利用多源重力观测数据反演渤海湾地区构造应力场

以最小二乘配置为基础,推导了基于观测信号的自适应融合算法。对渤海湾地区航空重力、陆地重力和卫星测高3类实测数据进行了基于观测信号的自适应融合处理,提高了融合区域重力观测数据精度。采用融合后的重力异常数据反演了渤海湾地区构造应力场,并结合地震历史资料进行初步分析,总结了该地区构造应力场的总体特征。反演结果表明,渤海湾地区构造应力场方向整体上呈现朝北方向,构造应力场清晰显现出郯庐断裂带和张家口-蓬莱断裂带分布,并且在郯庐和张家口-蓬莱断裂带唐山至张家口段构造应力聚集程度高、构造应力值也较大,表明该地区构造运动活跃,与该地区地震活动历史资料相符。     

基于最小二乘配置的航空和地面重力数据融合处理

本文首先通过延拓至地面的航空重力数据拟合出局部协方差函数,并以此作为整个航空重力测区的协方差函数。针对两种地面数据布设方案,利用最小二乘配置对航空重力数据和地面数据进行融合处理。结果表明通过融合能够有效地估计出航空重力数据中存在的系统偏差,格网数据的精度也有所提高,通过比较分析选取了合适的协方差函数参数,对不同参数及观测噪声大小对最终结果的影响进行了探讨。     

多源重力场信息融合处理方法

针对如何有效融合陆海交界区域不同分辨率的多源重力数据,本文重点研究了最小二乘配置、多分辨率最小二乘配置和点质量建模理论的数据融合处理方法。通过对实验区的多源观测数据融合处理,结果表明,3种融合方法反演的陆地重力异常数据的外符合精度在3×10-5m.s-2左右。多分辨率最小二乘配置和基于点质量理论的多源重力信息融合处理方法,能够达到有效融合各种分辨率数据的目的。     

海域多源重力数据融合处理的解析方法

在深入分析海域多源重力数据观测技术特性的基础上,提出了基于双权因子的多源数据网格化一步融合处理方法,以及基于分步平差、拟合、推估和内插相结合的多步融合处理方法,并通过实际算例验证了两种解析融合处理方法的有效性。     

航空重力向下延拓的最小二乘配置Tikhonov正则化法

基于最小二乘配置法向下延拓航空重力的过程中,由于协方差矩阵严重病态,影响延拓结果的稳定性和精度。针对这一问题,提出了航空重力向下延拓的最小二乘配置Tikhonov正则化法。基于全球协方差函数模型建立航空重力数据与地面重力数据的协方差关系,引入基于广义交叉验证法,选择正则化参数的Tikhonov正则化法改善协方差矩阵的病态性,抑制观测噪声对延拓结果的放大影响。基于EGM2008重力场模型,设计了山区、丘陵和海域3种不同地形区域的航空重力数据向下延拓的仿真实验,实验结果验证了该方法的有效性。     

基于方差分量估计的正则化配置法及其在多源重力数据融合中的应用

针对信号与误差的方差分量不一致问题及协方差阵病态性问题,分别在多源重力数据最小二乘配置融合过程中引入方差分量估计方法及Tikhonov正则化方法,得到基于方差分量估计的正则化配置法,实际算例结果表明,利用该方法能够有效削弱上述问题,减小重力数据融合结果的系统差,提高数据融合的精度及可靠性。     

确定大地水准面的Tikhonov最小二乘配置法

LSC法（最小二乘配置法）因能融合不同种类重力观测数据确定大地水准面的特性而受到广泛关注,但由于协方差矩阵存在病态性,微小的观测误差将被协方差矩阵的小奇异值放大,导致计算的配置结果不稳定且精度偏低。本文提出Tikhonov_LSC法,即在LSC法中引入Tikhonov正则化算法,基于GCV法选择协方差矩阵的正则化参数,利用正则化参数修正协方差矩阵的小奇异值,以抑制其对观测误差的放大影响。基于Tikhonov_LSC法计算大地水准面,能有效提高其稳定性和精度。通过以EGM2008重力场模型分别计算山区、丘陵和海域重力异常作为基础数据确定相应区域大地水准面的实验,验证了该方法的有效性。     

大地测量数据融合模式及其分析

一般情况下,基于观测信息和基于各类导出信息(如平差结果)的最小二乘融合是等价的,但若函数模型和随机模型存在误差时,则不同的数据融合模式会得出不同的结果.讨论了具有函数模型误差、随机模型误差的两种数据融合模式,即基于观测信息的融合模式和基于平差结果的融合模式,从理论和实际计算两个方面对两种融合模式的优缺点进行了讨论和分析.     

航空和地面重力测量数据的一体化处理方法

在三维经典扰动位协方差模型基础上,推导获得局部重力异常协方差模型、局部扰动重力协方差模型,以及扰动重力和重力异常的互协方差模型,这3个模型在忽略小项后是一致的,即航空扰动重力数据与地面重力异常数据的联合处理采用一个模型即可,大大简化了处理流程.以最小二乘配置理论及本文推导的协方差模型为基础,构建了航空扰动重力测线数据与地面重力异常数据一体化处理的具体方法,利用该方法可推估地面待求点的重力异常数据,且处理过程自动完成了航空扰动重力数据的向下延拓,同时也大大削弱了航空数据中存在的系统偏差影响.在某试验区开展了一体化处理试验,结果表明,采用一体化处理得到的重力异常数据比单独使用5'分辨率航空重力数据推估获得的数据精度提高2.4 mGal,比单独使用2.5'分辨率地面重力数据推估获得的数据精度提高1.2 mGal.     

