基于共轭梯度搜索的病态问题处理方法

在最小二乘平差准则基础上,把病态平差问题转化为无约束的二次规划问题,并利用优化理论分析病态对平差解的影响。通过共轭梯度搜索算法在可行域中寻找最优步长因子,自动寻找最速下降方向,并给出迭代初值的设置方法。分析近似计算中病态问题与局部最优解的关系,讨论局部最优解的快速迭代方法,并通过实例验证算法的有效性,计算迭代的速度。由于整个过程没有对法方程系数矩阵进行求逆计算,该算法可用于处理大规模系数矩阵高病态的平差问题。     

海量卫星重力梯度观测数据确定地球重力位模型的数值方法

基于空域最小二乘法,对卫星重力梯度数据确定地球重力场中的Cholesky分解法、预条件共轭梯度法以及OpenMP并行算法3种数值方法进行比较与分析。研究表明,在计算机硬件资源有限的情况下,传统的Cholesky分解法已经无法满足求解要求;预条件共轭梯度法的求解效率较之Cholesky分解法有改进,但其以损失小量精度为代价;OpenMP并行算法在不损失求解精度的条件下,可提高求解的效率。     

高精度曲面建模的一种快速算法

 高精度曲面建模(HASM)是一种全新的曲面建模方法,其整个过程可分为偏微分方程的离散、采样方程建立和代数方程组求解3个阶段。目前所采用的求解对称正定方程组的方法主要是共轭梯度法。为了解决HASM的计算速度问题,本文给出了2种新的预处理共轭梯度算法,分别为不完全Cholesky分解共轭梯度法和对称逐步超松弛预处理共轭梯度法。实验表明,不完全Cholesky分解共轭梯度法收敛速度最快,且这2种预处理方法均比其他方法具有更快的收敛速度。     

Full waveform inversion based on improved MLQN method

Full waveform inversion( FWI) is a challenging data-fitting procedure between model wave field value and theoretical wave field value. The essence of FWI is an optimization problem,and therefore,it is important to study optimization method. The study is based on conventional Memoryless quasi-Newton( MLQN)method. Because the Conjugate Gradient method has ultra linear convergence,the authors propose a method by using Fletcher-Reeves( FR) conjugate gradient information to improve the search direction of the conventional MLQN method. The improved MLQN method not only includes the gradient information and model information,but also contains conjugate gradient information. And it does not increase the amount of calculation during every iterative process. Numerical experiment shows that compared with conventional MLQN method,the improved MLQN method can guarantee the computational efficiency and improve the inversion precision.     

卫星重力梯度数据的向下延拓

在利用空域法恢复地球重力场时,向下延拓是卫星重力梯度数据预处理必不可少的步骤。将航空重力数据处理中的球内Dirichlet法、泊松积分迭代法、谱方法引入卫星重力梯度数据的向下延拓中,建立了相应的数学模型,解决了传统的球内Dirichlet问题存在的数值矛盾,利用模拟的卫星重力梯度数据对3种方法的向下延拓效果进行了分析和讨论。结果表明：当延拓距离为5 km时,谱方法所获得的延拓结果精度最高,其次为球内Dirichlet法,泊松积分迭代法精度最差;当延拓距离是250 km时,泊松积分迭代法的精度最好,其次为谱方法,球内Dirichlet法的精度最差。     

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中国似大地水准面模型CQG2000的梯度分析

为满足高程转换需要,计算CQG2000模型的梯度信息,分析其在全国范围空间域内的变化相关性。首先确定CQG2000的梯度模型;然后利用三阶反距离平方权差分方法计算CQG2000格网点的梯度数值,推导梯度数值及方向上的误差;最后利用CQG2000的梯度信息分析全国高程异常变化趋势。结果表明,102°E以东地区的梯度数值较小、变化平缓,方位角方向为东向;102°E以西地区梯度数值较大,局部变化剧烈,方位角局部存在明显的趋势性变化;在新疆、青藏等西部地区存在多个梯度扩散和会聚中心,梯度变化较大,其中梯度最大值（0.625 m/(′)）位于墨脱附近。     

岩层断裂的最大转动梯度准则及其在构造地质中的应用

认为微观转动不协调是产生断裂的原因。在现代有限变形力学Ｓ（应变）－Ｒ（转动）分解定理基础上提出了断裂扩展的最大转动梯度准则，可直接确定断裂产生的位置和扩展方向。初步应用该准则对雁行裂纹的形成过程进行了数值模拟。     

