变分伴随正则化方法从雷达回波反演海洋波导 Ⅰ.理论推导部分

针对传统统计反演算法在雷达回波反演海洋波导(RFC)方面计算量过大的问题,提出一种变分伴随正则化物理反演算法.在变分伴随方法中分别导出切线性模式、伴随方程及伴随边界条件、伴随方程求解表达式、以及泛函梯度的数学表达形式;讨论了伴随方法求泛函梯度对复方程如何协调的问题.考虑到雷达电磁波传播的特征,选择了适当的正则化项来解决反演中的不适定问题.最后给出反演算法实施中的迭代格式.     

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.     

L曲线方法在地基红外高光谱反演温度廓线中的应用

利用地基红外高光谱辐射数据可以反演得到高时间分辨率的边界层大气温度廓线。目前的AERIoe最优化反演算法相比于传统的“剥洋葱”算法有较大的改进,且对初值的依赖程度较低。但AERIoe算法中正则化算子的选择对反演结果的稳定性和反演时间有重要影响。目前主要采用经验的方法选择正则化算子,迭代步数较多,耗费大量的计算时间。提出了利用L曲线方法代替经验法选取正则化算子的改进方案,以提高AERIoe方法的反演速度。改进后的算法通过绘制解范数和残余范数的二维曲线图,取其拐点作为最优的正则化参数,相比于传统的经验法有着更好的理论基础。采用2011年美国大气辐射测量计划中SGP站点的晴空大气红外辐射数据进行反演实验。结果表明,利用该方法得到的反演结果具有很好的稳定性、收敛性和精度。相比于经验的方法,利用L曲线方法获得的正则化算子反演温度廓线时的收敛速度更快,迭代步数较少,可以节约大量的计算时间;在反演精度方面,L曲线方法在边界层中上层的反演精度更高,1～3 km高度上温度廓线的RMSE值提高了大约0.2 K。     

基于自适应差分进化算法的阵列侧向测井快速反演

严格意义上的电测井反演在每一次反演算法迭代过程中都要进行多次正演计算,耗时长,在复杂三维地层模型中电测井数据的实时反演不太可能实现,对现场实时高效处理电测井数据提出了挑战.本文基于径向阶跃介质模型,预先计算正演响应,在反演过程中直接进行线性插值调用,大大节省反演时间.提出一种自适应差分进化算法,将阵列侧向反演问题转化为一种非线性的全局优化问题,通过与经典差分进化算法、马奎特算法进行比较,自适应差分进化算法具备寻优成功率高（90%）、平均迭代次数少（21）、抗噪性好的特点.利用不同侵入条件下的层状介质模型进行算法验证,结果表明改进算法反演的电阻率较视电阻率更加接近储层真实电阻率,可以满足油气藏评价的需要.     

基于微波链路的降雨场反演方法研究

本文基于微波雨衰的幂律关系, 研究了使用微波链路反演降雨场的方法, 采用层析技术建立了降雨场反演模型. 并利用SIRT算法与正则化算法实现对降雨场层析反演模型的求解. 数值模拟结果表明, 该模型与反演算法能够较为准确地重建降雨场强度与空间分布特征, 能够提供高时空分辨率的二维降雨强度分布. 因此, 利用微波衰减数据进行降雨探测可以作为常规的雨量计与天气雷达观测手段的有效补充. 关键词： 微波雨衰 微波链路 降雨场重建 层析反演     

变分伴随正则化方法从雷达回波反演海洋波导(Ⅱ):实际反演试验

在理论推导的基础上,分别利用模拟和实测的雷达回波资料进行反演试验.在模拟雷达回波资料反演时,分别对不引入正则化项和引入正则化项的反演结果进行讨论;在实际雷达回波资料反演时,讨论了反演结果对初猜值精度的依赖性,分别考虑初猜值为经验模型给定时和初猜值为统计反演结果时对最后反演精度的影响.最后比较了变分伴随正则化方法与传统统计反演算法的优缺点,指出下一步反演算法的改进方向.     

核磁共振二维谱反演技术综述

二维谱的出现是核磁共振（NMR）检测技术的一次飞跃,从二维谱中可以快速、精确地对不同组分进行区分,因而在测录井和常规实验中被广泛采用. 为了给相关研究提供借鉴和参考,推动二维反演技术的发展,该文对近年来国内外在核磁共振二维谱反演技术领域的研究进展进行了综述. 从实验采集数据中反演出二维谱的过程,比一维反演需要解决更多、更复杂的问题. 通过研究罚函数正则化和子空间正则化两大类方法,分析了不同二维反演算法的优点和不足. 根据对近年来国内外相关文献的深入分析可知,虽说目前已有的二维反演算法都存在一定的局限性,但其仍然具有很大的发展空间.     

