Regularization of the solution of one class of inverse problems of remote atmospheric measurements

A regularized inversion method for a certain narrow class of atmospheric measurement problems is proposed. An example of the use of the method to determine the components of a multicomponent continuum in the medium ir-band is given.     

Aspects of the use of orthogonal basis functions in the element‐free Galerkin method

The element‐free Galerkin (EFG) method is probably the most widely used meshless method at present. In the EFG method, shape functions are derived from a moving least‐squares approximation using a polynomial basis, a calculation involving the inversion of a small matrix. A new implementation of the EFG method was published soon after the original where an alternative approach using an orthogonal basis was proposed to avoid matrix inversion in the formulation of the shape functions. In this paper we revisit this topic and show that the difficulties associated with the use of a polynomial basis remain present in the orthogonal case. We also show that certain terms in the derivative expressions are omitted in the new implementation of the EFG, which can lead to errors. Finally, we propose a new approach that avoids inversion while maintaining accuracy. Copyright © 2009 John Wiley & Sons, Ltd.     

用SIR-C航天飞机双频极化干涉雷达估计植被高度的方法研究

基于重复轨道航天飞机SIR—C的L和C波段极化干涉雷达数据,提出了一种将三阶段反演方法(Three—Stage Inversion)和ESPRIT(Estimation of Signal Parameters via Rotational Invariance Techniques)算法相结合的新的相位基植被高度估计方法。首先,基于L波段极化干涉数据,用三阶段反演方法获取植被覆盖地表下地形有效散射中心的相位;接着,基于c波段极化干涉数据,用ESPRIT算法估计植被冠层有效散射中心的相位;最后,对二者的相位差进行相位到高度的转换得到植被的高度。根据研究区域的实测林相数据,对该算法估计的植被高度结果进行了比较和验证,结果表明：该方法具有足够高的植被高度估计精度,如果能得到P和X波段的双频极化干涉雷达数据,该方法估计植被高度的精度将会得到进一步的提高。     

Correction of instrument line shape in Fourier transform spectrometry using matrix inversion

A novel matrix inversion approach is proposed to correct several contributions to the instrument line shape (ILS) of a Fourier transform spectrometer. The matrix formalism for the ILS is first quickly reviewed. Formal inversion of the ILS matrix is next discussed, along with its limitations. The stability of the inversion process for large field-of view- (FOV-) limited and highly off-axis line shapes is investigated. The effect of inversion on the noise that is present in the spectrum is also presented. Use of classical iterative inversion methods, coupled with efficient synthesis algorithms, is proposed as a way to drastically speed up the inversion process. The method is applied to correct HBr spectra obtained from a laboratory spectrometer that has an adjustable field of view. ILSS from six FOVs are brought to the same spectral axis and to the same ideal sinc shape.     

负跃层条件下浅海海底单参数反演技术

海底参数反演是获取海底声学特性一种经济高效的办法。近年来,课题组提出用小掠射角下海底反射损失随掠射角的变化率F_dB（dB·rad^-1）作为描述海底的单参数,建立了浅海均匀水层和负跃层水文条件下的海底单参数模型。负跃层单参数模型的建立,为海底单参数反演提供了新的设计思路。文章基于浅海负跃层海底单参数模型,设计海底单参数地声反演方法。首先对负跃层水文条件下浅海海底单参数模型进行简单的描述和介绍;然后在浅海负跃层单参数模型基础上,利用声传播损失对海底单参数进行反演;最后利用实验数据对反演方法的有效性进行了验证。     

Application of a modified collocation method in the theory of antennae

Collocation on a step basis, which is one of the most widely used methods in the theory of antennae, is insufficiently effective in solving excitation problems. A more effective modified method, which is based on analytical inversion of the main part of the hypersingular operator, is proposed.     

An approximate laplace transform inversion using exponential series representation

A numerical Laplace transform inversion technique is described, which is a modification of the inversion method using an exponential series representation. By adding an auxiliary function and using Erdélyi's inversion formula, the proposed technique provides the inverse approximation with improved accuracy near t = 0. Numerical illustrations shows that this procedure also works in cases when the original method of schapery fails to give satisfactory results.     

