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.     

2D地震数据规则化中随机稀疏采样方案

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。     

基于优化聚类的人工源电磁法数据信噪分离方法

为了降低强电磁干扰对人工源电磁法(Controlled Source Electromagnetic Method, CSEM)有效信号的影响, 改善CSEM实测数据处理结果因人而异且效率低的不足, 本文针对CSEM有效信号周期性特征提出了一种加权自适应带宽均值漂移聚类(Weighted Adaptive Bandwidth Mean-Shift Clustering, WAB-MSC)信噪分离方法.首先在传统均值漂移聚类(Mean-Shift Clustering, MSC)算法的基础上增加核函数, 降低处理结果对带宽选择的敏感度, 提高算法的稳健性; 其次结合实测CSEM数据的分布特征提出了一种基于局部密度梯度的带宽估计方法, 实现了自适应带宽选择; 最后通过仿真数据与实测数据对本文方法进行了验证, 结果表明: 本文方法能有效消除强电磁干扰对CSEM数据的影响, 最大程度保留受噪声影响较小或未受噪声影响的数据, 提高数据信噪比, 降低强干扰噪声对CSEM初始资料的影响程度, 获得更为真实的地电响应模型, 为后续数据处理提供保障.

     

On correct application of one-step inversion of gravity data

One of the main problems on the numerical solution of integral equations is the resolution of input data. Among the integral equations used in geodesy we have the “onestep inversion” based on the first derivative of the Poisson integral, which transforms gravity values on the Earth’s surface to the gravity potential on the reference ellipsoid. In this study, it is shown that the required spatial resolution of the input gravity data on the Earth’s surface for correct one-step inversion depends on the height of the computational region, the fact that if overlooked can cause totally wrong results. Consequently the following two major questions are posed: (i) How could one know whether the spatial resolution of the input gravity data for correct one-step inversion is sufficient? (ii) What should be done if the spatial resolution is not sufficient? By studying the behaviour of the integral kernel, an algorithm is presented which enables an appropriate answer to the former question. In order to address the latter question, a method is proposed to modify the integral kernel which overcomes the adverse effect of insufficient spatial resolution of the input gravity data. Our answers, which possess the novelty of the study, are numerically verified by means of real and simulated gravity data. The numerical results approve the efficiency of the proposed method in solving the problem of insufficient spatial resolution of the input gravity data for correct one-step inversion.     

Functional time series analysis of spatio–temporal epidemiological data

Spatio–temporal statistical models have been proposed for the analysis of the temporal evolution of the geographical pattern of mortality (or incidence) risks in disease mapping. However, as far as we know, functional approaches based on Hilbert-valued processes have not been used so far in this area. In this paper, the autoregressive Hilbertian process framework is adopted to estimate the functional temporal evolution of mortality relative risk maps. Specifically, the penalized functional estimation of log-relative risk maps is considered to smooth the classical standardized mortality ratio. The reproducing kernel Hilbert space (RKHS) norm is selected for definition of the penalty term. This RKHS-based approach is combined with the Kalman filtering algorithm for the spatio–temporal estimation of risk. Functional confidence intervals are also derived for detecting high risk areas. The proposed methodology is illustrated analyzing breast cancer mortality data in the provinces of Spain during the period 1975–2005. A simulation study is performed to compare the ARH(1) based estimation with the classical spatio–temporal conditional autoregressive approach.     

Suppressing random noise to broaden the useful bandwidth of seismic reflection data

The signal-to-noise ratio （SNR） of seismic reflection data in many areas is rather poor and conventional two-dimensional filters designed to suppress noise with different moveout from the signal tend to generate artifacts. We have extended a method of multichannel filtering, based on the hypothesis that signals on adjacent channels are similar, for enhancing the SNR on stacked sections. Using only the mid-range frequencies where the SNR is highest, the event trend is found for overlapping windows on the section and the average signal vector is calculated. Then the data from the full bandwidth section are projected onto the spatially varying unit similarity vectors and the results are merged for the overlapping windows. Application of the method to synthetic data containing steeply dipping events and to a stacked section for a marine 2D line has produced good results. The modifications we have introduced carry a small overhead in computing time but they should enable the method to be used effectively even on sections containing steep dips.     

