基于k阶Voronoi多边形划分的k阶数据场拟合

讨论了k阶Voronoi图的离散点集的生成算法,挖掘了k阶Voronoi图的性质并加以证明;参照k阶Voronoi图的定义提出了k阶空间数据场的定义,并结合参考点利用其影响因子给出了低阶空间数据场的拟合函数通式;利用k阶Voronoi图对平面空间的平面区域最近邻近划分实现了对空间数据场的分割,从而将大量参考点集数据场化解为多个单元数据场的低阶拟合,有效地降低了数据场拟合的难度;提出了合并拟合和叠加拟合策略,实现了将单元数据场综合为完整的空间数据场。     

垂向非均匀介质中转换波转换点计算

转换点位置的计算是转换波资料处理中的一个关键问题. 本文提出了分别基于速度随深度线性变化、速度随垂直走时线性变化、慢度随深度线性变化和慢度随垂直走时线性变化四种等效垂向非均匀介质情况下转换点位置的计算方法. 研究了通过速度拟合、走时近似和相似系数谱三种方式选择合适的等效速度方法. 结合理论模型对非均匀介质转换点计算方法、渐进转换点计算方法、Thomsen近似公式和均匀介质解析计算方法的误差进行了分析,结果表明非均匀介质转换点计算方法能更准确地计算转换点位置.     

Chebyshev逼近滤波器在位场分离中的应用

在对经典FIR数字滤波器的设计方法进行研究的基础上,提出了一种可以用于位场分离的基于Chebyshev最佳一致逼近原理的FIR滤波器的设计方法.在理论模型实验中,采用基于Hanning窗的低通滤波器计算出的区域异常最大误差为6.266×10-6 m/s2 ,均方差为2.115×10-6 m/s2 ,最大百分比误差为22.2%,而且计算点在±9 km以外的误差均大于10.1%.而利用最佳一致逼近原理分离出的区域场和局部场与理论异常值拟合得较好,曲线基本重合.分离出的区域异常最大误差为3.101×10-6 m/s2 ,均方差为0.989×10-6 m/s2 ,最大百分比误差仅在边部的几个数据上,为7.76%,其余各点的误差均小于4.1%.实例检验中将该方法用于孙吴-嘉荫剖面布格重力异常场的分离,分离出的区域场中局部场残留少,分离彻底,效果较为理想.     

边界层内冷锋流场的动力学特征

文中求解了锋面存在时地转动量近似下的大气边界层运动方程,得到了边界层内冷锋流场的一些特征,如冷锋坡度随地转涡度增加而增加,随地转风速时间倾向的增加而增加,随沿锋面传播方向的热成风分量的减少而增加。而边界层内冷锋面上下的流场与锋面坡度、地转风及其时空变化特征有关,共同特点是在冷锋面高度以下有下滑运动,而其上有一层上滑运动区。     

计算最小走时和射线路径的界面网全局方法

用慢度分块均匀正方形模型将介质参数化,仅在正方形单元的边界上设置计算结点,这些结点构成界面网．根据Ｈｕｖｓｅｎｓ和Ｆｅｒｍａｔ原理,由不断扩张、收缩的波前点扫描代替波前面搜索,在波前点附近点的局部最小走时计算中对波前点之间的走时使用双曲线近似,通过比较确定最小走时和相应的次级源位置,记录在以界面网点位置为指针的３个一维数组中．借助这些数组通过向源搜索可计算任意点（包括界面网以外的点）上的全局最小走时和射线路径．这一方法不受介质慢度差异大小限制,占内存少,计算速度较快,适于走时反演和以Ｍａｓｌｏｖ射线理论为基础的波场计算．     

非线性模型线性近似的容许曲率

由于不同的非线性模型具有不同的非线性强度,使得一些非线性模型可以线性近似,而另一些则不能。本文介绍度量非线性强度的方法,提出判断非线性模型能否线性近似的数值标准——容许曲率。     

内蕴大地边值问题

提出内蕴大地边值问题,使得有可能利用重力场边界观测研究地球重力场的内蕴结构。文中构造了椭球问题的迭代逼近求解程式,并给出了具体解式。     

Observations and modelling of the travel time delay and leading negative phase of the 16 September 2015 Illapel,Chile tsunami

