反演问题

P-wave AVO inversion is a complicated constrained nonlinear optimization problem, which is better achieved using global optimization methods.

AVO反演是一个非线性优化问题，因此采用非线性的反演方法，其解空间的性质、状态应优于线性反演方法。

A new non-linear quadratic programming Bayesian prestack three-terms inversion method is developed; Firstly, this method is based on Bayesian parameter estimation theory, Gaussian distribution is used for likelihood function and modified Cauchy distribution is used for prior distribution; Secondly, covariance matrix is used to describe the degree of correlation between the parameters; rock physics relations are used to constrain the inversion results; at last, this method is transformed into non-linear quadratic programming problem, and inversion results are acquired under several constraints.

本文提出了一种基于非线性二次规划的叠前三参数反演方法。首先基于贝叶斯参数估计理论，假设似然函数服从高斯分布，并使待反演的参数服从于改进的Cauchy分布，从而提高了反演结果的分辨率；其次用协方差矩阵来描述参数间的相关程度，进一步提高了反演结果的稳定性；最后将问题转化为一个非线性二次规划的求解问题，并在多种约束下得到问题的解。

The inversion of particle size distribution from measured data of light scattering, as a typical inverse problem, has been studied by many reseachers and solved by several numerical methods. Among which, direct Tikhonov regularization method with Morozov discrepancy principle, is often used to overcome the ill-posedness linked with the Fredholm integral equation of the first kind, so the stability of inversion has been heightened. But there has much room for improvement of the inversion accuaracy, especially for the double-peak problems.

由测量得到的散射光强数据来反演颗粒粒径分布是一个典型的反问题，它已为许多的学者所研究，并用多种数值方法来求解，其中带Morozov偏差原理的直接Tikhonov正则化方法经常被采用，以便用来克服与上述反演相联系的第一类Fredholm积分方程的不适定性带来的困难，因而反演的精度得到了提高；然而仍有许多改进的余地，特别是对于所谓"双峰"问题更是如此。

Based on the principle of inversion analysis , applications of inversion analysis in welding field including material properties, heat source model, boundary conditions were introduced.

在阐述了反演分析原理的基础上，介绍了国内外焊接领域，包括材料性能，热源模型，边界条件等问题中反演分析的应用，及反演分析各种算法的原理及特点。

Aimed at the zone of interest in the Q 3D seismic survey, which is characterized by thin sand body as well as the quickly lateral alternation, three inversion methods of Strata software are put into use, including the 3-D wave impedance inversion, the well log parameter inversion, and multi\|attribute gamma inversion.

针对Q三维地震工区目的层砂体薄、横向变化快的特点，在Strata软件上相继采用了三维波阻抗反演、测井参数反演和多属性伽马反演3种反演方法进行试验，最终确定了多属性伽马反演方法能较好地解决利用地震资料进行储层预测的一些问题，从而为工区勘探开发提供了可靠的高精度反演资料。

5Topological inversion is applied to solve the transition problems from topological graph to practical gear train mechanisms. Four variant directions of topological inversion is noted and topological inversion chart library is founded.

5运用拓扑反演解决了由轮系拓扑图过渡到实际轮系机构的转换问题，指出拓扑反演的四个变化方向，建立了周转轮系的拓扑反演图库。

In this project, we have deduced the joint inversion model of geodetic data, seismic data and geological data considering about their weight ratio; presented Bayes-iterative search inversion algorithm which improved on the traditional Bayes algorithm and strengthen the stability of inversion solutions; enriched and developed geodetic joint inversion theory and method of tectonic stress field; joint with geodetic, seismic, geological and geophysical data, we have inverted the temporal and spatial variation characteristics of crustal deformation of active tectonic blocks in North China and the present-day cruatal movement and strain-stress field by FEM, DDA and bi-cubic spline function fit method; especial for the crustal deformation result in some typical areas, we have presented geodynamical interpretation and done some seismic dangerous estimations.

大地测量联合反演构造应力场属于大地测量与地球动力学和地震学的交叉研究领域，主要内容是研究用大地测量地壳运动监测数据定量研究地壳运动和变形的动力学问题及分析预测地震，本项目推导了兼顾权比确定的大地测量、地震和地质三类数据的联合反演模型；提出贝叶斯-轮回搜索反演算法，改进传统的贝叶斯方法，改善反演解的稳定性；丰富、发展了大地测量反演构造应力场理论及方法；联合大地测量、地震、地质、地球物理数据采用有限单元法、块体不连续变形分析法和双三次样条函数拟合方法反演分析了华北地区活动地块运动时空变化特征以及中国大陆现今地壳运动与应变-应力场，对典型地区地表形变结果进行地球动力学解释并进行地震危险性估计。

It is very important in improving the accuracy of demarcating the reservoir boundaries. Also 3D inversion of borehole vertical bipole will base on it.

它对提高井中垂直双极源圈定储层范围的精度有着非常重要的意义，同时也为井中垂直双极源三维反演问题奠定了基础。

For the coarsest scale there are fewer local minima and further apart from each other. Thus, at the coarsest scale linearized methods can get closer to the neighborhood of the global minimum, and its final result is implemented as an initial model of the inverse problem of the second coarsest scale.

大尺度上反问题的目标函数局部极小少而且互相分得很开，因而用常规的反演方法可以较容易地收敛到全局极小的邻域内；将大尺度的解当作次一级尺度反问题的初始模型，再进行反演。

Mathematical models for timelapse seismic inversion are designed, which depend on the prospecting time. On the basis of this kind of models, the globally convergent continuous and recursive algorithms are constructed.

针对时间推移地震反演问题建立了依赖勘探时间的数学模型，并在此基础上设计了全局收敛的连续型及逐次递归算法。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。