一类具有等式约束的带乘性噪声系统的最优滤波算法

针对动态数据处理领域观测方程中存在乘性噪声的情况,提出在乘性噪声系统中状态附等式约束的一套滤波算法。该算法首先通过把观测向量进行扩维,然后基于投影定理进行滤波求解得到基于线性最小方差的最优滤波算法。通过与基于最优化理论的方法求解得到的算法进行对比分析及仿真对比验证了该算法的有效性。     

平面六边形格网上格点多边形的面积计算方法

全球离散格网系统是一种新型的全球多尺度空间数据模型,相关问题的研究已引起学术界的广泛关注并已取得可喜进展。其中,格网量测体系的建立是当前学术界的研究难点,同时也是格网实用化必须解决的核心问题。文中将平面六边形格网上任意覆盖区域抽象为"格点多边形",推导并证明了其面积计算公式,通过对比算例验证了结论的正确性和优越性。     

空间直角坐标与大地坐标转换的拉格朗日反演方法

以拉格朗日反演理论为基础,导出空间直角坐标向大地坐标转换的一种新的直接解法：该方法将归化纬度的正弦函数sinμ表达为以空间直角坐标（X,Y,Z）为基础的相关变量的多项式     

双圆盾构穿越下立交结构的流-固耦合数值模拟

依托上海轨道交通M10线双圆盾构区间隧道工程,对自由场下双圆盾构隧道施工力学行为进行三维有限差分数值模拟,分析了盾构施工地表沉降及超孔隙水压力的特征、量值与范围,并与监测结果进行对比,以得到能够反映施工技术水平的模拟施工参数。将该模拟施工参数应用于下立交下双圆盾构的推进,用以预测盾构掘进对下立交底板的影响。研究结果表明,在三面封闭的条件下,盾构施工引起的正超孔压很难向外界消散、负超孔压也很难得到外界水位的补给;在开挖面前方,底板受到挤压力,且挤压力主要由超孔隙水压力组成;沿横向方向,作用在下立交底板下的超孔隙水压力分布较均匀,而土体颗粒的挤压力则主要分布在其中线附近;下立交结构的刚性位移是引起底板沉降的主要原因,底板变形引起的沉降较小,变形最大值在盾尾脱离时取得。     

Research Note: Internal/external seismic source wavefield separation and cancellation

A compact representation is obtained for the separation of a scalar wavefield on a closed surface into parts due to internal and external sources. The formula assumes that the total field and its gradients are known on the surface, as is the exact Green function of the medium. The derivation involves four rather straightforward applications of Green’s theorem or the representation theorem, though it is a remarkable result in that waves from either source that traverse the boundary many times are appropriately separated. The intermediate results at the four steps of the derivation also shed light on the possibility of acoustic shielding from unwanted sources without knowledge of the Green function for the medium.     

基于Hoek-Brown破坏准则的浅埋条形锚板抗拔力上限分析

现有的锚板极限承载力研究大多是采用线性或非线性Mohr-Coulomb破坏准则在砂质地基中进行的,然而Mohr-Coulomb破坏准则并不适合分析岩质地基中的抗拔结构。采用Hoek-Brown破坏准则构建了一个曲线型的破坏机制,根据极限分析上限定理求出了条形锚板抗拔力的表达式。通过变分计算,得到了极限状态下条形锚板的抗拔力和岩体破裂面的上限解。为了证明所采用方法的有效性,当材料参数B =1时,采用与Mohr-Coulomb破坏准则等效的土体参数,计算了曲线型破坏机制下条形锚板的极限抗拔力,并与已有计算结果进行了比较。结果表明,采用曲线型破坏机制得到的锚板极限抗拔力与直线型多块体破坏机制的结果基本一致,证明了所采用的曲线形破坏机制是正确的。参数研究表明：在其他参数不变的情况下,锚板极限抗拔力和破坏面都随岩体参数B的增大而减小。     

On the existence of characteristic shapes for desert dunes

The existence of an angle of repose for sand implies that, in any given wind regime, there is at least one configuration of sand dunes which will not be altered by that wind regime. The existence of implies that the land forms constitute a convex compact subset of a Banach space, and the result then follows from Shauder's theorem.     

Construction of ray synthetic seismograms using interpolation of travel times and ray amplitudes

The seismic wave field, in its high-frequency asymptotic approximation, can be interpolated from a low- to a high-resolution spatial grid of receivers and, possibly, point sources by interpolating the eikonal (travel time) and the amplitude. These quantities can be considered as functions of position only. The travel time and the amplitude are assumed to vary in space only slowly, otherwise the validity conditions of the theory behind would be violated. Relatively coarse spatial sampling is then usually sufficient to obtain their reasonable interpolation. The interpolation is performed in 2-D models of different complexity. The interpolation geometry is either 1-D, 2-D, or 3-D according to the source-receiver distribution. Several interpolation methods are applied: the Fourier interpolation based on the sampling theorem, the linear interpolation, and the interpolation by means of the paraxial approximation. These techniques, based on completely different concepts, are tested by comparing their results with a reference ray-theory solution computed for gathers and grids with fine sampling. The paraxial method holds up as the most efficient and accurate in evaluating travel times from all investigated techniques. However, it is not suitable for approximation of amplitudes, for which the linear interpolation has proved to be universal and accurate enough to provide results acceptable for many seismological applications.     

三维非静力平衡大气中平行切变流上重力内波的不稳定及半椭圆定理

本文应用守恒型非弹性模式研究了三维非静力平衡大气中平行切变流上重力内波的不稳定，推广了Miles定理和半圆定理，得到了有限深度气层的半椭圆定理。该定理指出不稳定波的复波速被限制在相速复平面上一个内接于霍华德（Howard）半圆的半椭圆内。该半椭圆长轴重合于半圆的直径，而短轴则取决于最小Ri数、波长、波宽等因素。     

视电阻率对模型电阻率的偏导数矩阵计算方法

按Tripp et al.(1984)提出的理论，给出了一种视电阻率对模型电阻率的偏导数矩阵简便计算方法，它的核心是互换定理。只要得到所有供电和测量电极节点分别供单位电流时各有限元网格节点上的电位，通过线性组合就可得到视电阻率对模型电阻率的偏导数。