可展宽地震资料有效频宽的随机噪声衰减方法

很多地区地震资料的信噪比较低,而用于压制与信号具有不同方向的随机噪声的常规二维滤波方法常常产生假信息。基于相邻信号具有相干性这一假设,本文提出了一种叠后衰减随机噪声的多道滤波方法。该方法利用信噪比最高的中频段信息(含有主频的这一频率区间)分时窗计算信号单位矢量,并将该时窗内全频段数据向信号单位矢量方向投影,对各时窗(包括时间方向和空间方向)重叠部分按比例进行加权。我们利用这种方法对含有陡倾角的合成地震数据和海上二维实际地震资料进行了处理,处理效果很好。这种方法较为费时,但不受倾角限制,应用范围广。     

任意扫描轨迹下三维Shepp-Logan体模的投影方法

图像重建是将二维投影数据转换为三维体数据的数学过程。分析图像重建算法性能的常用手段是数值仿真,而获取数字体模的投影数据是仿真实验的第一步。Shepp-Logan体模应用最为广泛,本文首先介绍三维Shepp-Logan体模及其改进形式。重点讨论在任意扫描轨迹下三维Shepp-Logan体模的投影方法。并运用该方法模拟了工业CT中常用的圆轨迹与螺旋轨迹成像过程。数值分析结果显示,两种扫描轨迹得到的重建图像均方误差均小于2‰,本文的方法可以达到较高的精度。     

基于核主成分分析的时间域航空电磁去噪方法

时间域航空电磁数据往往在测量过程中受到天然和人文噪声的干扰.如果不能很好滤除这些电磁噪声,那么将会降低资料质量、影响反演的精度,甚至获得错误的解释结果.本文提出了一种基于核主成分分析的去噪方法,通过核主成分分析提取叠加后衰减曲线的主成分,然后使用能量占比方法分离反映地下介质的有效信号和噪声,最后使用反映地下介质的特定成分进行重构.本文所推荐的去噪方法不仅能剔除天然噪声,例如天电产生的尖脉冲或者振荡,而且能有效地抑制人文噪声.分别使用基于核主成分分析的去噪方法,以及AeroTEM软件的处理方法对同样的吊舱式时间域直升机航空电磁勘查系统实测数据进行处理,并比较其结果.处理结果表明：所推荐的去噪方法要优于AeroTEM软件.     

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.     

体积CT投影数据的模拟方法

体积CT是目前研究的热点,也是医疗CT和工业CT的发展方向。在研究体积CT重建算法的过程中,模拟投影数据是必不可少的一部分。本文提出一种体积CT投影数据的模拟方法。这种方法的特点是准确、适用性广,模拟得到的投影数据能够准确反映各断层的细节信息,一方面可以为后继体积CT重建算法提供可靠的投影数据,另一方面也可以根据需要有选择地模拟失真的投影数据。我们利用此方法对人脑部及某工件的CT投影数据进行了模拟,并对模拟得到的数据采用滤波反投影算法进行重建,将重建后的断层图像与原始图像进行比较,得到了很好的重建结果,进一步验证了该投影数据模拟方法的可行性。     

基于加权K均值聚类的多属性初至拾取方法

为提高初至拾取方法的准确性和自适应能力,将变异系数加权K均值聚类算法引入初至拾取中。首先提取均方根振幅、相邻道相关性、线积分、振幅谱主频等多种地震属性;然后针对地震属性进行加权K均值聚类,自动识别初至所在时窗;最后结合相位校正法,实现时窗内初至波起跳时间的拾取。在此基础上通过实际数据测试,并与长短时窗能量比法、反向传播神经网络方法对比,验证了本文方法的有效性与可行性。结果表明,基于加权K均值聚类的多属性初至拾取方法能较快速、准确地拾取低信噪比数据的初至,并且无需人为判断时窗,从而提高了拾取的自适应能力。      

基于一种改进凸集投影方法的地震数据同时插值和去噪

基于稀疏反演的地震插值方法是一种重要的插值方法, 然而大多数这类方法只针对无噪声数据或者高信噪比数据插值.实际上, 地震数据含有各种噪声, 使得插值问题变得更加困难.凸集投影方法是一种高效的插值算法, 但是对于含噪声数据的插值效果不理想, 针对含噪声数据提出的加权凸集投影方法能够实现同时插值和去噪, 但是除了最小阈值需要认真选取外, 增加一个权重因子来实现去噪功能.本文由迭代阈值算法推导出加权凸集投影方法, 证明其是解无约束优化问题的一种方法, 加权因子可以看作拟合误差项的系数.本文还提出了一种改进的凸集投影方法, 与原始凸集投影方法相比该方法不需要增加任何计算量, 只要通过阈值的选择来进行插值和去噪.数值模拟证明了该算法的计算效率, 并且对含噪声数据能够实现较好的插值效果; 先插值后去噪的结果证明了同时去噪和插值算法的可靠性和稳定性.     

