核磁共振二维谱反演

核磁共振二维谱包含扩散系数 D 和横向弛豫时间 T₂ 的信息,利用核磁共振仪来测量多孔介质中物质的信息,根据其弛豫时间和扩散系数的差别来区分不同物质;利用全局反演方法,提出了核磁共振二维谱反演的物理模型和数学模型;介绍了传统的奇异值分解（SVD）和改进的奇异值分解反演算法;采用改进的奇异值分解法对核磁共振二维谱进行反演,其反演算法具有计算速度快和二维谱分布连续等优点. 它适合于信噪比较高的数据反演,当原始数据信噪比SNR≥100时,可以对二维谱图进行定量分析;当60≤SNR<100时,可以对二维谱图进行定性分析. 核磁共振二维谱可以一次性直接区分油和水,为核磁共振测井提供了新的科学技术.     

基于迭代TSVD的NMR二维谱反演算法

针对现有基于TSVD的二维反演算法中截断位置判断不准确、容易产生虚假峰等问题,提出了一种改进的方法. 首先,通过逐步求精的方法对L曲线上的拐角位置进行定位,得到迭代的最大截断位置;然后,根据反演核奇异值的集中程度获取迭代的最小截断位置;最后,在给定的截断位置范围内从小到大进行TSVD,每次迭代都以上一次迭代的结果为依据. 对仿真数据和实验数据的反演结果表明,该算法都能够得到比较好的二维反演效果. 与现有基于TSVD的方法相比,该算法具有更高的鲁棒性,能够得到更清晰的二维谱,可满足实际应用需求.     

低场核磁共振扩散-横向弛豫二维反演算法

针对低场核磁共振一维反演中无法分辨一维谱中重叠组分和目前报道的扩散-横向弛豫二维反演算法计算量大、计算耗时长的问题,提出了一种计算量小、计算效率高、耗时短的扩散-横向弛豫二维反演算法. 首先对扩散系数D-和横向弛豫时间T₂进行布点;其次根据信号采集条件计算出两个核心矩阵,并分别进行奇异值分解;然后,由所采集信号计算出两个核心矩阵的奇异值截断值,分别对两个核心矩阵的奇异值矩阵进行截断并求其逆矩阵;最后计算出初始反演结果,并添加非负约束经过多次迭代得到最终反演结果. 实验结果证明,提出的扩散-横向弛豫二维反演算法在不影响反演结果准确性的基础上,能极大提高计算效率.     

水驱油过程的核磁共振二维谱研究

岩心水驱油过程中油水分布状况是岩心多孔介质的重要性质. 水驱油过程的研究是进一步进行提高采收率研究的基础. 核磁共振扩散-弛豫二维谱提供了岩心中流体性质的多方面信息,与核磁共振一维弛豫谱相比极大地提高了区分油水的能力. 该文通过2组岩心水驱油实验,从不同含油饱和度的扩散-弛豫二维谱中提取出水的一维弛豫谱,在原油粘度比较高的情况下获得了驱替过程中油水在不同孔隙中的分布状况以及润湿性等信息, 解决了单独用一维弛豫谱方法难以区分油水的问题. 该文的研究方法对油田提高采收率的研究有比较大的参考价值.     

一种基于组分补偿的二维核磁共振测井数据高精度处理方法

二维核磁共振技术能够对储层中各类含氢流体进行无损、快速、定量的测量和表征，但受限于采集方式和参数，核磁共振设备在对页岩油等致密储层中的有机质、沥青等超快弛豫组分进行检测时，经常出现由于信号采集不完整所导致的二维谱中流体组分缺失或不准的问题.本文提出了基于超快弛豫组分补偿技术的T₂-T₁二维谱高精度反演方法，该方法将一维核磁共振前端信号补偿技术进行推广，通过在二维核磁数据反演前对回波数据进行组分补偿，能够有效解决二维核磁共振测井前端信号漏失的问题.实验及测井数据的应用表明，该方法在页岩油等富含快弛豫组分信号的储层中，可以得到更加精准和完整的储层信息.     

