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.     

基于稀疏反演的OBS数据多次波压制方法

自由表面多次波压制是海底地震仪（Ocean Bottom Seismometer,OBS）数据处理和成像中的难点,OBS数据多次波能量强,周期长,严重影响深层一次反射波的处理和成像.不同于常规拖缆观测系统,OBS数据站点一般相隔较远,仅仅利用检波点稀疏的波场信息难以压制OBS数据中的自由表面多次波.本文采用拖缆数据与OBS数据联合,利用稀疏反演估计（Estimation of Primaries and Multiples by Sparse Inversion,EPSI）方法,研究了OBS数据自由表面多次波压制理论,分析了OBS多次波产生的机理,详细推导了拖缆数据与OBS数据联合预测OBS多次波的EPSI方法基本原理.通过利用拖缆数据的信息,实现了OBS检波点稀疏数据多次波的压制问题.EPSI方法通过稀疏反演直接估计一次反射波,避免了SRME（Surface Related Multiple Elimination）方法中自适应相减对有效信号的损害,保真了一次反射有效信号,理论模拟OBS数据验证了方法的有效性.     

基于曲波变换的大地电磁二维稀疏正则化反演

为了提高二维大地电磁反演对异常体边界的刻画能力,我们引入曲波变换建立一种新的稀疏正则化反演方法.与传统的在空间域中对模型电阻率参数求解的方式不同,我们借助曲波变换将二维电阻率模型转换为曲波系数,并采用L1范数约束以保证系数的稀疏性.曲波变换是一种多尺度分析方法,其系数分为粗尺度系数和精细尺度系数,粗尺度的系数代表电阻率模型的整体概貌,而精细尺度中较大系数代表目标体的边缘细节.此外,曲波变换的窗函数满足各向异性尺度关系,并具有多方向性,因此曲波变换可以近似最佳地提取目标体的边缘特征信息,这为我们在反演中恢复边界提供有利条件.通过对大地电磁的理论模型合成数据和实测数据反演,验证了基于曲波变换稀疏正则化反演对异常体边界的刻画能力优于常规的L2范数和L1范数反演方法.     

Using surface multiples to estimate primaries by sparse inversion from blended data

For data acquired with conventional acquisition techniques, surface multiples are usually considered as noise events that obscure the primaries. However, in this paper we demonstrate that for the situation of blended acquisition, meaning that different sources are shooting in a time‐overlapping fashion, multiples can be used to ‘deblend’ the seismic measurements. We utilize the recently introduced estimation of primaries by sparse inversion (EPSI) methodology, in which the primary impulse responses are considered to be the unknowns in a large‐scale inversion process. With some modifications the estimation of primaries by sparse inversion method can be used for blended seismic data. As output this process gives unblended primary impulse responses with point sources and receivers at the surface, which can be used directly in traditional imaging schemes. It turns out that extra information is needed to improve on the deblending of events that do not have much associated multiple energy in the data, such as steep events at large offsets. We demonstrate that this information can be brought in during acquisition and during processing. The methodology is illustrated on 2D synthetic data.     

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2DCurvelet变换和小波变换,在2DCurvelet-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.     

稀疏反演多次波去除策略与效果分析

多次波去除是海上勘探中的一项关键技术,在一定程度上决定着最终成像结果的质量.表面相关多次波去除方法(Surface-Related Multiple Elimination,SRME)是一种基于反馈迭代模型的数据驱动类方法,该方法利用地震数据本身预测多次波,进一步对其进行匹配相减获得一次波结果,这往往导致与多次波重叠的一次波被错误地去除.稀疏反演一次波估计方法(Estimation of Primaries by Sparsity Inversion,EPSI)在原理上同样基于反馈迭代模型,通过求解一次波和表面相关多次波总残差最小化问题直接获得一次波.该方法无多次波的匹配相减过程,可减少与多次波发生重叠的一次波产生损失.另外,EPSI可以很好地解决SRME无法解决的近道缺失问题.理论数据和实际资料处理对比表明SRME对数据完整性以及一次波和多次波的分布情况有较强的依赖性,而EPSI几乎不受这两个因素的影响.EPSI相比SRME方法计算成本高,尚未在工业界广泛应用,但随着高性能计算的普及,该方法的实用性有望得到突破.     