不依赖于子波的声波多尺度全波形反演方法

伴随着油气勘探目标复杂性的日益增加,对速度场建模和成像方法都提出了更高的要求。声波介质下的全波形反演方法是现阶段精度最高的速度场建模方法,在复杂介质速度场建模方面具有一定的应用前景。然而,传统的波形反演方法对地震子波的准确性具有较高的依赖性,并且在地震数据主频较高的情况下难以得到有效的反演结果。为此,基于声波方程,通过修改维纳滤波器,通过利用参考道构建滤波器,提出了一种不依赖于子波的全波形反演方法,能够有效避免波形反演对子波的依赖性。由于滤波器目标子波选取较为自由,该方法可以与多尺度反演策略有机结合,实现频率由低到高的递进反演,能够进一步提高反演的稳定性。理论分析和模型试算证明,采用不依赖于子波的多尺度反演方法能够有效避免子波提取问题,在子波错误的情况下可以得到准确的反演结果,并且能够在保证反演稳定性的基础上提高反演精度,反演效果优于传统的波形反演方法。     

基于周期统计平均的结构动力复合反演研究

研究了输入未确知条件下的参数识别、荷载反演问题。根据激励的周期特性，运用统计平均的思想，构造出一类时域识别反演算法。数值算例表明，该算法的参数识别精度高，且具有很强的噪声适应能力和初参数选择鲁捧性。将本算法与全量补偿算法有机会结合，可更好地解决在旋转动力设备周期激振力作用下的结构参数识别及荷载反演问题。     

A versatile analytical expression for the inverse Abel transform applied to experimental data with noise

A method for reconstruction of radially distributed plasma emission coefficients from projections with noise is proposed. The method represents the projections based on overlapping piecewise polynomial least squares fitting to take the inversion. Parameters that affect the inversion accuracy are analyzed and discussed in detail. Results for profiles with various shapes are presented and compared with those obtained with other methods. It is shown that for data with different numbers of points and different levels of noise, our method is more accurate and yields markedly better results for very sparse data. In addition, excellent results have been obtained from experimental intensities of an arc plasma without filtering of noise.     

Application of evolution strategies for the solution of an inverse problem in near-field optics

We introduce an inversion procedure for the characterization of a nanostructure from near-field intensity data. The method proposed is based on heuristic arguments and makes use of evolution strategies for the solution of the inverse problem as a nonlinear constrained-optimization problem. By means of some examples we illustrate the performance of our inversion method. We also discuss its possibilities and potential applications.     

Discrete numerical solution of the generalized boussinesq problem

A family of stable algorithms for integration in time of the spatially discretized generalized Boussinesq equation is presented. In space, the finite element approximation is employed enabling arbitrary layout and variable physical properties. Furthermore, the proposed spatial–temporal discretization neither involves inversion of non-diagonal matrices of large scale nor even their storage. The method is theoretically investigated and numerically tested. Comparison is made with known results.     

A gradient computational procedure for the solution of large problems arising from the finite element discretization method

A computational procedure based on gradient iterative techniques is proposed for the solution of large problems to which the finite element method is applicable. In linear problems the procedure can be used either for solving the set of algebraic equations or for the complete inversion of the matrix of coefficients. Special attention is focused on the practical aspects of the procedure concerning its realization on the digital computer.     

A new hybrid boundary node method based on Taylor expansion and the Shepard interpolation method

A novel meshless method based on the Shepard and Taylor interpolation method (STIM) and the hybrid boundary node method (HBNM) is proposed. Based on the Shepard interpolation method and Taylor expansion, the STIM is developed to construct the shape function of the HBNM. In the STIM, the Shepard shape function is used as the basic function, which is the zero‐level shape function, and the high‐power basic functions are constructed through Taylor expansion. Four advantages of the STIM are the interpolation property, the arbitrarily high‐order consistency, the absence of inversion for the whole process of shape function construction, and the low computational expense. These properties are desirable in the implementation of meshless methods. By combining the STIM and the HBNM, a much more effective meshless method is proposed to solve the elasticity problems. Compared with the traditional HBNM, the STIM can improve accuracy because of the use of high‐power basic functions and can also improve the computational efficiency because there is no inversion for the shape function construction process. Numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

New results on electromagnetic imaging based on the inversion of synthetic and measured scattered-field data

A new approach for the inversion of synthetic and measured scattered data is proposed in this paper. The approach is based on an iterative technique in which the nonlinear equations of the inverse-scattering problem are solved within the pth-order Born approximation. A regularization scheme based on an inexact-Newton method is applied. Several numerical simulations and experimental results are reported. Multiple separated dielectric cylinders are localized and reconstructed in a noisy environment.     

