Closed-loop SRME based on 3D L1-norm sparse inversion

In many situations, the quality of seismic imaging is largely determined by a proper multiple attenuation as preprocessing step. Despite the widespread application of surface-related multiple elimination (SRME) and estimation of primaries by sparse inversion (EPSI) for the removal of multiples, there still exist some limitations in the process of prediction and subtraction (SRME) or inversion (EPSI), which make the efficiency of multiple attenuation less satisfactory. To solve these problems, a new fully data-driven method called closed-loop SRME was proposed, which combines the robustness of SRME and the multi-dimensional inversion strategy of EPSI. Due to the selection of inversion approach and constraint, primary estimation by closed-loop SRME may fall into a local optimum during the solving process, which lowers the accuracy of deep information and weakens the continuity of seismic events. To avoid these shortcomings, we first modified the solving method for closed-loop SRME to an L1 norm-based bi-convex optimization method, which stabilizes the solution. Meanwhile, in the L1 norm constraint-based optimization process, the 3D sparsifying transform, being a 2D Curvelet-1D wavelet transform, is brought in as a 3D sparse constraint. In the 3D sparsifying domain, the data become sparser, thus making the result of optimization more accurate, the information of seismic events more continuous and the resolution higher. Examples on both synthetic and field data demonstrate that the method proposed in this paper, compared with the traditional SRME and closed-loop SRME, have an excellent effect on primary estimation and suppress multiples effectively.     

L1范数约束被动源数据稀疏反演一次波估计

对于被动源地震数据,运用常规的互相关算法得到的虚拟炮记录中,不仅含有一次波反射信息,还包括了表面相关多次波.然而,通过传统的被动源数据稀疏反演一次波估计(EPSI)方法,可以求得只含有一次波,不含表面相关多次波的虚拟炮记录.本文改进了传统的被动源数据稀疏反演一次波估计问题的求解方法,将被动源稀疏反演一次波估计求解问题转化为双凸L1范数约束的最优化求解问题,避免了在传统的稀疏反演一次波估计过程中用时窗防止反演陷入局部最优化的情况.在L1范数约束最优化的求解过程中,又结合了2D Curvelet变换和小波变换,在2D Curvelet-wavelet域中,数据变得更加稀疏,从而使求得的结果更加准确,成像质量得到了改善.通过简单模型和复杂模型,验证了本文提出方法的有效性.     

基于L1范数的瞬变电磁非线性反演

瞬变电磁反演存在高度的非线性特征,常用的最小二乘等线性反演方法往往对初始模型高度依赖,并且极易陷入局部最优解.本文基于观测数据与模拟数据的L1范数建立目标函数,采用模拟退火非线性全局最优化方法实现瞬变电磁一维反演.初始模型完全随机产生,通过指数函数退温机制模拟系统能量最小实现迭代,通过接收概率函数评价当前模型,实现局部最优解的跳出,最终实现全局最优化求解.通过数值算例发现,无论给定的反演层数等于还是大于设计模型,都可以获得较好的反演效果,因而可以在反演初始就设计较多的层数,实现反演模型的自动拟合;同时,利用含噪声数据反演进一步验证算法的稳定性.最后,对实测数据进行了反演测试,结果与钻孔编录基本一致,表明提出的基于L1范数的模拟退火反演可用于实测数据处理.

     

Three‐dimensional potential field data inversion with L0 quasinorm sparse constraints

The quantitative explanation of the potential field data of three‐dimensional geological structures remains one of the most challenging issues in modern geophysical inversion. Obtaining a stable solution that can simultaneously resolve complicated geological structures is a critical inverse problem in the geophysics field. I have developed a new method for determining a three‐dimensional petrophysical property distribution, which produces a corresponding potential field anomaly. In contrast with the tradition inverse algorithm, my inversion method proposes a new model norm, which incorporates two important weighting functions. One is the L0 quasi norm (enforcing sparse constraints), and the other is depth‐weighting that counteracts the influence of source depth on the resulting potential field data of the solution. Sparseness constraints are imposed by using the L0 quasinorm on model parameters. To solve the representation problem, an L0 quasinorm minimisation model with different smooth approximations is proposed. Hence, the data space (N) method, which is much smaller than model space (M), combined with the gradient‐projected method, and the model space, combined with the modified Newton method for L0 quasinorm sparse constraints, leads to a computationally efficient method by using an N × N system versus an M × M one because N ? M. Tests on synthetic data and real datasets demonstrate the stability and validity of the L0 quasinorm spare norms inversion method. With the aim of obtaining the blocky results, the inversion method with the L0 quasinorm sparse constraints method performs better than the traditional L2 norm (standard Tikhonov regularisation). It can obtain the focus and sparse results easily. Then, the Bouguer anomaly survey data of the salt dome, offshore Louisiana, is considered as a real case study. The real inversion result shows that the inclusion the L0 quasinorm sparse constraints leads to a simpler and better resolved solution, and the density distribution is obtained in this area to reveal its geological structure. These results confirm the validity of the L0 quasinorm sparse constraints method and indicate its application for other potential field data inversions and the exploration of geological structures.     