中子深度分析反演算法研究

针对中子深度分析技术,研究几类反演算法：概率迭代法、奇异值分解求解最小二乘法、线性正则化方法及约束线性正则化法.开展相关数值实验,分别在欠定方程、超定方程情况下,对反演算法的结果进行比较.一般情况下几种算法都能得到较为理想的结果,概率迭代法和约束线性正则化法由于有迭代过程,因此在离子源强度发生阶跃处得到的结果并不理想.在超定方程情况下,当选取的反演范围较为随意时,线性正则化方法可能使得解的稳定性较差,而约束线性正则化法能够很好地抑制求解过程中的不稳定性.对实际测量能谱进行反演时,由于能谱有随机误差,线性正则化方法不能很好地抑制误差的影响,反演结果振荡较强,其余方法的结果与参考值符合很好.     

二维核磁共振观测岩石润湿性

润湿性是反映储层中油水分布状况的一个重要表征参数,因此研究储层岩石的润湿性对原油开采有着重要的意义. 扩散弛豫二维谱可展示扩散系数与弛豫时间的相关性,并可以对油水的弛豫时间、扩散系数分别进行研究,与核磁共振一维弛豫谱相比极大地提高了区分油水的能力. 该文首先通过多组实验验证扩散-弛豫二维谱可以很好地观测到油水共存状态下玻璃珠表面的润湿性,继而通过对3组人造岩心表面润湿性的测量,获得了人造岩心表面润湿性的信息,解决了此时单独用一维弛豫谱方法难以区分油水的问题. 利用二维谱观察岩石润湿性的研究对油田提高采收率的研究有较大的参考价值.     

核磁自旋回波串的液体分量分解快速反演法(英文)

该文叙述核磁自旋回波串的液体分量分解快速反演法.此方法假定液体,无论是在散装形式或饱和多孔介质中,可以用一个或一组核磁弛豫线形来表征.对一维核磁共振的拉普拉斯反演,它可以是预先确定的一个或一组T2或T1分布.对二维核磁共振的拉普拉斯反演,它可以是一个或一组预先确定的( D, T2)或( T1, T2)二维分布.对三维核磁共振的拉普拉斯反演,它可以是一个或一组预先设定的( D, T1, T2)三维分布.这些预先确定的线形,可以是高斯、B样条或预先由实验或经验确定的任何线形.这种方法可以显着降低核磁共振数据反演的计算时间,特别是从石油核磁共振测井采集的多维数据反演,它不需牺牲反演所得的分布的平滑性和准确性.这种方法的另一个新应用是作为一种约束求解方法来过滤相邻深度所采集的数据噪音.核磁共振测井的噪音信号,往往造成在相邻深度的同一岩性岩层有不同的T2分布.在此情况下, T2分布就不能用来识别岩性.通过非一般的矩阵操作,作者成功实现了对相邻深度的回波串实施约束求解方法,从而使得T2分布成为一种可靠的岩性识别指标.     

基于逆散射理论的地震波速度正则化反演

本文基于逆散射理论利用正则化有限差分对比源反演算法对地震波传播速度进行反演, 该方法是基于波动方程的频率域波形反演算法, 利用非线性共轭梯度法, 通过最小化目标优化函数不断迭代更新速度模型. 由于地球物理反演问题的病态性和不稳定性, 通过基于反演参数总变差的正则化处理, 使反演问题变为良性问题且算法具有较强的抗噪声干扰能力. 反演过程中使用了频率-空间域9点差分正演算子以及PML吸收边界条件. 与其他反演算法相比, 由于背景模型在反演迭代过程中保持不变, 可以避免在每次迭代过程中重新构造正演算子及矩阵分解等相关计算过程, 使得该算法非常适合于大规模三维反演计算. 此外, 本文采用基于MPI的并行计算, 进一步提高了反演计算的效率. 二维CSEG模型反演结果表明该方法可以反演得到高分辨率的地震波速度重建结果, 为地震勘探数据处理及解释提供准确的速度信息.     

4,4,5,5-四甲基-1,3,2-二氧硼戊环的11B NMR及1H-11B HMQC研究

以4,4,5,5-四甲基-1,3,2-二氧硼戌环分子为研究对象,对碳硼烷类化合物的核磁共振(NMR)检测方法进行了研究.除了采用常规的核磁共振碳谱(~(13)C NMR)、氢谱(~1H NMR)及其二维相关谱外,引入核磁共振硼谱(~(11)B NMR)与二维异核多量子相关谱(~1H-~(11)B HMQC),对含硼类化合物结构进行了测定,该方法对于准确解析硼烷类化合物的结构具有较好的参考意义.     

