于混合数据,无论是去噪效果还是成像精度都得到显著改善. 相似文献
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A new seismic interpolation and denoising method with a curvelet transform matching filter, employing the fast iterative shrinkage thresholding algorithm (FISTA), is proposed. The approach treats the matching filter, seismic interpolation, and denoising all as the same inverse problem using an inversion iteration algorithm. The curvelet transform has a high sparseness and is useful for separating signal from noise, meaning that it can accurately solve the matching problem using FISTA. When applying the new method to a synthetic noisy data sets and a data sets with missing traces, the optimum matching result is obtained, noise is greatly suppressed, missing seismic data are filled by interpolation, and the waveform is highly consistent. We then verified the method by applying it to real data, yielding satisfactory results. The results show that the method can reconstruct missing traces in the case of low SNR (signal-to-noise ratio). The above three problems can be simultaneously solved via FISTA algorithm, and it will not only increase the processing efficiency but also improve SNR of the seismic data. 相似文献
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针对利用地震道进行相对波阻抗反演中遇到的横向连续性难以保持、初始子波容错度差以及随机噪声干扰影响反演结果等问题,提出了一种基于矩阵Toeplitz稀疏分解的相对波阻抗反演方法.该方法将地震数据剖面的Toeplitz稀疏分解问题分解为两个子反演问题,其一以Toeplitz子波矩阵元素为待反演的参数,用Fused Lasso方法求解,可保证子波具有紧支集且是光滑的;其二以稀疏反射系数矩阵元素为待反演参数,用基于回溯的快速萎缩阈值迭代算法求解,大大降低了目标函数中参数选择的难度.通过交替迭代求解上述两个子反演问题可将地震数据剖面因式分解为一个Toeplitz子波矩阵和一个稀疏反射系数矩阵;然后由反射系数矩阵递推反演可以得到高分辨率的相对波阻抗剖面;利用测井资料加入低频分量后,也可得到高分辨率的绝对波阻抗剖面.Marmousi2模型生成的合成记录算例和实际地震资料算例均表明:本文方法可以从带限地震数据中有效地反演相对波阻抗,反演结果分辨率高并且能够很好地保持地震数据的横向连续性;即使在初始估计子波存在误差和地震数据被随机噪声污染的情况下也能取得较好的效果. 相似文献
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Missing data are a problem in geophysical surveys, and interpolation and reconstruction of missing data is part of the data processing and interpretation. Based on the sparseness of the geophysical data or the transform domain, we can improve the accuracy and stability of the reconstruction by transforming it to a sparse optimization problem. In this paper, we propose a mathematical model for the sparse reconstruction of data based on the L0-norm minimization. Furthermore, we discuss two types of the approximation algorithm for the L0-norm minimization according to the size and characteristics of the geophysical data: namely, the iteratively reweighted least-squares algorithm and the fast iterative hard thresholding algorithm. Theoretical and numerical analysis showed that applying the iteratively reweighted least-squares algorithm to the reconstruction of potential field data exploits its fast convergence rate, short calculation time, and high precision, whereas the fast iterative hard thresholding algorithm is more suitable for processing seismic data, moreover, its computational efficiency is better than that of the traditional iterative hard thresholding algorithm. 相似文献
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An efficient Auto-Regressive Moving–Average (ARMA) approximation method is presented for simulating stationary random processes with specified (target) power spectra in conjunction with structural dynamics applications. It involves an iterative algorithm developed for minimizing a physically motivated ‘energy’ measure, in the frequency domain, of the ARMA approximation of an AR representation of the target spectrum. The iterative algorithm can be used to adjust, for better spectral matching, the parameters of an arbitrary ARMA approximation of the random process determined by any other method; this is accomplished without increasing the requisite order of the ARMA approximation. The efficiency of the proposed method is demonstrated by considering spectra which are commonly used in earthquake engineering and ocean engineering. 相似文献
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In the analysis of the unsaturated zone, one of the most challenging problems is to use inverse theory in the search for an optimal parameterization of the porous media. Adaptative multi-scale parameterization consists in solving the problem through successive approximations by refining the parameter at the next finer scale all over the domain and stopping the process when the refinement does not induce significant decrease of the objective function any more. In this context, the refinement indicators algorithm provides an adaptive parameterization technique that opens the degrees of freedom in an iterative way driven at first order by the model to locate the discontinuities of the sought parameters. We present a refinement indicators algorithm for adaptive multi-scale parameterization that is applicable to the estimation of multi-dimensional hydraulic parameters in unsaturated soil water flow. Numerical examples are presented which show the efficiency of the algorithm in case of noisy data and missing data. 相似文献