Suppressing multiples using an adaptive multichannel filter based on L1-norm

Adaptive subtraction is an important link for removing surface-related multiples in the wave equation-based method. In this paper, we propose an adaptive multichannel subtraction method based on the L1-norm. We achieve enhanced compensation for the mismatch between the input seismogram and the predicted multiples in terms of the amplitude, phase, frequency band, and travel time. Unlike the conventional L2-norm, the proposed method does not rely on the assumption that the primary and the multiples are orthogonal, and also takes advantage of the fact that the L1-norm is more robust when dealing with outliers. In addition, we propose a frequency band extension via modulation to reconstruct the high frequencies to compensate for the frequency misalignment. We present a parallel computing scheme to accelerate the subtraction algorithm on graphic processing units (GPUs), which significantly reduces the computational cost. The synthetic and field seismic data tests show that the proposed method effectively suppresses the multiples.     

Estimating primaries by sparse inversion of the 3D curvelet transform and the L1-norm constraint

In this paper, we built upon the estimating primaries by sparse inversion (EPSI) method. We use the 3D curvelet transform and modify the EPSI method to the sparse inversion of the biconvex optimization and L1-norm regularization, and use alternating optimization to directly estimate the primary reflection coefficients and source wavelet. The 3D curvelet transform is used as a sparseness constraint when inverting the primary reflection coefficients, which results in avoiding the prediction subtraction process in the surface-related multiples elimination (SRME) method. The proposed method not only reduces the damage to the effective waves but also improves the elimination of multiples. It is also a wave equationbased method for elimination of surface multiple reflections, which effectively removes surface multiples under complex submarine conditions.     

基于稀疏表达的OBS去噪方法

海底地震仪（OBS）采集数据的去噪处理是开展OBS震相分析及后续处理反演的基础.本文结合曲波（Curvelet）变换及压缩感知提出一种稀疏化表达的OBS去噪方法,并通过与小波变化对比等探讨去噪效果.曲波变换具有抛物尺度及识别线性异常的优点,可以稀疏地表示OBS数据,再结合压缩感知思想对稀疏表达OBS数据进行去噪处理和重构.通过对变换后的系数进行基于L₁范数的冷却阈值迭代滤波,获得最优的变换系数,本文指出基于曲波变换的冷却阈值迭代法能够很好地对OBS数据去噪.对比小波和曲波两种变换在相同迭代次数下对理论模型数据进行去噪处理,表明曲波变换得到的结果信噪比更高.利用本文方法对渤海地区采集的OBS数据进行去噪处理获得了更加清晰连续的震相,噪声压制效果更明显,为震相拾取及后续速度模型反演奠定了良好的基础.

     

The utilization of the double focal transformation for sparse data representation and data reconstruction

In many cases, seismic measurements are coarsely sampled in at least one dimension. This leads to aliasing artefacts and therefore to problems in the subsequent processing steps. To avoid this, seismic data reconstruction can be applied in advance. The success and reliability of reconstruction methods are dependent on the assumptions they make on the data. In many cases, wavefields are assumed to (locally) have a linear space–time behaviour. However, field data are usually complex, with strongly curved events. Therefore, in this paper, we propose the double focal transformation as an efficient way for complex data reconstruction. Hereby, wavefield propagation is formulated as a transformation, where one‐way propagation operators are used as its basis functions. These wavefield operators can be based on a macro velocity model, which allows our method to use prior information in order to make the data decomposition more effective. The basic principle of the double focal transformation is to focus seismic energy along source and receiver coordinates simultaneously. The seismic data are represented by a number of localized events in the focal domain, whereas aliasing noise spreads out. By imposing a sparse solution in the focal domain, aliasing noise is suppressed, and data reconstruction beyond aliasing is achieved. To facilitate the process, only a few effective depth levels need to be included, preferably along the major boundaries in the data, from which the propagation operators can be calculated. Results on 2D and 3D synthetic data illustrate the method's virtues. Furthermore, seismic data reconstruction on a 2D field dataset with gaps and aliased source spacing demonstrates the strength of the double focal transformation, particularly for near‐offset reflections with strong curvature and for diffractions.     