Methods and limitations of NMR data inversion for fluid typing

We introduce two NMR inversion methods within the framework of 1D NMR to extract fluid saturations by varying echo spacing and wait time. The first method connects the T2 distribution of each fluid with the overall apparent T2 distribution using a shift matrix. Each fluid's saturation and T2 distribution are extracted by minimizing the difference between the model T2 distributions and measured apparent T2 distributions. The second method relates a model T2 distribution of each fluid with CPMG echo trains using a global evolution matrix that governs the evolution of magnetization under T1, T2 relaxation, and diffusion. These methods will be useful whenever data are not sufficient for 2D NMR inversion. They are also much faster than 2D for fluid typing. We also point out an inherent limitation associated with NMR inversion methods for fluid typing. Whenever there is singularity in the inversion matrix caused by similar behavior of model function for different fluids, most inversion algorithms remove the solution space associated with the singularity and choose a solution vector of the minimum length. This results in equal proportions of different fluids in the final answer. If prior knowledge such as saturation or T2 shape of the oil is available, there are several methods to tailor the solution to our desired outcome. However, if there is no prior knowledge available, such ambiguity always exists irregardless of the inversion schemes.     

On the inversion of diffusion NMR data: Tikhonov regularization and optimal choice of the regularization parameter

The analysis of diffusion NMR data in terms of distributions of diffusion coefficients is hampered by the ill-posed nature of the required inverse Laplace transformation. Na?ve approaches such as multiexponential fitting or standard least-squares algorithms are numerically unstable and often fail. This paper updates the CONTIN approach of the application of Tikhonov regularization to stabilise this numerical inversion problem and demonstrates two methods for automatically choosing the optimal value of the regularization parameter. These approaches are computationally efficient and easy to implement using standard matrix algebra techniques. Example analyses are presenting using both synthetic data and experimental results of diffusion NMR studies on the azo-dye sunset yellow and some polymer molecular weight reference standards.     

A novel improved method for analysis of 2D diffusion-relaxation data--2D PARAFAC-Laplace decomposition

This paper demonstrates how the multi-linear PARAFAC model can with advantage be used to decompose 2D diffusion-relaxation correlation NMR spectra prior to 2D-Laplace inversion to the T(2)-D domain. The decomposition is advantageous for better interpretation of the complex correlation maps as well as for the quantification of extracted T(2)-D components. To demonstrate the new method seventeen mixtures of wheat flour, starch, gluten, oil and water were prepared and measured with a 300 MHz nuclear magnetic resonance (NMR) spectrometer using a pulsed gradient stimulated echo (PGSTE) pulse sequence followed by a Carr-Purcell-Meiboom-Gill (CPMG) pulse echo train. By varying the gradient strength, 2D diffusion-relaxation data were recorded for each sample. From these double exponentially decaying relaxation data the PARAFAC algorithm extracted two unique diffusion-relaxation components, explaining 99.8% of the variation in the data set. These two components were subsequently transformed to the T(2)-D domain using 2D-inverse Laplace transformation and quantitatively assigned to the oil and water components of the samples. The oil component was one distinct distribution with peak intensity at D=3 x 10(-12) m(2) s(-1) and T(2)=180 ms. The water component consisted of two broad populations of water molecules with diffusion coefficients and relaxation times centered around correlation pairs: D=10(-9) m(2) s(-1), T(2)=10 ms and D=3 x 10(-13) m(2) s(-1), T(2)=13 ms. Small spurious peaks observed in the inverse Laplace transformation of original complex data were effectively filtered by the PARAFAC decomposition and thus considered artefacts from the complex Laplace transformation. The oil-to-water ratio determined by PARAFAC followed by 2D-Laplace inversion was perfectly correlated with known oil-to-water ratio of the samples. The new method of using PARAFAC prior to the 2D-Laplace inversion proved to have superior potential in analysis of diffusion-relaxation spectra, as it improves not only the interpretation, but also the quantification.     