顾及地形坡度的非线性最小二乘相位解缠

InSAR相位解缠是利用干涉合成孔径雷达(InSAR)数据,提取数字高程模型,进行精确差分干涉测量的关键技术之一。然而缠绕的差分相位信息在地形陡峭或者坡度变化较大区域的解缠结果会有较大的误差传递的问题,针对此问题将干涉图中的地形坡度表示为距离向和方位向的局部相位频率,利用局部相位频率估计地形坡度和推导缠绕相位梯度概率密度函数(PG-PDF)参数模型,并将参数模型作为非线性最小二乘相位解缠模型约束条件,平滑不满足要求的缠绕相位梯度,经过迭代求解得到的解缠结果可以在消除噪声的同时减少地形因素的欠采样对相位解缠结果的影响,提高相位解缠的精度。最后,利用欧空局ENVISAT ASAR卫星获取的干涉数据进行实验,验证了算法在解缠精度和对地形的适应性方面优于直接加权的相位解缠算法,在频域下顾及地形的方法能有效克服LS对于相位坡度欠估计的缺点,具有较高的精度和稳定性,能够有效地考虑地形坡度的影响,抑制误差传递。     

Joint inversion of magnetotelluric and fullwaveform seismic data based on alternating cross-gradient structural constraints

Magnetotelluric(MT)inversion and seismic inversion are important methods for the interpretation of subsurface exploration data,but separate inversion of MT and seismic produces ambiguous and non-unique results due to various factors.In order to achieve accurate results,the authors propose a joint inversion method of two-dimensional MT and seismic data in the frequency domain.The finite element method is used for numerical simulation of electromagnetic data in the forward modelling,and the Gauss-Newton method is used for the inversion.The 9-point-finite-difference method is used to solve the seismic wave field in the acoustic wave equation,and the inverse problem of seismic data is solved by full waveform inversion with a conjugate gradient,a simple and fast method.Cross gradient functions are used to provide constraint structure between resistivity and velocity parameters to carry out the joint inversion.The joint inversion algorithm is tested by double-rectangular model synthesis data,and the accuracy of the algorithm is verified.The results show that the joint inversion results are better than those from separate inversion.The algorithm is applied to a geophysical model of a metalliferous deposit in Jinchuan and is compared with the separate inversion results.It shows that the results obtained with joint inversion are much closer to the real model.     

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Development of a preliminary slope stability calculation method based on internal horizontal displacements

This paper proposes a horizontal displacement-based approach to determine the potential slip surface of the slope. Firstly, a group of in-situ inclinometers with an appropriate spacing in the horizontal direction is located in the model slope. The equation of horizontal displacement with time for each in-situ inclinometer is fitted during the whole simulation process. Furthermore, the intersection of each inclinometer with potential slip surface is determined by using an optimization model. The slip surface can be obtained by using least square fitting method. Finally, the feasibility and accuracy of the method are validated by a series of numerical simulations. It is noted that the optimization model taking the maximum value of displacement increment gradient as an objective has higher accuracy when compared with other optimization models. This method employed in this study provides a preliminary approach to determine the real-time slope stability based on displacement, which can also be measured by using conventional instruments on site.     

A LAYERED NUMERICAL MODEL FOR SIMULATING THE GENERATION AND PROPAGAYION OF INTERNAL TIDES OVER CONTINENTAL SLOPE Ⅰ.MODEL DESIGN

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A LAYERED NUMERICAL MODEL FOR SIMULATING THE GENERATION AND PROPAGATION OF INTERNAL TIDES OVER CONTINENTAL SLOPE I. MODEL DESIGN

A layered three-dimensional nonlinear numerical model was constructed to simulate the generation and propagation of internal tides over the continental slope. The simulation was split into external mode computation (EMC) and internal mode computation (IMC) to minimize the computational load. IMC was carried out once after EMC was implemented N times. As to EMC, a semi-implicit numerical scheme was applied in such a way that the pressure gradient terms and the velocity divergence terms were discretized semi-implicitly, but the other terms were discretized explicitly. Eulerian-Lagrangian explicit discretization was applied to the convective terms simultaneously. As a result, the stability of EMC did not depend on the wave celerity and time step was not limited by the CFL condition. More than that, use of the conjugate gradient accelerated Jacobi method further improved the computational efficiency of the model.     