基于稀疏约束反演的三维混采数据分离

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.

     

基于数据空间和稀疏约束的三维重力和重力梯度数据联合反演

随着重力和重力梯度测量技术的日趋成熟,基于重力和重力梯度数据的反演技术得到了广泛关注.针对反演多解性严重、计算效率低和内存消耗大等难点问题,本文开展了三维重力和重力梯度数据的联合反演研究,该方法结合重力和重力梯度两种数据,将L0范数正则化项加入到目标函数中,并在数据空间下采用改进的共轭梯度算法求解反演最优化问题.同时,本文摒弃了依赖先验信息的深度加权函数,引入了自适应模型积分灵敏度矩阵,用来克服因重力和重力梯度数据核函数随深度增加而衰减引起的趋肤效应问题.为了提高反演计算效率,本文又推导出基于规则网格化的重力和重力梯度快速正演计算方法.模拟试算表明,改进的共轭梯度法可以降低反演的迭代次数,提高反演的收敛速度;自适应模型积分灵敏度矩阵,可以有效解决趋肤效应,提高反演纵向分辨能力;数据空间和改进的共轭梯度算法结合,可以更好地降低反演求解方程的维度,避免存储灵敏度矩阵,有效地降低反演计算时间和内存消耗量.野外实例表明,该算法可以在普通计算机下快速地获得地下密度分布模型,表现出较强的稳定性和适用性.

     

Seismic data reconstruction based on CS and Fourier theory

Traditional seismic data sampling follows the Nyquist sampling theorem. In this paper, we introduce the theory of compressive sensing (CS), breaking through the limitations of the traditional Nyquist sampling theorem, rendering the coherent aliases of regular undersampling into harmless incoherent random noise using random undersampling, and effectively turning the reconstruction problem into a much simpler denoising problem. We introduce the projections onto convex sets (POCS) algorithm in the data reconstruction process, apply the exponential decay threshold parameter in the iterations, and modify the traditional reconstruction process that performs forward and reverse transforms in the time and space domain. We propose a new method that uses forward and reverse transforms in the space domain. The proposed method uses less computer memory and improves computational speed. We also analyze the antinoise and anti-aliasing ability of the proposed method, and compare the 2D and 3D data reconstruction. Theoretical models and real data show that the proposed method is effective and of practical importance, as it can reconstruct missing traces and reduce the exploration cost of complex data acquisition.     

基于压缩感知的Curvelet域联合迭代地震数据重建

由于野外采集环境的限制,常常无法采集得到完整规则的野外地震数据,为了后续地震处理、解释工作的顺利进行,地震数据重建工作被广泛的研究.自压缩感知理论的提出,相继出现了基于该理论的多种迭代阈值方法,如CRSI方法（Curvelet Recovery by Sparsity-promoting Inversion method）、Bregman迭代阈值算法（the linearized Bregman method）等.CSRI方法利用地震波形在Curvelet的稀疏特性,通过一种基于最速下降的迭代算法在Curvelet变换域恢复出高信噪比地震数据,该迭代算法稳定,收敛,但其收敛速度慢.Bregman迭代阈值法与CRSI最大区别在于每次迭代时把上一次恢复结果中的阈值前所有能量都保留到本次恢复结果中,从而加快了收敛速度,但随着迭代的进行重构数据中噪声干扰越来越严重,导致最终恢复出的数据信噪比低.综合两种经典方法的优缺点,本文构造了一种新的联合迭代算法框架,在每次迭代中将CRSI和Bregman的恢复量加权并同时加回本次迭代结果中,从而加快了迭代初期的收敛速度,又避免了迭代后期噪声干扰的影响.合成数据和实际数据试算结果表明,我们提出的新方法不仅迭代快速收敛稳定,且能得到高信噪比的重建结果.     

基于泊松碟采样的地震数据压缩重建

在地震资料处理领域,数据的压缩和重建是非常重要的问题,但往往由于数据的严重缺失或采样原因而达不到理想的效果.新发展起来的压缩感知理论为重建欠采样数据提供了可能,而选用合适的采样方法是其中的关键技术之一.本文基于傅里叶变换和压缩感知理论,采用泊松碟采样,对不完整地震数据进行恢复重建.数值实验表明,与传统的单纯随机采样方法相比,泊松碟采样方法在保持采样随机性的同时,使采样点的分布更加均匀,有效地调节了采样间距,从而达到更好的恢复效果,可以有效地指导地震数据采集设计及重建.     

