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.     

Entropic criterion for model selection

Model or variable selection is usually achieved through ranking models according to the increasing order of preference. One of methods is applying Kullback–Leibler distance or relative entropy as a selection criterion. Yet that will raise two questions, why use this criterion and are there any other criteria. Besides, conventional approaches require a reference prior, which is usually difficult to get. Following the logic of inductive inference proposed by Caticha [Relative entropy and inductive inference, in: G. Erickson, Y. Zhai (Eds.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conference Proceedings, vol. 707, 2004 (available from arXiv.org/abs/physics/0311093)], we show relative entropy to be a unique criterion, which requires no prior information and can be applied to different fields. We examine this criterion by considering a physical problem, simple fluids, and results are promising.     

Moment searching algorithm for bioluminescence tomography

To avoid the ill-posedness in the inverse problem of bioluminescence tomography, a moment searching algorithm fusing the finite element method （FEM） with the moment concept in theoretical mechanics is developed. In the algorithm, the source＇s information is mapped to the surface photon flux density by FEM, and the source＇s position is modified with the feedback through the algorithm of barycenter searching, which makes full use of the position information of the photon flux density on surface. The position is modified in every iterative step and will finally converge to the real source＇s value theoretically.     

Gibbs–Jaynes Entropy Versus Relative Entropy

The maximum entropy formalism developed by Jaynes determines the relevant ensemble in nonequilibrium statistical mechanics by maximising the entropy functional subject to the constraints imposed by the available information. We present an alternative derivation of the relevant ensemble based on the Kullback–Leibler divergence from equilibrium. If the equilibrium ensemble is already known, then calculation of the relevant ensemble is considerably simplified. The constraints must be chosen with care in order to avoid contradictions between the two alternative derivations. The relative entropy functional measures how much a distribution departs from equilibrium. Therefore, it provides a distinct approach to the calculation of statistical ensembles that might be applicable to situations in which the formalism presented by Jaynes performs poorly (such as non-ergodic dynamical systems).     

Radiative perturbation theory for polarized radiances: 1. Theory

Radiative perturbation theory has proven to be a useful tool in radiative transfer calculations, especially in situations where repeated solution of the radiative transfer equation is required. So far however, its use has been restricted to non-polarized situations, including such applications as surface fluxes, UV indices, and the inversion of satellite radiance observations. Here, we extend the structure of radiative perturbation theory to incorporate the full Stokes formalism of polarization, to obtain the relevant equations for the first order term. This formalism will be applied to fluxes in a follow-up paper, and eventually to satellite observations.     

利用U-Net网络增强骨密度全波形反演

该文设计了一种使用U-Net网络解决骨密度全波形反演的初值依赖、多解、病态等问题的方法。首先使用逆时偏移成像，将其结果输入神经网络得到模型的预分布。将该分布作为全波形反演目标函数的约束，可以使反演的结果更接近最优值，还可以减小反演对初始值的依赖。该文进行了一些模拟实验，得出该文的方法可以改进全波形反演对初始值的依赖和容易陷入局部极值的问题。     

Maximum-entropy data analysis

The reconstruction of physical quantities from (computer-) experimental data is very often hampered by the presence of noise, insufficient information and above all by the ill-posed nature of the underlying inversion problem. It will be demonstrated that the maximum entropy concepts is particularly suited for this type of data-analysis problems. It is based on Bayesian statistics and provides a consistent probabilistic theory to obtain unbiased results, independent of any model assumptions. This is particularly desirable if there is no additional information to justify these hypotheses. If, on the other hand, additional prior knowledge is available, it can be effectively incorporated into the computation, leading to more stringent confidence intervals.     

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。     

Deconvolution of complex echo signals by the maximum entropy method in ultrasonic nondestructive inspection

The problem of inversion of convolution with the echo signal point source function is considered with the use of the regularization and maximum entropy method and further reconstruction of two-dimensional images by the method of projection in the spectral domain. The inverse convolution problem is solved for the complex-valued signal that is obtained from the real valued signal through the Hilbert transform. Numerical and experimental simulation is performed. A possibility of enhancing the echo signal along the ray’s resolution and of lowering the spectrum’s noise level with the use of complex signals (pseudo-random sequences) is demonstrated. The results are compared with those obtained using the autoregression method and the reference hologram method.     