Identification of material constants for piezoelectric transformers by three-dimensional,finite-element method and a design-sensitivity method

In this paper, an inversion scheme for piezoelectric constants of piezoelectric transformers is proposed. The impedance of piezoelectric transducers is calculated using a three-dimensional finite element method. The validity of this is confirmed experimentally. The effects of material coefficients on piezoelectric transformers are investigated numerically. Six material coefficient variables for piezoelectric transformers were selected, and a design sensitivity method was adopted as an inversion scheme. The validity of the proposed method was confirmed by step-up ratio calculations. The proposed method is applied to the analysis of a sample piezoelectric transformer, and its resonance characteristics are obtained by numerically combined equivalent circuit method.     

Multiply scattered aerosol lidar returns: inversion method and comparison with in situ measurements

A novel aerosol lidar inversion method based on the use of multiple-scattering contributions measured by a multiple-field-of-view receiver is proposed. The method requires assumptions that restrict applications to aerosol particles large enough to give rise to measurable multiple scattering and depends on parameters that must be specified empirically but that have an uncertainty range of much less than the boundary value and the backscatter-to-extinction ratio of the conventional single-scattering inversion methods. The proposed method is applied to cloud measurements. The solutions obtained are the profiles of the scattering coefficient and the effective diameter of the cloud droplets. With mild assumptions on the form of the function, the full-size distribution is estimated at each range position from which the extinction coefficient at any visible and infrared wavelength and the liquid water content can be determined. Typical results on slant-path-integrated optical depth, vertical extinction profiles, and fluctuation statistics are compared with in situ data obtained in two field experiments. The inversion works well in all cases reported here, i.e., for water clouds at optical depths between ~0.1 and ~4.     

Inversion of low-angle elastic light-scattering data with a new method devised by modification of the Chahine algorithm

A new inversion method, devised by modification of the nonlinear iterative method originally proposed by Chahine [J. Opt. Soc. Am. 58, 1634 (1968)] is applied to the inversion of low-angle elastic light-scattering data. The algorithm was tested by computer simulations carried out within the wave-vector range 2.5 x 10(2) -2.5 x 10(4) cm(-1). The particle-size distributions were recovered in the 0.70-77-mum range of radii. Compared with the original method of Chahine, this algorithm is much more stable and reliable with respect to random noise, improves the overall reliability of the fitting, and allows both number and weight particle-size distributions to be retrieved accurately. When the performances of the method are investigated with respect to the noise, the results of the simulations show that the particle-size distributions can be recovered accurately up to noise levels of several rms percent.     

Stable inversion method for a polarized-lidar: analysis and simulation

A new inversion inhomogeneous atmosphere (IA) method that is more stable than Fernald's method for two-component (molecule and aerosol) scattering analysis of polarized Mie lidar signals is proposed and examined. The backscattering coefficient and the extinction-to-backscattering ratio (EBR) can be calculated for specified regions at which the depolarization ratio is less than that of molecule without further assumptions. The inversion procedure can be extended to both inward stepwise and outward stepwise integration algorithms. Simulation results indicate that a higher precision was achieved with the IA method than with Fernald's method in terms of error and random noise in estimating boundary value and EBR. Experimental results were also better with the IA method than with Fernald's method.     

Modified Fourier-Hankel method based on analysis of errors in Abel inversion using Fourier transform techniques

Errors in discrete Abel inversion methods using Fourier transform techniques have been analyzed. The Fourier expansion method is very accurate but sensitive to noise. The Fourier-Hankel method has a significant systematic negative deviation, which increases with the radius; inversion error of the method can be reduced by adjusting the value of a factor. With a decrease of the factor both methods show a noise filtering property. Based on the analysis, a modified Fourier-Hankel method that is accurate, computationally efficient, and has the ability to filter noise in the inversion process is proposed for applying to experimental data.