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We present a fast approximate method for three‐dimensional low frequency controlled source electro‐magnetic modeling. We apply the method to a synthetic model in a typical marine controlled source electromagnetic scenario, where conductivity and permittivity are different from the known background medium. For 3D configurations, fast computational methods are relevant for both forward and inverse modelling studies. Since this problem involves a large number of unknowns, it has to be solved efficiently to obtain results in a timely manner, without compromising accuracy. For this reason, the Born approximation, extended Born approximation and iterative extended Born approximation are implemented and compared with the full solution of the conjugate gradient fast Fourier transformation method. These methods are based on an electric field domain integral equation formulation. It is shown here how well the iterative extended Born approximation method performs in terms of both accuracy and speed with different configurations and different source positions. The improved accuracy comes at virtually no additional computational cost. With the help of this method, it is now possible to perform sensitivity analysis using 3D modelling in a timely manner, which is vital for controlled source electromagnetic applications. For forward modeling the solution at the sea‐bottom is of interest, because that is where the receivers are usually located. For inverse modeling, the accuracy of the solution in the target zone is important to obtain reasonably accurate conductivity values from the inversion using this approximate solution method. Our modelling studies show that the iterative extended Born approximation method is fast and accurate for both forward and inverse modelling. Sensitivity analysis as a function of the source position and different reservoir sizes validate the accuracy of the iterative extended Born approximation. 相似文献
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本文将多次波自适应相减问题表示为一个多道卷积信号的盲分离问题.利用2D卷积核来表示预测多次波和实际多次波之间的差异,并采用分离出的一次波信号的非高斯性最大化作为优化目标,我们提出一种基于多道卷积信号盲分离的多次波自适应相减算法.为了求解上述非线性优化问题,所提方法将其转化为一个迭代线性优化问题,采用迭代最小二乘方法加以实现.由于采用了多道卷积信号盲分离模型,所提方法能够适应预测和真实多次波之间在时间及空间上的变化.通过对简单模型数据、Pluto数据和实际数据进行处理,验证了所提算法的有效性. 相似文献
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Multi-source seismic technology is an efficient seismic acquisition method that requires a group of blended seismic data to be separated into single-source seismic data for subsequent processing. The separation of blended seismic data is a linear inverse problem. According to the relationship between the shooting number and the simultaneous source number of the acquisition system, this separation of blended seismic data is divided into an easily determined or overdetermined linear inverse problem and an underdetermined linear inverse problem that is difficult to solve. For the latter, this paper presents an optimization method that imposes the sparsity constraint on wavefields to construct the object function of inversion, and the problem is solved by using the iterative thresholding method. For the most extremely underdetermined separation problem with single-shooting and multiple sources, this paper presents a method of pseudo-deblending with random noise filtering. In this method, approximate common shot gathers are received through the pseudo-deblending process, and the random noises that appear when the approximate common shot gathers are sorted into common receiver gathers are eliminated through filtering methods. The separation methods proposed in this paper are applied to three types of numerical simulation data, including pure data without noise, data with random noise, and data with linear regular noise to obtain satisfactory results. The noise suppression effects of these methods are sufficient, particularly with single-shooting blended seismic data, which verifies the effectiveness of the proposed methods. 相似文献
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将理论反射率与偏移反射率的差作为目标函数，给出一种迭代振幅补偿保幅偏移方法.把偏移看作一个反问题，寻找反问题中的最优解.偏移算子是正演算子的伴随共轭，其伴随矩阵非对角占优.通过预条件优化伴随矩阵，使Hessian矩阵准对角化.依据地震波传播稳定相位理论，计算反射点，以反射点为中心、菲涅耳带为半径偏移.考虑振幅几何扩散补偿、散射角度补偿，在迭代反演过程求出最优解，即保幅偏移解.本文给出了一个保幅数值模拟结果和一个实际地震数据实例. 相似文献
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Tomohide Ishiyama Mohammed Y. Ali Satoshi Ishikawa Gerrit Blacquiere Shotaro Nakayama 《Geophysical Prospecting》2019,67(7):1852-1866