On the Concept of Entropy for Quantum Decaying Systems

The classical concept of entropy was successfully extended to quantum mechanics by the introduction of the density operator formalism. However, further extensions to quantum decaying states have been hampered by conceptual difficulties associated to the particular nature of these states. In this work we address this problem, by (i) pointing out the difficulties that appear when one tries a consistent definition for this entropy, and (ii) building up a plausible formalism for it, which is based on the use of coherent complex states in the context of a path integration.     

测量低频大电流的自积分罗氏线圈设计

为测量电容储能脉冲功率源模块电流,设计了磁芯式自积分罗氏线圈。给出了磁芯的选择方法,分析了磁芯饱和问题。解决饱和问题的方法是使用饱和磁感应强度较大的材料,对测量线圈施加去磁磁场,以及等效减小线圈的励磁电流。分析表明:通过增大磁芯直径和截面积,选取线径合适的导线多层绕制的方法来增大线圈自感与电阻比值,可以有效提高线圈的测量幅值范围。使用设计的线圈实测了脉冲功率源模块电流,通过改变模块的充电电压,可以得到线圈出现饱和时对应的电流值。实验结果与理论分析相符合。对于脉冲功率源模块的ms量级脉冲电流信号,改进后的自积分线圈测量范围可以超过50kA。     

Using relative entropy to find optimal approximations: An application to simple fluids

We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist of (a) justifying the use of relative entropy as the uniquely natural criterion to select a preferred approximation from within a family of trial parameterized distributions, and (b) to obtain the optimal approximation by marginalizing over parameters using the method of maximum entropy and information geometry. As an illustration we apply our method to simple fluids. The “exact” canonical distribution is approximated by that of a fluid of hard spheres. The proposed method first determines the preferred value of the hard-sphere diameter, and then obtains an optimal hard-sphere approximation by a suitably weighed average over different hard-sphere diameters. This leads to a considerable improvement in accounting for the soft-core nature of the interatomic potential. As a numerical demonstration, the radial distribution function and the equation of state for a Lennard-Jones fluid (argon) are compared with results from molecular dynamics simulations.     

散射光谱的目标材质及比例反演研究

研究了基于散射光谱的点目标在远距离条件下表面材质及比例反演方法,旨在为空间碎片探测及预报提供数据参考。首先根据散射光谱的远距离目标探测物理模型,建立了基于散射光谱的目标参数反演物理模型,给出了基于最小二范数理论方法的目标表面材质及比例信息的反演算法,结合光源照射特性、目标材料表面光学反射特性、入射、反射及探测角等信息,利用双向反射分布函数(BRDF) 的多级融合模型,表征复杂材料表面的光学反射特性, 将BRDF中对应的面积量作为待反演参数,给出了目标表面材质及比例信息的反演算法;其次进行了实验验证,搭建了室内散射光谱探测及采集系统,进行了单一材质及多种材质不同比例的目标散射光谱探测及数据采集,经过对散射光谱数据进行预处理,截取有效波长范围为400～800 nm;结合理论分析及反演算法,对于四种材质组合的样品,进行了相同和不同比例组合的材质及比例反演,等比例反演结果最小误差为0.8%。最大误差为13.6%,平均误差为4.9%;不等比例反演结果最小误差为6%,最大误为12%,平均误差为9.25%;综合以上测试结果可以得出,反演平均误差最大为9.25%,考虑到入射光源稳定性有2.89%的误差,反演结果最大平均误差将小于6.36%。得到了平均反演误差小于10%的良好效果,验证了该方法的准确性;最后以某失效卫星为例,对其在轨的散射光谱信息,进行了材质及比例反演计算,给出了其主要材质为太阳能帆板、保温膜及碳纤维板,与真实情况相符较好。该研究为点目标远距离材质比例反演识别提供了新的技术途径。     

探地雷达反问题的小波-同伦混合反演算法

构造一种求解探地雷达反问题的小波-同伦混合反演算法.利用小波将反问题分解到不同尺度上,在最大尺度上采用同伦反演方法,求得次级尺度的初始近似解,在其余尺度上进行多次迭代修正,以获得全局最小点.算法结合小波反演和同伦反演的优点,数值结果表明其具有较强的全局搜索能力.     