Inverse data-space multiple elimination with 3D curvelet sparsity promotion

This paper describes an effective implementation of the inverse data-space multiple elimination method via the three-dimensional (3D) curvelet domain. The method can separate the surface-related operator (A) and primaries (P ₀) through seismic data matrix inversion. A 3D curvelet transform is introduced to sparsely represent the seismic data in the inverse data space. Hence, this approach is suitable for obtaining an accurate solution because of its multiscale and multidirectional analysis properties. The L1 norm is used to promote sparseness in the transform domain. Then, a high-fidelity separation of the operator (A) and the primaries (P ₀) is realized. The proposed method is applied to synthetic data from a model containing a salt structure. We compare the results with that of the traditional inverse data-space multiple elimination method and also with that of two-dimensional surface-related multiple elimination. The findings fully demonstrate the superiority of the proposed method over the traditional inverse method; moreover, the proposed method protects the primary energy more effectively than the SRME method.     

基于Curvelet变换的探地雷达资料噪声衰减方法

噪声衰减是探地雷达信号处理中的关键问题之一。当探测目标埋藏深度比较浅时,其反射信号与直耦信号和地面回波信号相互重叠,直接影响目标反射波到达时刻的检测及目标的正确定位。针对这个问题,本文提出了一种基于Curvelet变换的噪声衰减方法。通过对理论数值模拟数据和实测数据的处理,以及与平均消去法和二维连续小波该方法处理结果的对比,验证了该方法的可行性和有效性。处理结果显示,该方法不仅可以去除背景噪声、同时可以衰减倾斜相关的相干干扰和数据中的随机噪声。与二维连续小波变换方法相比有更高的计算效率。     

Seismic data reconstruction using a sparsity-promoting apex shifted hyperbolic Radon-curvelet transform

Apex shift hyperbolic Radon transform (ASHRT) is an extension of hyperbolic Radon transform (HRT). We have developed a novel sparsity-promoting framework for ASHRT by employing curvelet transform (CT) in the sparse inversion. RT-based seismic data processing can be considered as an optimization problem and a mixed norms inversion, therefore, objective function with CT can promote the sparsity of the transformed domain, which makes the sparse inversion more efficient. Compared with the conventional sparse inversion of ASHRT, the proposed method weights the sparse penalization, which indicates a sparser solution of ASHRT. We use synthetic and field data examples to demonstrate the performance of ASHRT. Compared to the conventional solution, the ours may lead to more accurately reconstructed results and have a better noise immunity.     

INVERSION OF POST-STACK SEISMIC DATA USING SIMULATED ANNEALING1

Model-based inversion of seismic reflection data is a global optimization problem when prior information is sparse. We investigate the use of an efficient, global, stochastic optimization method, that of simulated annealing, for determining the two-way traveltimes and the reflection coefficients. We exploit the advantage of an ensemble approach to the inversion of full-scale target zones on 2D seismic sections. In our ensemble approach, several copies of the model-algorithm system are run in parallel. In this way, estimation of true ensemble statistics for the process is made possible, and improved annealing schedules can be produced. It is shown that the method can produce reliable results efficiently in the 2D case, even when prior information is sparse.     

A SIMULATED ANNEALING APPROACH TO SEISMIC MODEL OPTIMIZATION WITH SPARSE PRIOR INFORMATION1

It is well known that seismic inversion based on local model optimization methods, such as iterative use of linear optimization, may fail when prior information is sparse. Where the seismic events corresponding to reflectors of interest remain to be identified, a global optimization technique is required. We investigate the use of a global, stochastic optimization method, that of simulated annealing, to solve the seismic trace inversion problem, in which the two-way traveltimes and reflection coefficients are to be determined. The simulated annealing method is based on an analogy between the model-algorithm system and a statistical mechanical system. We exploit this analogy to produce improved annealing schedules. It is shown that even in cases of virtually no prior information about two-way traveltimes and reflection coefficients, the method is capable of producing reliable results.     