The systematic discrepancies in both tsunami arrival time and leading negative phase (LNP) were identified for the recent transoceanic tsunami on 16 September 2015 in Illapel, Chile by examining the wave characteristics from the tsunami records at 21 Deep-ocean Assessment and Reporting of Tsunami (DART) sites and 29 coastal tide gauge stations. The results revealed systematic travel time delay of as much as 22 min (approximately 1.7％ of the total travel time) relative to the simulated long waves from the 2015 Chilean tsunami. The delay discrepancy was found to increase with travel time. It was difficult to identify the LNP from the near-shore observation system due to the strong background noise, but the initial negative phase feature became more obvious as the tsunami propagated away from the source area in the deep ocean. We determined that the LNP for the Chilean tsunami had an average duration of 33 min, which was close to the dominant period of the tsunami source. Most of the amplitude ratios to the first elevation phase were approximately 40％, with the largest equivalent to the first positive phase amplitude. We performed numerical analyses by applying the corrected long wave model, which accounted for the effects of seawater density stratification due to compressibility, self-attraction and loading (SAL) of the earth, and wave dispersion compared with observed tsunami waveforms. We attempted to accurately calculate the arrival time and LNP, and to understand how much of a role the physical mechanism played in the discrepancies for the moderate transoceanic tsunami event. The mainly focus of the study is to quantitatively evaluate the contribution of each secondary physical effect to the systematic discrepancies using the corrected shallow water model. Taking all of these effects into consideration, our results demonstrated good agreement between the observed and simulated waveforms. We can conclude that the corrected shallow water model can reduce the tsunami propagation speed and reproduce the LNP, which is observed for tsunamis that have propagated over long distances frequently. The travel time delay between the observed and corrected simulated waveforms is reduced to <8 min and the amplitude discrepancy between them was also markedly diminished. The incorporated effects amounted to approximately 78％ of the travel time delay correction, with seawater density stratification, SAL, and Boussinesq dispersion contributing approximately 39％, 21％, and 18％, respectively. The simulated results showed that the elastic loading and Boussinesq dispersion not only affected travel time but also changed the simulated waveforms for this event. In contrast, the seawater stratification only reduced the tsunami speed, whereas the earth's elasticity loading was responsible for LNP due to the depression of the seafloor surrounding additional tsunami loading at far-field stations. This study revealed that the traditional shallow water model has inherent defects in estimating tsunami arrival, and the leading negative phase of a tsunami is a typical recognizable feature of a moderately strong transoceanic tsunami. These results also support previous theory and can help to explain the observed discrepancies.     

An enhanced ensemble Kalman filter scheme incorporating model error in sequential coupling between flow and geomechanics

In this work, we construct a new methodology for enhancing the predictive accuracy of sequential methods for coupling flow and geomechanics while preserving low computational cost. The new computational approach is developed within the framework of the fixed-stress split algorithm procedure in conjunction with data assimilation based on the ensemble Kalman filter (EnKF). In this context, we identify the high-fidelity model with the two-way formulation where additional source term appears in the flow equation containing the time derivative of total mean stress. The iterative scheme is then interlaced with data assimilation steps, which also incorporate the modeling error inherent to the EnKF framework. Such a procedure gives rise to an “enhanced one-way formulation,” exhibiting substantial improvement in accuracy compared with the classical one-way method. The governing equations are discretized by mixed finite elements, and numerical simulation of a 2D slab problem between injection and production wells illustrate the tremendous achievement of the method proposed herein.     

Algorithms for Stellar Perturbation Computations on Oort Cloud Comets

We investigate different approximate methods of computing the perturbations on the orbits of Oort cloud comets caused by passing stars, by checking them against an accurate numerical integration using Everhart’s RA15 code. The scenario under study is the one relevant for long-term simulations of the cloud’s response to a predefined set of stellar passages. Our sample of stellar encounters simulates those experienced by the Solar System currently, but extrapolated over a time of 10¹⁰ years. We measure the errors of perihelion distance perturbations for high-eccentricity orbits introduced by several estimators – including the classical impulse approximation and Dybczyński’s (1994, Celest. Mech. Dynam. Astron. 58, 1330–1338) method – and we study how they depend on the encounter parameters (approach distance and relative velocity). We introduce a sequential variant of Dybczyński’s approach, cutting the encounter into several steps whereby the heliocentric motion of the comet is taken into account. For the scenario at hand this is found to offer an efficient means to obtain accurate results for practically any domain of the parameter space.