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By singular value decomposition method, we obtain inversion formula of the generalized Radon transform with weight function, and study the support and range condition of it.

用奇异值分解的方法对带权的广义Radon变换的反演作了讨论，得到了反演公式并对其支集定理和值域条件进行了研究。

The simulated data show that the time-lapse seismic AVO inversion is feasible. The formula derived in this paper is effective for discriminating the variations of oil saturation and effective pressure and for improving the precision of time-lapse seismic interpretation.

试验结果表明，在S油田进行时移地震AVO反演是可行的，推导的时移地震AVO反演计算方法能有效地分离油藏含油饱和度和有效压力的变化，真正实现对油藏的定量解释。

The one order differential model and convolutional model of impedance formula of amplitude versus offset inversion were established. Impedance inversion formula from AVO was derived based on Bayesian framework. Methods of using Huber function as prior model parameter distribution and covariance matrix from well log as constrains were developed. The P-wave impedance, S-wave impedance and density were calculated by the conjugate gradient algorithm.

为此建立了振幅随偏移距变化波阻抗反演公式的一阶差分模型及褶积模型，推导了基于贝叶斯理论的AVO波阻抗反演公式，给出了采用Huber分布作为模型参数的先验分布及测井数据的参数协方差矩阵作为约束条件的实现方法，并利用共轭梯度法计算了纵、横波阻抗及密度。

We establish the relation of inversion formulas among generalized Radon transform with known weight functions, the exponential Radon transform and classical Radon transform, furthermore obtain approximate inversion formula of the exponential Radon transform, the idea of approach above is applied to contour reconstruction and is generalized to n-dimentional euclidean space case. We discuss the support theorem, range condition of the exponential Radon transform.

本文建立了带权广义Radon变换、指数型Radon变换与古典Radon变换反演公式的关系，从而得到指数型Radon变换的近似反演公式，并且应用这种思想方法于轮廓重构，并将这一结果推广到任意维欧氏空间的情形；讨论了指数型Radon变换的支集定理及值域条件。

On the basis of introducing the spectroellipsometric principle,the inversion ofspectroscopic ellipsomtric data has been studied systematically and a novel dataanalysis method has been achieved.

本文在介绍椭圆偏振光谱原理的基础上，对椭偏数值反演进行了系统的研究，提出了独特的数据分析处理方法，并利用这种新颖的数值反演方法研究了几种新型材料的光学性质，取得了以下新结果。

Second, transient flow for vertical well and fractural well in porous media with arealanisotropy has been researched in this paper. The analytic solution for vertical well andsemi-analytic solution for vertical fractural well is developed by using image inversion,superposition principle, Laplace transformation, Fourier transformation, as well as theirinverse transforms, and storage and skin are taken into account. For vertical fractural well,influence of pressure and productivity is studied when the orientation of artificial fractureisn't in accordance with the direction of major permeability, it is fundamental to evaluatepotential and analyze well test data.

文中研究了平面各向异性储层不定常渗流问题，建立了平面各向异性储层交叉直线边界中一口直井渗流的数学模型，利用镜像反演、Laplace变换、Fouier变换及其反变换推导了不同边界条件下直井的Laplace空间解析解，考虑井储和表皮的影响，分析了曲线特征及影响因素的敏感性曲线；并运用影响椭圆及Duhamel叠加原理，推导了平面各向异性储层中垂直裂缝井的压力分布方程，考虑了水力裂缝与主渗透率轴成一定角度对压力及产能的影响，为垂直裂缝井的产能评价及试井分析提供依据。

Finally, seismic Rayleigh wave velocity inversion for P-SV wave S-statics isstudied, which is mainly including the flowing contents: the separation of Rayleighwave signals from seismic data, the pickup of Rayleigh dispersion curves, seismicRayleigh wave velocity inversion, and the principle and the processing flow ofresolving P-SV wave S-statics.

最后研究了地震瑞雷面波速度反演求取P-SV波横波静校正量，包括地震瑞雷波信号分离方法、地震瑞雷波频散曲线拾取方法、地震瑞雷波速度反演以及P-SV波横波静校正量求取方法和处理流程。

The forward problem is solved using a finite element technique in two dimensions that is a foundation of the inversion problem.

正演计算是电阻率反演成像的基础，本文从二维有限元基本理论出发，完成了高密度电法的二维有限元正演模拟程序，为后期多方法反演奠定了基础。

Next, the author discussed the application problem of the inversion, researched the controllable effects in inversion from different viewpoints.

可信度是反演中无法回避的问题，通常的反演需要做很多的试验才能获得可用的结果。

Sharp boundary inversion is a relatively difficult problem in magnetotelluric and other geophysical inversion, which has been studied by many researchers.

尖锐边界反演是大地电磁及其他地球物理反演中的一个较难解决的问题，目前有不少专家正对这方面进行研究。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。