Ground Penetrating Radar Nondestructive Testing Based on Wavelet Sparse Representation

Now Ground penetrating radar (GPR) nondestructive testing methods have been applied to many fields of physics. But traditional electromagnetic methods (usually based on least square and local iteration) just roughly give the information of location, level and quality. In this paper we consider inverse electromagnetic problem which is concerned with the estimation of electric conductivity of Maxwell’s equations. A wavelet multilevel representation is proposed to inversion of GPR nondestructive testing. Once we decompose the objective functional onto different levels from the smallest to the largest, there are very few local minimum on the largest level component of the problem. Then local convergent Gauss-Newton method could easily find the global minimum on this level which is close to the global optimization solution on the second largest level. So, Gauss-Newton method with initial value which is solved on the largest level has serious possibility to find the global minimum of the second largest level. Repeating this step one could find the global optimization solution of the original inverse problem. On each level, the stable and fast local convergent Gauss-Newton method is carried out. Results exhibits clear advantages over damping Gauss-Newton method and testify that it is an available method, especially on aspects of wide convergence and precision.     

基于脉冲耦合神经网络和图像熵的各向异性扩散模型研究

在图像去噪过程中, 大部分基于偏微分方程的各向异性扩散模型均使用梯度信息检测边缘, 当边缘部分被噪声严重污染时, 这些方法不能有效检测出这些边缘, 因而无法保留边缘特征. 为了较完整的保留图像的区域信息, 用脉冲耦合神经网络(PCNN)能使具有相似输入的神经元同时产生脉冲的性质对噪声图像做处理, 得到图像熵序列, 并将图像熵序列作为边缘检测算子引入到扩散方程中, 不仅能克服仅用梯度作为边缘检测算子易受噪声影响的弊端, 而且能较完整地保留图像的区域信息. 然后, 用最小交叉熵准则搜索使去噪前后图像信息量差异最小的阈值, 设计最佳阈值控制扩散强度, 建立基于脉冲耦合神经网络与图像熵改进的各向异性扩散模型(PCNN-IEAD). 分析与仿真结果表明, 该模型与经典模型相比, 保留了更多的图像信息, 能够兼顾去除图像的噪声和保护图像的边缘纹理等细节信息, 较完整的保留了图像的区域信息, 性能指标同样也证实了新模型的优越性. 另外, 该模型的运行时间较经典模型的短, 因此, 该模型是一个理想的模型.     

Generalized measures of quantum correlations for mixed states

The exponential speedup achieved in certain quantum algorithms based on mixed states with negligible entanglement has renewed the interest on alternative measures of quantum correlations. Here we discuss a general measure of quantum correlations for composite systems based on generalized entropic functions, defined as the minimum information loss due to a local measurement. For pure states, the present measure becomes an entanglement entropy, i.e., it reduces to the generalized entropy of the reduced state. However, for mixed states it can be nonzero in separable states, vanishing just for states diagonal in a general product basis, like the quantum discord. Quadratic measures of quantum correlations can be derived as particular cases of the present formalism. The minimum information loss due to a joint local measurement is also considered. The evaluation of these measures in a simple yet relevant case is also discussed.     

Methods for ELNES-quantification: characterization of the degree of inversion of Mg-Al-spinels

The energy loss near-edge structures in electron energy-loss spectra contain information about bonding characteristics, the electronic structure and coordinations of the excited atoms. We have calculated sets of reference spectra for the normal and for the inverse Mg-Al-spinel using a full multiple scattering approach. By a quantitative comparison of these reference spectra with experimental data ELNES-quantification becomes possible. We characterized the degree of inversion lambda by the analysis of the relative peak-intensities and the relative peak-positions within 35 eV beyond the edge onset. The results demonstrate that by using the provided methods ELNES-quantification will become possible when uncertainties in the experiment are reduced and a better fit of the simulations to the experiment is achieved.     

Full waveform inversion with optimal basis functions

Based on the approach suggested by Tarantola, and Gauthier et al., we show that the alternate use of the step (linear) function basis and the block function (quasi-delta function) basis can give accurate full waveform inversion results for the layered acoustic systems, starting from a uniform background. Our method is robust against additive white noise (up to 20% of the signal) and can resolve layers that are comparable to or smaller than a wavelength in thickness. The physical reason for the success of our approach is illustrated through a simple example.