Deep-seated structure and gold content of Russia and China contiguous territories

On the contiguous territories of southeastern Russia and northeastern China,many gold-bearing areas are conjugate in space with the gradient zones of the gravity field.Large gold-ore districts,defining in many respects the metallogenic signature of the region,are located on the joints of differently oriented gradient zones.In the best-studied districts,the Precambrian protrusions,staged distribution of magmatic chambers (by vertical) above the Mohorovicic discontinuity and restriction to the peripheral parts of intrusive massifs have been recognized.Different-type gold deposits in the studied ore-placer districts and nodes are often located on the areas of joint of the granitoid massifs and subvolcanic bodies with depressions.Availability of areals of metasomatic alterations of rocks,placers,and ore occurrences of precious metals on such but poorly studied areas can serve as the basis for the revision and detailed forecasting-prospecting works to develop the mineral-raw material base of the region for precious metals.     

A layered numerical model for simulating the generation and propagation of internal tides over continental slope

A layered three-dimensional nonlinear numerical model was constructed to simulate the generation and propagation of internal tides over the continental slope. The simulation was split into external mode computation (EMC) and internal mode computation (IMC) to minimize the computational load. IMC was carried out once after EMC was implemented N times. As to EMC, a semi-implicit numerical scheme was applied in such a way that the pressure gradient terms and the velocity divergence terms were discretized semi-implicitly, but the other terms were discretized explicitly. Eulerian-Lagrangian explicit discretization was applied to the convective terms simultaneously. As a result, the stability of EMC did not depend on the wave celerity and time step was not limited by the CFL condition. More than that, use of the conjugate gradient accelerated Jacobi method further improved the computational efficiency of the model. Contribution No. 3588 from the Institute of Oceanology, Chinese Academy of Sciences. Project 49676275 supported by NSFC and National Special Research Program 97-925-05-02.     

重力异常反映的郯庐带中南段构造边界与应力场

为解决传统基于重力场数据一阶导数定义的总水平导数和解析信号振幅存在无法均衡深浅异常振幅的问题,应用重力全张量梯度数据,提出改进的倾斜导数地质体边界识别方法NTD_M。经模型验证,NTD_M在收敛性、抑噪性和边界识别精度方面均有提升。利用NTD_M将郯庐带中南段及邻区划分为14个边界较为清晰的构造单元,借助垂线偏差数据对郯庐带中南段的构造应力场和壳幔密度差进行反演。结果显示,二者在水平方向上存在显著差异,在空间上显著相关,构造应力最大差异值约为16 MPa,壳幔密度差约为0.2 g/cm³,构造应力等值线密集处与构造单元划分的边界以及地震分布情况对应较好。郯庐带中段最大主应力方向为NEE-EW,南段主应力方向以EW-NWW为主,总体呈EW向,与震源机制解、地应力测量和GPS反演结果具有较好的一致性。     

Multi-component joint inversion of gravity gradient based on fast forward calculation

With the development of gravity gradient full tensor measurement technique , three-dimensional (3D) inversion based on gravity gradient tensor can provide more accurate information .But the forward calcula-tion of 3D full tensor sensitivity matrix is very time-consuming, which restricts its development and application . According to the symmetry of the kernel function , the authors reconstruct the underground source of geological body to avoid repeat computation of the same value , and work out the corresponding relationship between the re-sponse of geological body to the observation point and the response of reconstructed geological body to the obser -vation point .According to the relationship , rapid calculation of full tensor gravity sensitivity matrix can be achieved .The model calculation shows that this method can increase the speed of 30-45 times compared with the traditional calculation method .The sensitivity matrix is applied to the multi-component inversion of gravity gradient .The application of this method on the measured data provides the basis for the promotion of the meth -od.     

阳光直射、室内遮阴和涂保护层对恐龙化石风化影响的模拟研究

恐龙化石是地史时期保存在地层中的生物遗体或遗迹,一旦因自然原因或经人工发掘暴露地表后,则面临着严重的风化破坏问题,其中最严重的破坏因素主要是来自于太阳光照。化石长期遭受日照影响,周而复始,受热应力作用使化石表面产生裂缝,最终化石整体破碎。化石受热情况不同,包括阳光直射、室内遮阴和化石表面涂保护层三种不同情况下受热。该文从这三种不同情况出发,通过数值模型对化石及围岩对温度的敏感性进行分析研究。研究发现,阳光直射时温度梯度大小和温度梯度产生的温度应力远远大于室内遮阴和涂保护层后的温度梯度和温度应力;不涂保护层,化石部分温度梯度和温度梯度产生的温度应力大于涂保护层温度梯度和温度应力。