Unbiased estimation formula of unit weight standard deviation in regularization solution

Regularization method is an effective method for solving ill-posed equation. In this paper the unbiased estimation formula of unit weight standard deviation in the regularization solution is derived and the formula is verified with numerical case of 1 000 sample data by use of the typical ill-posed equation, i. e. the Fredholm integration equation of the first kind.     

On the effective inversion by imposing a priori information for retrieval of land surface parameters

The anisotropy of the land surface can be best described by the bidirectional reflectance distribution function (BRDF). As the field of multiangular remote sensing advances, it is increasingly probable that BRDF models can be inverted to estimate the important biological or climatological parameters of the earth surface such as leaf area index and albedo. The state-of-the-art of BRDF is the use of the linear kernel-driven models, mathematically described as the linear combination of the isotropic kernel, vo...     

Voigt regularization for the explicit time stepping of the Hall effect term

This article studies the stabilization of the explicit time stepping methods for Hall Maxwell and incompressible Hall MHD equations. Since the Hall effect term contains two spatial derivatives, classical time-stepping schemes result in very restrictive CFL condition. We consider weakening the restrictive time step condition via Voigt regularization. We establish the energy stability result and validate our approach numerically. Numerical experiments demonstrate that we are able to take larger time steps, compared to classical schemes, at additional, negligible computational cost.     

重力数据3D密度成像中EXTR方法的各参数变化对反演结果的影响(英文)

Tikhonov正则化(TR)方法在重磁数据处理中发挥了重要的作用,本文在研究如何利用Tikhonov正则化方法方法解决重力数据3D反演的同时,深入讨论了可进一步提高拟合误差的Extrapolation Tikhonov正则化方法(EXTR)的原理,并就其参数选择方法及各参数对拟合误差、迭代次数及反演结果的影响进行研究。常密度及变密度组合模型试算结果表明,与TR方法相比,EXTR方法不仅可以达到解释人员设定的先验拟合误差水平,在计算时间及迭代次数相应增加的前提下有更高的拟合精度;同时其反演结果也更加紧致,进一步改善了TR反演结果的发散性;并且其反演数据范围更贴近预设模型参数范围,模型特征与预设模型密度分布吻合较好。     

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。     

航空重力测量数据向下延拓的正则化算法及其谱分解

基于Poisson积分方程,提出了以地面重力观测值作为控制并顾及外区影响的向下解析延拓数学模型,推导了向下解析延拓的谱分解式,在频域内分析了造成向下延拓结果不稳定的原因,进而给出了向下延拓的正则化算法,并讨论了向下延拓中的地形影响.通过对我国首次航空重力测量试验数据的处理表明,提出的方法可获得稳定、精确的向下延拓结果.     

基于贝叶斯正则化改进BP神经网络的页岩气有机碳含量预测模型

页岩气总有机碳(TOC)含量是评价岩性气藏的关键指标,受复杂地质及岩芯采集等多种因素的影响,常规室内测试分析获得的TOC含量的数据有限且结果有失准确。为合理准确预测页岩气TOC含量,本文首先通过对页岩气储层TOC含量测井资料综合分析选取8条测井曲线,并结合主成分分析法(Principal Component Analysis,PCA)提取四个主成分;其次基于贝叶斯正则化(Bayesian Regularization)改进的BP神经网络方法建立页岩气TOC含量预测的BR-BP模型;最后利用该模型对研究区A区页岩气TOC含量进行预测,并与常规的LM-BP神经网络模型的预测结果进行对比。结果表明：BR-BP模型有较强的非线性拟合能力,能够真实地反映出页岩气TOC含量与各测井参数之间的非线性关系,其模型预测结果与实际值基本吻合,与常规的LM-BP神经网络模型相比,其数据敏感性增强,预测精度有所提高,该研究方法具有一定的理论意义和参考价值,为我国TOC含量预测提供了一种新的技术方法和手段。     

病态总体最小二乘的混合正则化算法

病态问题在大地测量数据处理中广泛存在,单一的Tikhonov正则化算法会造成求解过度平滑,而TV正则化可以更有效地抵抗噪声。本文将Tikhonov正则化和TV正则化两种方法有效结合,推导了具体求解公式并给出相应迭代算法。计算表明,本文提出的方法在处理病态总体最小二乘问题上稳定性更高。     

Development of dynamic slip model for a shear crack

<正>The objective of this paper is to develop a dynamic slip model for a shear crack under constant stress drop.This crack problem is formulated by a traction boundary integral equation(BIE) in the frequency domain and then solved by the hyper-singular boundary element method as well as the regularization technique proposed in this paper.Based on the spectral integral form of the kernel function,the unbounded term can be isolated and extracted from the hyper-singular kernel function by using the method of subtracted and added back in wave number domain.Finally,based on the inverse transformation from the frequency domain to the time domain,the time histories of crack opening displacement under constant stress drop can be determined.Three rupture models(simultaneous rupture model,symmetric bilaterally-propagating model and unilaterally propagating model) with specified time histories of stress drop are considered in this paper.Even though these three models will cause the same final slip shapes because of the same constant stress drop,the associated slip time functions differ significantly from each other during the rupture process.     

Unbiased estimation formula of unit weight standard deviation in regularization solution

Regularization method is an effective method for solving ill-posed equation. In this paper the unbiased estimation formula of unit weight standard deviation in the regularization solution is derived and the formula is verified with numerical case of 1000 sample data by use of the typical ill-posed equation, i.e. the Fredholm integration equation of the first kind.