基于模型融合的有限角度CT迭代重建方法

针对有限角度扫描的CT重建,提出一种基于模型融合的CT迭代重建方法。模型来源于患者的早期Dicom图像。对扫描角度有限的投影数据,用统计迭代算法进行初步重建,得到预重建图像;将预重建图像与模型进行融合,得到融合图像;然后再次投影,补全原始投影缺失的部分,根据补全的投影数据重建出中间结果,之后重复投影、融合、重建过程直到满足终止条件。仿真实验表明,该算法能完整重建整个目标,在有效保留原目标特征的同时提高了小角度投影数据重建的质量。     

核磁共振与瞬变电磁三维联合解释方法

传统核磁共振地下含水量解释多采用基于均匀半空间或层状导电模型的一维反演, 分层给出地下含水信息.然而, 这些方法忽略了地下复杂电阻率分布信息对结果的影响, 也不能很好地反映局部三维含水构造.本文从三维电介质中核磁共振响应的正演理论出发, 提出首先利用瞬变电磁数据进行基于等效导电平面法的快速电阻率成像, 然后将成像结果作为核磁共振三维反演的电性模型, 进行联合解释.激发磁场的分布采用有限元法直接求解, 通过引入伪δ源实现电流源的加载, 并强加散度条件排除了三维磁场模拟中"弱解"的影响.针对核磁共振灵敏度矩阵的病态性和数据中存在的干扰信号, 提出考虑罚项的非线性拟合目标函数, 利用线性化方法进行核磁共振反演.模型数据表明该方法能较准确反映地下三维含水构造, 实测算例进一步证明了方法的有效性.本研究将促使核磁共振方法在岩溶、裂隙水、孤立水体等复杂水文地质条件及隧道、矿井灾害水源探测等方面得到有效应用.     

Spatial prediction using bivariate exponential distribution

In this paper, a certain bivariate exponential distribution is used for the spatial prediction. The unobserved random variable is predicted by the projection onto the space of all linear combinations of the powers, up to degree m, of the observed random variables plus the constant 1. We obtain a solution by assuming that all the bivariate distributions follow Gumbel’s type III or logistic form of bivariate exponential. The method is implemented on two data sets and the results are presented. The predictions are compared with the original values through Mean Structural Similarity (MSSIM) index of Wang et al. (IEEE Trans Image Process 13(4):600–612, 2004). Using the MSSIM index the proposed method is also compared with Ordinary Kriging and with Simple Kriging after normal score transform.     

Conditional components for simulation of vector random fields

Conditional component random fields (CC) based on Cholesky decomposition of the multivariate spectra are introduced in this study to develop a new method for conditional simulation of vector attributes in environmental and geological phenomena. The CC are independent random fields with covariance models obtained from projections and conditioning in the frequency domain. The approach is to simulate one attribute in the physical space and use the results to estimate the other attributes in the frequency domain. Then, a CC for the next attribute is simulated and projected on the other attributes. In general, any attribute is built as the sum of inverse Fourier transform of the orthogonal projection of previous simulated CC plus a last CC simulated in the physical space. This simulation approach continues in this fashion for several attributes and the order of them may be changed for different realizations. This method allows for data conditioning and simulation. A simplified version for intrinsically correlated random fields allows for an approach that avoids the frequency domain.     

基于GPU实现的数字合成X射线体层成像投影数据的模拟方法

数字合成X射线体层成像技术能利用有限角度下的投影数据重建物体任意断层的图像。在数字合成X射线体层成像重建算法研究中,模拟投影数据是重要的步骤,本文提出了一种基于GPU光线投射算法的数字合成X射线体层成像投影数据模拟方法。比较传统CPU模拟手段,GPU模拟方法计算速率快,且基于硬件支持的三线性插值能够得到更加接近实际的投影结果。本文采用传统CPU模拟方法和GPU模拟方法分别计算投影数据,对两种方法获得投影使用ART算法和小波-伽辽金方法进行重建,得到较好的重建效果。     

基于全变分原理的多震源混合数据直接偏移方法

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.     

拉东投影法三维叠前深度偏移

对地下地质构造进行正确成像是地震勘探的最终目的,由于三维地震资料采集不可能都沿垂直构造走向的方向进行,为地震资料的三维处理带来了许多困难. 本文将三维叠后拉东投影偏移思想应用于三维叠前处理中,提出了三维叠前投影偏移算法. 利用拉东投影变换的原理,将整个三维叠前数据体投影到一系列各方向的径向线上,各方位角的构造都包含在其中某条或多条径向剖面上. 投影完成后,形成一系列的独立的二维叠前测线,可采用二维叠前深度偏移成像方法来实现各径向线的叠前偏移,当各径向剖面偏移完成后,在时间切片上进行反投影,从而最终形成三维叠前深度偏移结果. 实际应用表明,用本方法进行三维叠前深度偏移时,深度偏移剖面对横向分辨率有所提高,对陡地层和小断层的成像效果有所改善.