基于数据规则化和稀疏反演的三维表面多次波压制方法

表面多次波是海洋地震勘探中的主要问题.目前,二维数据驱动的表面多次波压制技术(SRME)已经比较成熟,并且已经成为工业界压制海洋表面多次波的主流方法.但是由于二维SRME算法没有考虑横测线方向上多次波的贡献,导致在处理实际三维海洋资料时存在比较大的误差.将二维SRME算法扩展到三维空间后可以得到三维SRME算法,但是由于目前实际采集的三维海洋资料的观测系统存在拖缆漂移,而且横测线方向采样过于稀疏,直接应用三维SRME算法无法准确预测表面多次波.本文提出的通过数据规则化配合稀疏反演的三维表面多次波压制方法能够解决这种实际资料和三维SRME算法之间的矛盾.本文通过研究数据规则化与反规则化技术,使得数据分布满足三维SRME的要求;通过研究稀疏反演技术,有效解决了横测线方向采样稀疏对于多次波预测的影响,三维实际海洋资料的应用结果验证了方法的有效性和可行性.     

基于稀疏反演三维表面多次波压制方法

三维表面多次波压制是海洋地震资料预处理中的重要研究课题,基于波动理论的三维表面多次波压制方法(3DSRME)是数据驱动的方法,理论上来说,可有效压制复杂构造地震数据表面多次波.但该方法因对原始地震数据采集要求高而很难在实际资料处理中广泛应用.本文基于贡献道集的概念,将稀疏反演方法引入到表面多次波压制中,应用稀疏反演代替横测线积分求和,无需对横测线进行大规模重建,进而完成三维表面多次波预测,这样可有效解决实际三维地震数据横测线方向稀疏的问题.基于纵测线多次波积分道集为抛物线的假设,为保证预测后三维表面多次波和全三维数据预测的多次波在运动学和动力学特征上基本一致,文中对预测数据实施基于稳相原理的相位校正.理论模型和实际数据的测试结果表明,本文基于稀疏反演三维表面多次波压制方法可在横测线稀疏的情况下,有效压制三维复杂介质地震资料中的表面多次波,从而更好地提高海洋地震资料的信噪比,为高分辨率地震成像提供可靠的预处理数据保障.     

Curvelet reconstruction of non-uniformly sampled seismic data using the linearized Bregman method

Seismic data reconstruction, as a preconditioning process, is critical to the performance of subsequent data and imaging processing tasks. Often, seismic data are sparsely and non-uniformly sampled due to limitations of economic costs and field conditions. However, most reconstruction processing algorithms are designed for the ideal case of uniformly sampled data. In this paper, we propose the non-equispaced fast discrete curvelet transform-based three-dimensional reconstruction method that can handle and interpolate non-uniformly sampled data effectively along two spatial coordinates. In the procedure, the three-dimensional seismic data sets are organized in a sequence of two-dimensional time slices along the source–receiver domain. By introducing the two-dimensional non-equispaced fast Fourier transform in the conventional fast discrete curvelet transform, we formulate an L1 sparsity regularized problem to invert for the uniformly sampled curvelet coefficients from the non-uniformly sampled data. In order to improve the inversion algorithm efficiency, we employ the linearized Bregman method to solve the L1-norm minimization problem. Once the uniform curvelet coefficients are obtained, uniformly sampled three-dimensional seismic data can be reconstructed via the conventional inverse curvelet transform. The reconstructed results using both synthetic and real data demonstrate that the proposed method can reconstruct not only non-uniformly sampled and aliased data with missing traces, but also the subset of observed data on a non-uniform grid to a specified uniform grid along two spatial coordinates. Also, the results show that the simple linearized Bregman method is superior to the complex spectral projected gradient for L1 norm method in terms of reconstruction accuracy.     