基于jitter采样和曲波变换的三维地震数据重建

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e-√x(0≤x≤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.     

基于非均匀曲波变换的高精度地震数据重建

在野外数据采集过程中,空间非均匀采样下的地震道缺失现象经常出现,为了不影响后续资料处理,必须进行高精度数据重建.然而大多数常规方法只能对空间均匀采样下的地震缺失道进行重建,而对于非均匀采样的地震数据则无能为力.为此本文在以往多尺度多方向二维曲波变换的基础上,首先引入非均匀快速傅里叶变换,建立均匀曲波系数与空间非均匀采样下地震缺失道数据之间的规则化反演算子,在L1最小范数约束下,使用线性Bregman方法进行反演计算得到均匀曲波系数,最后再进行均匀快速离散曲波反变换,从而形成基于非均匀曲波变换的高精度地震数据重建方法.该方法不仅可以重建非均匀带假频的缺失数据,而且具有较强的抗噪声能力,同时也可以将非均匀网格数据归为到任意指定的均匀采样网格.理论与实际数据的处理表明了该方法重建效果远优于非均匀傅里叶变换方法,可以有效地指导复杂地区数据采集设计及重建.

     

基于非均匀Fourier变换的地震数据重建方法研究

不规则采样地震数据会对地震数据的多道处理造成严重影响,将非均匀Fourier变换和贝叶斯参数反演方法相结合,对不规则空间带限地震数据进行反演重建.对每一个频率依据最小视速度确定出重建数据的带宽,然后从不规则地震数据中估计出重建数据的空间Fourier系数.将不规则地震数据重建视为信息重建的地球物理反演问题,运用贝叶斯参数反演理论来估计Fourier系数.在反演求解时,使用共轭梯度算法,以保证求解的稳定性,加快解的收敛速度.理论模型和实际资料处理验证了本方法的有效性和实用性.     

基于稀疏约束和多源激发的地震数据高效采集方法

地震勘探目标日趋复杂化和精细化,"两宽一高"等采集技术获得了广泛应用,从而导致当前地震数据采集周期越来越长、成本越来越高,如何解决日益增长的勘探成本问题成为当前地震采集领域的研究热点之一.针对上述问题,本文首先开展了基于稀疏性的地震数据高效采集方法理论研究,对地震数据稀疏性基本理论、稀疏约束下随机采样及其数据重建方法进行了深入探讨,提出使用改进的分段随机采样方法灵活地进行实际地震采集测网设计;详细阐述了多源地震激发方法,对多源地震数据分离方法开展了深入研究,提出了基于小窗口中值滤波与稀疏约束联合随机去噪的多源数据分离方法,并在数据分离处理中取得了较好的效果;将上述两种地震数据采集方案有机结合,提出了1）规则多源、随机检波点（DmsRg）、2）随机多源、规则检波点（RmsDg）和3）随机多源、随机检波点（RmsRg）等三种高效采集方案及相应的数据重建方案,满足了后续常规化数据处理的要求,并讨论了多源激发对数据成像的影响.基于Marmousi模型数据的数值试验表明,本文构建的基于稀疏约束和多源激发的高效采集方法理论对于提高地震数据采集效率、降低勘探成本具有重要的应用价值,建立的数据重建方法流程可以取得和常规数据接近的成像结果.本文方法虽然在数值试验中取得了较为理想的效果,但还需要得到野外实际数据采集的进一步检验.     

地震数据压缩重构的正则化与零范数稀疏最优化方法

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.     

哈拉湖地区低频可控震源天然气水合物地球物理响应特征研究

我国陆域天然气水合物主要分布于青藏高原和漠河地区.由于永久冻土层的存在,地震勘探很难获得高品质的资料,给天然气水合物勘探带来了诸多困难.为解决冻土层对地震信号的衰减问题,在哈拉湖地区采用低频可控震源进行地震资料采集试验,通过提高覆盖次数,获得了较高信噪比的地震资料.在高质量地震资料基础上,进行精细速度分析,获得了较准确的叠加速度谱资料;然后以层速度剖面为基础建立正演模型,开展天然气水合物地震正演模拟研究;最后利用叠后偏移地震数据进行地震属性分析.通过正演模拟和地震属性综合研究,总结了天然气水合物的地球物理响应特征,速度突变和空白反射带可作为哈拉湖地区陆域天然气水合物识别的敏感因素.     

Reconstruction method of irregular seismic data with adaptive thresholds based on different sparse transform bases

Oil and gas seismic exploration have to adopt irregular seismic acquisition due to the increasingly complex exploration conditions to adapt to complex geologica...