Application Based Construction and Optimization of Substitution Boxes Over 2D Mixed Chaotic Maps

Chaotic maps play a vital role in the development of cryptographic techniques being used in today’s world. Efficient and highly secure algorithms can be constructed based on chaotic maps. Chaotic maps have the intrinsic property of being highly sensitive to initial conditions. In this paper, we have presented a novel scheme for construction and optimization of substitution boxes (S-boxes) based on mixed two dimensional (2D) chaotic maps in which cryptographic properties of S-boxes are optimized based on initial conditions of their parent 2D chaotic map. The proposed scheme and the resulting substitution boxes are analyzed with existing cryptanalysis techniques and their results have been compared with some other algorithms available in literature. The proposed scheme has been found to be more efficacious than other algorithms. The outcomes of security analysis indicate that our proposed technique and resulting optimized non-linear component in the current era of information technology.

     

Relaxation Model and Mapping of Magnetic Field Gradients in MRI

The purpose of the work is development of algorithms for separate mapping of T ₂ relaxation time and gradients, using gradient recalled echo (GRE) sequence. Application of three-dimensional (3D) model of gradients and their volumetric averaging within a voxel lead to analytical model of relaxation function, which is consistent with experimental data for both regular macroscopic and randomized micro- and mesoscopic gradients. The model is verified by fitting into experimental data obtained on specially made phantoms. Verification of algorithms is completed by comparing gradient maps obtained on specially made cylindrical phantoms with theoretical maps of their exact 3D electro-dynamic solutions. Analytical model of relaxation function proved to be in good agreement with experimental relaxation curves. On the basis of this model, fast and unambiguous fittingless algorithms were developed. Gradient maps measured on special cylindrical phantoms are in good qualitative agreement with theory. 3D statistical model and fittingless algorithms provide the basis for separating the GRE signal into two meaningful parameters—T ₂ and gradients, thus doubling information from magnetic resonance imaging.     

2D NMR技术在石油测井中的应用

近几年,2D NMR技术得到迅速发展,特别是在核磁共振测井领域. 该文将主要介绍2D NMR技术的脉冲序列、弛豫原理以及2D NMR技术在石油测井中应用. 2D NMR技术是在梯度场的作用下,利用一系列回波时间间隔不同的CPMG脉冲进行测量,利用二维的数学反演得到2D NMR. 2D NMR技术可以直接测量自扩散系数、弛豫时间、原油粘度、含油饱和度、可动水饱和度、孔隙度、渗透率等地层流体性质和岩石物性参数. 从2D NMR谱上,可以直观的区分油、气、水,判断储层润湿性,确定内部磁场梯度等. 2D NMR技术为识别流体类型提供了新方法.     

Mri measurements of T1, T2 and D for gels undergoing volume phase transition

Gels consist of crosslinked polymer network swollen in solvent. The network of flexible long-chain molecules traps the liquid medium they are immersed in. Some gels undergo abrupt volume change, a phase transition process, by swelling-shrinking in response to external stimuli changes in solvent composition, temperature, pH, electric field, etc. We report that during volume phase transition changes of NMR longitudinal relaxation time T(1), NMR transverse relaxation time T(2), and diffusion coefficient D of the PMMA gel, and D of the NIPA gel. We describe how the gels were synthesized and the reason of using the snapshot FLASH imaging sequence to measure T(1), T(2), and D. Since T(1), T(2) and D maps have identical field of view and data are extracted from identical areas from their respective maps, these values can be correlated quantitatively on a pixel-by-pixel basis. Thus a complete set of NMR parameters is measured in-situ: the gels are in their natural state, immersed in the liquid, during the phase transition. The results of spectroscopic method agree with that of snapshot FLASH imaging method. For the PMMA gel T(1), T(2) and D decrease when gels undergo volume phase transition between deuterated acetone concentration of 30% and 40%. At its contracted state, T(1) is reduced to a little less than one order of magnitude, T(2) over two orders of magnitude, and D over one order of magnitude, smaller from values of PMMA gel at the swollen state. At an elevated temperature of 54 degrees C the thermosensitive NIPA gel is at a contracted state, with its D reduced to almost one order of magnitude smaller from that of the swollen NIPA at room temperature.