基于保幅拉东变换的多次波衰减

为在去除多次波时有效保护地震一次反射波数据的AVO现象,给后续反演、解释提供准确的地震数据,本文提出了一种基于保幅拉东变换的多次波衰减方法,该方法是对常规抛物拉东变换的修改,把常规的稀疏拉东变换在拉东域分成两部分：一部分用于模拟零偏移距处的反射波能量,增加的另一部分用于模拟反射波振幅的AVO特性.该方法不仅考虑了反射波同相轴的形状,还考虑了反射波同相轴振幅幅度的变化,从而可把反射波信息进行有效转换,进而有利于多次波的消除,更好地恢复有效波的能量.在把地震数据由时间域转换到拉东域时,本文采用了IRLS算法实现保幅拉东算子的反演.模型数据和实际地震道集的试算分析表明,与常规拉东变换相比,保幅拉东变换在去除多次波的同时可有效保护一次反射波的AVO现象.     

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.     

基于非二次幂Curvelet变换的最小二乘匹配算法及其应用

本文提出了基于非二次幂Curvelet变换的最小二乘匹配算法.首先,根据输入地震信号的频谱和方向等特征进行非二次幂Curvelet变换,根据其特征不同,最大程度地将有效信号和噪声分开;然后,在噪声能量集中的非二次幂Curvelet子记录上对输入数据和预测的噪声模型进行最小二乘匹配滤波处理.本方法提高了常规最小二乘匹配算法在时间空间域内进行信噪分离的稳定性和准确性.对含有面波的实际地震数据进行测试,其结果表明本方法可以有效地压制面波干扰,特别是当面波和有效信号有交叉或重叠等现象出现时,能较好地保护反射同相轴信息.本方法还可用于对含自由表面多次波和层间多次波等地震数据进行自适应信噪分离.     

基于复曲波变换的一次波和多次波分离方法

多次波压制方法的研究一直都是地震数据处理中非常重要的一个课题.由于常用的多次波匹配方法主要针对多次波模型和实际多次波存在的振幅或相位的差异进行匹配校正,而无法直接校正多次波模型和实际多次波存在时移误差.本文构建了一种复曲波变换的算法,利用复曲波变换的时移不变性质,通过调整复曲波系数的振幅和相位实现对多次波模型振幅和时移误差的校正.为了更好地保护有效信号,在一次波和多次波分离前,引入一个非线性屏蔽滤波器,可以事先分离出大部分有效波,然后再将剩余部分数据作为输入数据,在复曲波域进行剩余一次波和多次波分离.最后通过模型试算和实际资料处理验证了本文提出的一次波和多次波分离方法的有效性.     

Ground roll attenuation based on an empirical curvelet transform

In the field of seismic exploration, ground roll seriously affects the deep effective reflections from subsurface deep structures. Traditional curvelet transform cannot provide an adaptive basis function to achieve a suboptimal denoised result. In this paper, we propose a method based on empirical curvelet transform (ECT) for ground roll attenuation. Unlike the traditional curvelet transform, this method not only decomposes seismic data into multiscale and multi-directional components, but also provides an adaptive filter bank according to frequency content of seismic data itself. So, ground roll can be separated by using this method. However, as the frequency of reflection and ground roll components are close, we apply singular value decomposition (SVD) in the curvelet domain to differentiate the ground roll and reflection better. Examples of synthetic and field seismic data reveal that the proposed method based ECT performs better than the traditional curvelet method in terms of the suppression of ground roll.     

3D parallel inversion of time-domain airborne EM data

To improve the inversion accuracy of time-domain airborne electromagnetic data, we propose a parallel 3D inversion algorithm for airborne EM data based on the direct Gauss–Newton optimization. Forward modeling is performed in the frequency domain based on the scattered secondary electrical field. Then, the inverse Fourier transform and convolution of the transmitting waveform are used to calculate the EM responses and the sensitivity matrix in the time domain for arbitrary transmitting waves. To optimize the computational time and memory requirements, we use the EM “footprint” concept to reduce the model size and obtain the sparse sensitivity matrix. To improve the 3D inversion, we use the OpenMP library and parallel computing. We test the proposed 3D parallel inversion code using two synthetic datasets and a field dataset. The time-domain airborne EM inversion results suggest that the proposed algorithm is effective, efficient, and practical.