We introduce a concept of generalized blending and deblending, develop its models and accordingly establish a method of deblended-data reconstruction using these models. The generalized models can handle real situations by including random encoding into the generalized operators both in the space and time domain, and both at the source and receiver side. We consider an iterative optimization scheme using a closed-loop approach with the generalized blending and deblending models, in which the former works for the forward modelling and the latter for the inverse modelling in the closed loop. We applied our method to existing real data acquired in Abu Dhabi. The results show that our method succeeded to fully reconstruct deblended data even from the fully generalized, thus quite complicated blended data. We discuss the complexity of blending properties on the deblending performance. In addition, we discuss the applicability to time-lapse seismic monitoring as it ensures high repeatability of the surveys. Conclusively, we should acquire blended data and reconstruct deblended data without serious problems but with the benefit of blended acquisition. 相似文献
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即使采用分辨率很高的双曲Radon变换,对速度各向异性发育介质及长偏移距情况下的地震数据,其Radon域内能量仍不收敛.为了克服此难题,我们在Radon变换的积分路径中考虑了非双曲走时的影响,通过引入非双曲时差公式中的各向异性非椭圆率η参数,可以准确描述出长偏移距条件下来自同一层位的时距曲线,并推导了由偏移距、慢度、非椭圆率三参数控制的积分曲线正反变换公式,我们称之为各向异性Radon变换.离散化求解时,各向异性Radon变换是时变的,频率域快速算法已不适用,本文采用了最优相似系数加权Gauss-Seidel迭代算法,保持其计算精度的同时也有较高的计算效率.将此方法应用在模型数据以及实际长偏移距海上地震数据的多次波压制处理中,收到了较好的处理效果. 相似文献
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混合震源采集技术相对于传统的地震数据采集,在极大提高采集效率的同时引入了混叠噪声,很大程度上影响了成像结果的精度.二维混采数据中,我们通常利用混叠噪声在非共炮域呈非相干分布这一特点来压制混叠噪声,从而实现混合震源数据分离.相对于二维混采数据,三维混采数据具有数据量巨大,构建混合震源算子困难,混合度的增加引入了高强度混叠噪声的特点.针对上述问题,本文采用稀疏约束反演方法在Radon域实现混采数据分离,混叠噪声强度比较大的情况下,稀疏约束反演方法能够得到更高精度的分离结果;利用震源激发的GPS时间通过长记录的方式在共接收点道集对上一次迭代分离结果做混合、伪分离,实现了单个共接收点道集自身混合、伪分离,避免了对整个数据做运算,同时不需要构建混合震源算子.通过模拟数据和实际数据计算来验证上述方法的适用性. 相似文献
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为提高水平层状介质中三维电磁波散射和逆散射数值模拟的效率,在对角张量近似(DTA)的基础上根据不同回代方式得到了求解积分方程的DTA1和DTA2两种近似. 这两种近似可以作为计算积分方程稳定型双共轭梯度快速Fourier变换(BCGS-FFT)算法的初始猜测值和预条件因子，从而形成效率更高的混合DTA-BCGS算法. 散射实例说明了DTA2的高精度和混合DTA-BCGS算法尤其是混合DTA2-BCGS算法的高效率. 由于DTA2近似程度更高，将DTA2与变型Born迭代反演方法(DBIM)相结合形成了一种对三维异常体进行重构的快速电磁波逆散射技术. 文中的逆散射实例说明所开发的逆散射技术对重构水平层状介质中的任意三维异常体是非常有效的. 相似文献
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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. 相似文献
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The wavenumber iterative modelling (WIM) method was first introduced to estimate the static corrections for 2D land profiles by performing first-break inversion in the wavenumber domain. The WIM algorithm presents some useful advantages, of robustness, stability and flexibility. Robustness is obtained by intensive exploitation of all the available data and by application of an automatic function for mispick removal. Stability is the result of an iterative procedure that ensures convergence towards a stable and plausible solution even at the end of the profile where the problem is normally ill-posed. Finally, flexibility is due to the possibility of solving for multilayered structures and of estimating vertical gradients of the velocity.This work extends the WIM method to three dimensions. The extension is feasible because the three-dimensional (3D) problem can be decomposed into a number of small independent problems, one for any pair of wavenumbers k x , k y . The extension preserves the above-mentioned advantages. The parameters of the estimated model are affected differently by noise: the analysis of the input/output noise transfer function demonstrates that the high spatial frequencies of the velocity distributions are the components that are most affected by noise; thus, the algorithm includes a gradual damping of the higher wavenumbers of the velocity parameter. Although the WIM 3D algorithm requires a larger amount of RAM compared with other standard approaches, considerable reduction in CPU run time can be achieved as every wavenumber pair can be treated as an independent linear problem. 相似文献
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A solution technique based on the sequential linear programming (SLP) method is presented for the optimum design of braced and unbraced steel frames in seismic regions. First, the optimum rigidity distribution of the frames under static loading is computed, then the optimization procedure is repeated under the combined loading, setting lower bounds on the optimum static cross-sectional areas and increasing allowable stresses. The stiffness, stress, displacement and side constraints are included in the optimization problem. As a result, a highly non-linear mathematical programming problem is produced. A non-linear programming algorithm is offered for the solution which is based on the successive linearization of non-linear expressions and employs the simplex routine in an iterative manner. Design variables are chosen to be the free nodal displacements and the cross-sectional areas of the members, while the objective function is taken to be the minimization of the total volume of the structure. As numerical applications, optimum weights of several frames (unbraced, concentrically and eccentrically braced) under static and combined loading cases are computed and the results are compared with those available in the literature. 相似文献