迭代正则化方法求解电介质中空间电荷分布

首先介绍了迭代正则化方法的理论基础,建立了含有空间电荷密度分布的Fredholm第一类积分方程的反卷积算法,利用数值实验研究了加性高斯白噪声对迭代反卷积算法的影响,以及迭代停止标准对非适定问题的数值解的影响,最后使用该方法求解电介质样品中的空间电荷分布.结果表明,在无噪或者低噪环境下,反卷积算法能够非常好地计算出非适定问题的解.当噪声影响增大,信噪比降低时,反卷积的计算结果受到明显的影响.迭代停止标准对数值解的计算精度起着明显的作用.对实际测量数据进行处理表明,迭代正则化反卷积算法能够计算出固体电介质中的空间电荷分布.     

基于拟牛顿法的连铸结晶器热传导反问题求解

在实际的工业过程中,热传导反问题广泛的存在于各个应用领域。由于连铸的生产环境恶劣,给连铸钢坯的测温造成了很大的困难,导致连铸结晶器热传导反问题的求解是很困难的。在研究了热传导反演算法的基础上,基于连铸结晶器的有限的测量点,通过热传导反演算法可以求出结晶器的热流密度,给连铸的优化和控制提供依据。在建立了连铸热传导反问题模型的基础上,提出了基于拟牛顿法的连铸结晶器热传导反问题求解的改进算法,该算法可以有效的利用当前搜索过程中的信息,通过近似目标函数的二阶导数来加快算法的搜索效率,采用了Wolf步长选择规则克服了算法收敛速率慢的缺点,并且该算法无需计算Hessen矩阵,能够有效降低计算的复杂度。实验结果表明该算法能够快速有效的求解该问题。该方法用于连铸结晶器热传导反问题是可行的、有效的。     

改进的差分光柱像运动激光雷达的湍流廓线反演方法

阐述了差分光柱像运动激光雷达探测大气湍流廓线的基本原理,针对雷达现有Levenberg-Marquardt反演算法对高空湍流反演误差大的问题,提出了带不等式路径约束的反演新模型,并采用惩罚函数法处理该模型,通过增加高空湍流信息量,避免了非物理意义的反演解;同时为了减弱现有算法对初值和先验知识的依赖,进一步提出了基于遗传算法的初值寻优策略,能够将现有算法的初值定位在全局空间内。利用改进算法和现有算法数值仿真了典型的大气湍流廓线,并对合肥地区实测激光雷达数据进行了分析。结果表明,改进算法增强了迭代过程的全局搜索能力,对测量误差有较强的稳健性,能够有效提高反演精度和高空湍流的准确性,同时也加快了收敛速度。     

Interlocked optimization and fast gradient algorithm for a seismic inverse problem

We give a nonlinear inverse method for seismic data recorded in a well from sources at several offsets from the borehole in a 2D acoustic framework. Given the velocity field, approximate values of the impedance are recovered. This is a 2D extension of the 1D inversion of vertical seismic profiles [18]. The inverse problem generates a large scale undetermined ill-conditioned problem. Appropriate regularization terms render the problem well-determined. An interlocked optimization algorithm yields an efficient preconditioning. A gradient algorithm based on the adjoint state method and domain decomposition gives a fast parallel numerical method. For a realistic test case, convergence is attained in an acceptable time with 128 processors.     

Improving Seismic Inversion Robustness via Deformed Jackson Gaussian

The seismic data inversion from observations contaminated by spurious measures (outliers) remains a significant challenge for the industrial and scientific communities. This difficulty is due to slow processing work to mitigate the influence of the outliers. In this work, we introduce a robust formulation to mitigate the influence of spurious measurements in the seismic inversion process. In this regard, we put forth an outlier-resistant seismic inversion methodology for model estimation based on the deformed Jackson Gaussian distribution. To demonstrate the effectiveness of our proposal, we investigated a classic geophysical data-inverse problem in three different scenarios: (i) in the first one, we analyzed the sensitivity of the seismic inversion to incorrect seismic sources; (ii) in the second one, we considered a dataset polluted by Gaussian errors with different noise intensities; and (iii) in the last one we considered a dataset contaminated by many outliers. The results reveal that the deformed Jackson Gaussian outperforms the classical approach, which is based on the standard Gaussian distribution.     

High-performance modeling acoustic and elastic waves using the parallel Dichotomy Algorithm

A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant elliptic operator and different right-hand sides via the integral Laguerre transform. It is proposed to solve difference equations by the conjugate gradient method for acoustic equations and by the GMRES(k) method for modeling elastic waves. A preconditioning operator was the Laplace operator that is inverted using the variable separation method. The novelty of the proposed algorithm is using the Dichotomy Algorithm [26], which was designed for solving a series of tridiagonal systems of linear equations, in the context of the preconditioning operator inversion. Via considering analytical solutions, it is shown that modeling wave processes for long instants of time requires high-resolution meshes. The proposed parallel fine-mesh algorithm enabled to solve real application seismic problems in acceptable time and with high accuracy. By solving model problems, it is demonstrated that the considered parallel algorithm possesses high performance and efficiency over a wide range of the number of processors (from 2 to 8192).     

