利用GPS垂直位移反演区域陆地水储量变化的TSVD-Tikhonov正则化方法

利用GPS垂直位移反演区域陆地水储量变化（TWSC）属于典型的病态问题,其关键是如何进行稳定求解并提高反演结果的精度和可靠性.本文引入TSVD-Tikhonov组合正则化方法对利用GPS垂直位移反演区域TWSC的病态问题进行求解,并以四川省TWSC反演为例进行分析与验证.首先,通过数值模拟对TSVD、Tikhonov和TSVD-Tikhonov正则化方法采用不同正则化参数选取策略（RMSE最小准则、GCV法和L-curve法）进行反演,结果显示基于TSVD-Tikhonov正则化反演的TWSC比单独使用TSVD或Tikhonov正则化反演结果的精度和可靠性更高,这三种正则化方法反演2005年1月至12月的TWSC差值的平均STD分别为14.97 mm、7.03 mm和5.04 mm.其次,利用中国地壳运动观测网络（CMONOC）的72个GPS测站的垂直位移数据,基于TSVD-Tikhonov正则化反演了四川省2010年12月至2021年2月的TWSC时间序列,结果表明GPS反演的TWSC与GRACE/GFO Mascon模型（JPL、CSR和GSFC）的空间分布特征及季节性变化符合较好,但其TWSC信号的振幅比GRACE/GFO Mascon模型更强.最后,采用广义三角帽方法（GTCH）融合不同类型的降水、蒸散发和径流数据,并根据水量平衡方程计算的dTWSC/dt序列（PER-dS/dt）对GPS反演的dTWSC/dt序列（GPS-dS/dt）和GRACE/GFO Mascon模型融合的dTWSC/dt序列（GRACE/GFO-dS/dt）进行验证,结果表明这三类dTWSC/dt序列的季节性变化符合较好,平滑后GPS-dS/dt和GRACE/GFO-dS/dt序列与PER-dS/dt序列的相关系数分别为0.78和0.87,但GPS相比GRACE/GFO对降水变化的响应更为敏感.本文研究证明了TSVD-Tikhonov组合正则化方法能够提高GPS垂直位移反演区域TWSC的精度和可靠性,同时也表明GPS观测数据对局部水质量负荷变化更为敏感,可作为GRACE/GFO反演区域TWSC的有益补充.

     

抗差Tikhonov正则化方法及其应用

提出了抗差Tikhonov正则化方法,并给出了3种常用的计算正则化参数的抗差估计方法,即抗差L-曲线法、抗差广义交叉检核法和抗差广义不符原理。计算结果表明,抗差Tikhonov正则化方法不仅能克服方程病态,而且能有效地控制观测异常影响。     

Three-dimensional inversion of full magnetic gradient tensor data based on hybrid regularization method

Rapid developments in SQUID-based technology make it possible for geophysical exploration to direct measure, inverse and interpret magnetic gradient tensor data. This contribution introduces a novel three-dimensional hybrid regularization method for inversion of magnetic gradient tensor data, which is based on the minimum support functional and total variation functional. Compared to the existing stabilizers, for example, the minimum support stabilizer, the minimum gradient support stabilizer or the total variation stabilizer, our proposed hybrid stabilizer, in association with boundary penalization, improves the revision result greatly, including higher spatial and depth resolution, more clear boundaries, more highlighted images and more evident structure depiction. Moreover, suitable selection of model parameter λ will further improve the image quality of the recovered model. We verify our proposed hybrid method with various synthetic magnetic models. Experiment results prove that this method gives more accurate results, exhibiting advantages of less computational costs even when less prior information of magnetic sources are provided. Comparison of results with different types of magnetic data with and without remanence indicates that our inversion algorithm can obtain more detailed information on the source structure based on rational estimation of total magnetization direction. Finally, we present a case study for inverting SQUID-based magnetic tensor data acquired at Da Hinggan Mountains area, inner Mongolia, China. The result also certifies that the method is reliable and efficient for real cases.     