Three-dimensional emission tomography of a scattering plasma

The three-dimensional emission ray tomography of a plasma partially scattering its self-radiation is considered. The spatial distribution of scattering density and its angular distribution are assumed to be known. The model of projection-data acquisition taking into account single and multiple scattering is constructed. In terms of this model, the problem of determining the distribution of local emission coefficients is posed. For solving this problem, the algorithm based on the Neumann-series expansion of the product of the radiative-transfer operator for a scattering medium and the operator for solving the pure emission problem was proposed. The algorithm was investigated in detail using numerical simulation.     

Binary Level Set Methods for Dynamic Reservoir Characterization by Operator Splitting Scheme

In this paper, operator splitting scheme for dynamic reservoir characterization by binary level set method is employed. For this problem, the absolute permeability of the two-phase porous medium flow can be simulated by the constrained augmented Lagrangian optimization method with well data and seismic time-lapse data. By transforming the constrained optimization problem in an unconstrained one, the saddle point problem can be solved by Uzawas algorithms with operator splitting scheme, which is based on the essence of binary level set method. Both the simple and complicated numerical examples demonstrate that the given algorithms are stable and efficient and the absolute permeability can be satisfactorily recovered.     

基于几何级数展开的鬼波压制方法*

海上拖缆地震数据采集,检波器位于海平面以下,由于海平面的反射作用,检波器接收到的除了上行的一次波,还包括下行的鬼波,因为一次波和鬼波的干涉作用,导致地震信号的有效频带变窄,分辨率降低。为了恢复信号的有效频带,需要进行鬼波压制的宽频处理。该文提出了一种基于逆鬼波算子几何级数展开的鬼波压制技术。几何级数的每一项都是一个波场传播算子,级数的叠加可以实现鬼波的压制,通过对几何级数的截断,可以得到只含上行波的反射信号。数值算例证明了该文方法的有效性,因为波场延拓算子在频率波数域进行,借助快速傅里叶变换,该文方法的效率很高。     

各向异性介质三维电磁响应模拟的Ho-GEBA算法

本文基于积分方程法研究并建立了一种模拟横向同性介质中任意各向异性异常 体三维电磁响应的高阶广义扩展Born近似(Ho-GEBA)算法. 首先利用逐次迭代技术给出积分方程的广义级数展开解, 为保证其收敛性, 引入一种各向异性条件下满足压缩映射的迭代算子. 然后利用异常体区域分解技术, 并结合扩展Born近似原理, 得到各向异性介质三维电磁响应的Ho-GEBA解. 为提高效率, 计算过程中采用并矢Green函数的解析表达式. 最后通过数值计算实例对比验证了本文算法的有效性. 关键词： 高阶广义扩展Born近似 积分方程 电磁模拟 解析Green函数     

红外无损探测中多宗量多热源反演问题的研究

为研究红外无损探测稳态多热源反演逆问题, 建立不同形状的均质与非均质稳态热传导模型, 其中内热源个数、位置、强度、面积均为未知项. 基于数值算法中有限元算法对模型进行离散分析, 化简有限元矩阵方程, 最终转化为对Ax = b高度欠定方程的求解. 首次利用分段多项式谱截断奇异值分解法处理内热源逆问题, 并对算法进行改进, 有效改善了该算法在处理多热源反演时存在的严重的热源叠加效应. 根据反演出的内热源信息, 利用有限元算法计算重构出整个模型内所有节点的温度分布. 运用数值仿真Comsol软件和具体实物实验对算法进行有效性评估, 并验证算法在不同热传导模型中的表现. 结果表明, 算法能够准确反演出多热源各参量信息, 在非均质材料模型中仍能准确地反演出热源项, 并有效重构出模型内温度场. 该算法可应用于材料无损检测及人体红外医学成像等领域.     

Computation of dynamic seismic responses to viscous fluid of digitized three-dimensional Berea sandstones with a coupled finite-difference method

The seismic response of saturated porous rocks is studied numerically using microtomographic images of three-dimensional digitized Berea sandstones. A stress-strain calculation is employed to compute the velocities and attenuations of rock samples whose sizes are much smaller than the seismic wavelength of interest. To compensate for the contributions of small cracks lost in the imaging process to the total velocity and attenuation, a hybrid method is developed to recover the crack distribution, in which the differential effective medium theory, the Kuster-Tokso?z model, and a modified squirt-flow model are utilized in a two-step Monte Carlo inversion. In the inversion, the velocities of P- and S-waves measured for the dry and water-saturated cases, and the measured attenuation of P-waves for different fluids are used. By using such a hybrid method, both the velocities of saturated porous rocks and the attenuations are predicted accurately when compared to laboratory data. The hybrid method is a practical way to model numerically the seismic properties of saturated porous rocks until very high resolution digital data are available. Cracks lost in the imaging process are critical for accurately predicting velocities and attenuations of saturated porous rocks.