一种基于Helmert方差分量估计的岭参数确定方法

为了使岭参数具有一个明确的含义,提出了一种基于Helm ert方差分量估计的岭参数确定方法。该方法把约束条件作为一类参数之间互相独立的虚拟观测,从而把岭参数转变为两类观测值的权比,然后用Helm ert方差分量估计的方法确定岭参数。通过算例,比较了该方法与岭迹法、L曲线法的效果。结果表明,该方法不仅计算过程简单、直接,而且精度也优于其他几种方法。     

贝叶斯正则化的Elman神经网络电离层TEC预报模型

利用2017年中低纬电离层总电子含量、地磁活动指数、年积日等参数,首次建立基于贝叶斯正则化(Bayesian regularization)的Elman回归神经网络(BR-Elman)的电离层TEC预报模型。同时,根据地磁活动指数的变化特征,分别进行平静电离层和扰动电离层预报建模。实验结果表明,该方法在平静期5 d预测值的均方根误差为1.19 TECu,残差为1.03 TECu,相关系数为0.93;在扰动期5 d预测值均方根误差为1.34 TECu,残差为1.01 TECu,相关系数为0.91。贝叶斯正则化的BP神经网络模型以及传统BP神经网络模型在平静期与扰动期5 d的预测上,均方根误差最小为1.87 TECu,残差最小为1.50 TECu,相关系数最优为0.87。通过对比分析,该模型较其他2个模型的预报效果有明显改善。     

等式约束病态总体最小二乘模型的正则化解及其精度评定

利用平差参数间合理的先验信息能够显著提高解的精度。在病态总体最小二乘模型的基础上,引入等式约束条件,建立等式约束病态总体最小二乘模型,构建该模型的约束正则化准则,并根据拉格朗日极值法导出参数的迭代解及方差-协方差阵,最后以数值算例和病态测边网算例验证公式的正确性。结果表明,新方法通过正则化准则能改善法矩阵的病态性,且遵从EIV准则顾及系数阵的误差,同时还考虑参数间合理的先验信息,其解的精度得到显著提升。     

Numerical Treatment of Small Stellar Systems with Binaries

The use of regularization methods based on the Kustaanheimo-Stiefel transformation (KS) is reviewed. The history of the development of such methods is summarized and anecdotal information about the related events is told. Details of the multi-particle regularization methods are given, including the most recent developments. This revised version was published online in August 2006 with corrections to the Cover Date.     

Inversion and III-Posed Problem Solutions in Atmospheric Remote Sensing

With the swift advances in earth observation,satellite remote sensing and application of atmospheric radiation theory have been developed in the past decades,atmospheric sensing inversion with its algorithms is getting more and more importance.It is known that since a remote sensing equation falls into an integral equation of the first kind,thus leading to the fact that it is ill-posed and particularly the solution is unsteady,tremendous difficulties arise from the retrieval.This paper will present a simple review on the inversion techniques with some necessary remarks,before introducing the successful efforts with respect to such equations and the encouraging solutions achieved in recent decades by researchers of the world.     

改进型BP神经网络对民勤绿洲地下水位的模拟预测

以具有代表性的民勤绿洲为研究对象,以Matlab7.0为工作平台,对沙漠绿洲地下水埋深预测的三层前馈神经网络（BP神经网络）进行了改进。输入端因子选取民勤绿洲逐月灌溉量、红崖山水库下泄水量、月降水量、月蒸发量（20 cm）、月平均气温、时间序列6项,输出因子为民勤绿洲地下水位。通过在模型的输入层增加时间序列引导因子的方法使BP神经网络对输入端数据具备时间敏感性;通过Levenberg-Marquardt算法使网络误差最小化,并配合Bayesian正则化使网络的误差平方和、网络权重以及阈值平方和实现最优组合,最后使用相关系数、相对误差、效率系数等指标对模型的模拟结果进行检验。结果表明,通过以上一系列改进可以有效提高模型的模拟精度,增强模型的稳定性,并使模型具有良好的“泛化性”。