RAE并行滤波的重力异常匹配算法

扩展卡尔曼滤波技术可以利用序列观测重力异常数据以及航行区域重力异常基准图来校正惯性导航系统漂移误差。针对因重力测量环境的变化、测量仪器扰动等因素造成的重力异常观测噪声不确定问题,提出了基于量测残差自适应估计观测噪声协方差(residual-based adaptive estimation,RAE)的重力异常滤波匹配算法;设计了一组并行卡尔曼滤波器,并简化了最优滤波器的选择准则。不同重力特征区域的实验表明,该算法能够有效降低惯性导航系统经纬向漂移误差,提高系统的导航定位精度。     

最小二乘配置的SVD分解解法

最小二乘配置最初是在组合各种资料来研究地球形状与重力场的一种数学方法,目前最小二乘配置已经在测绘数据处理中得到广泛应用。本文首先分析了目前采用的最小二乘配置法解算方法,在讨论了矩阵的奇异值分解(Singular Value Decomposition,SVD)方法的基础上,推导得出了矩阵SVD分解与广义逆矩阵的关系,得出了可以直接利用SVD分解求解矩阵的Moore-Penrose广义逆,并推导了应用SVD分解求解最小二乘配置的估值计算公式和精度估算公式,最后通过重力异常实例进行了计算,得出矩阵的SVD分解用于最小二乘配置解算的正确性和可行性,为最小二乘配置的求解提供了一种新方法。     

利用少量地面重力数据估计航空重力数据的系统偏差

航空重力数据与地面重力数据之间存在的系统偏差,是亟待解决的一个问题,为了能够在缺乏地面重力点的山区有效地利用航空重力数据,本文利用少量地面点的控制分别利用最小二乘配置法和加权平均法对航空重力数据的系统偏差进行了估计及改正,通过实测数据计算表明,两种方法都较好地估计出了航空重力数据存在的系统偏差,数据精度也有所提高,同时也验证了两种地面数据布设方案的有效性,通过分析得出加权平均法适合于同类重力数据的联合处理,而最小二乘配置则更适合于不同重力数据处理。     

Local geoid determination combining gravity disturbances and GPS/levelling: a case study in the Lake Nasser area, Aswan, Egypt

 The use of GPS for height control in an area with existing levelling data requires the determination of a local geoid and the bias between the local levelling datum and the one implicitly defined when computing the local geoid. If only scarse gravity data are available, the heights of new data may be collected rapidly by determining the ellipsoidal height by GPS and not using orthometric heights. Hence the geoid determination has to be based on gravity disturbances contingently combined with gravity anomalies. Furthermore, existing GPS/levelling data may also be used in the geoid determination if a suitable general gravity field modelling method (such as least-squares collocation, LSC) is applied. A comparison has been made in the Aswan Dam area between geoids determined using fast Fourier transform (FFT) with gravity disturbances exclusively and LSC using only the gravity disturbances and the disturbances combined with GPS/levelling data. The EGM96 spherical harmonic model was in all cases used in a remove–restore mode. A total of 198 gravity disturbances spaced approximately 3 km apart were used, as well as 35 GPS/levelling points in the vicinity and on the Aswan Dam. No data on the Nasser Lake were available. This gave difficulties when using FFT, which requires the use of gridded data. When using exclusively the gravity disturbances, the agreement between the GPS/levelling data were 0.71 ± 0.17 m for FFT and 0.63 ± 0.15 for LSC. When combining gravity disturbances and GPS/levelling, the LSC error estimate was ±0.10 m. In the latter case two bias parameters had to be introduced to account for a possible levelling datum difference between the levelling on the dam and that on the adjacent roads. Received: 14 August 2000 / Accepted: 28 February 2001     

A comparison of Stokes' numerical integration and collocation,and a new combination technique

Summary Basically two different evaluation methods are available to compute geoid heights from residual gravity anomalies in the inner zone: numerical integration and least squares collocation.If collocation is not applied to a global gravity data set, as is usually the case in practice, its result will not be equal to the numerical integration result. However, the cross covariance function between geoid heights and gravity anomalies can be adapted such that the geoid contribution is computed only from a small gravity area up to a certain distance _o from the computation point. Using this modification, identical results are obtained as from numerical integration.Applying this modification makes the results less dependent on the covariance function used. The difference between numerical integration and collocation is mainly caused by the implicitly extrapolated residual gravity anomaly values, outside the original data area. This extrapolated signal depends very much on the covariance function used, while the interpolated values within the original data area depend much less on it.As a sort of by-product, this modified collocation formula also leads to a new combination technique of numerical integration and collocation, in which the optimizing practical properties of both methods are fully exploited.Numerical examples are added as illustration.     

多源遥感影像融合

遥感影像融合能富集同一地区不同数据源的信息大跨度波谱特性影像数据的融合,提供了有关各单个传感器的互补信息,使分类更精确;大跨度空间分辨力影 融合,有利于改善２多光谱影像的度,增强特征提取和目视判读能力,能有效地用于变化监测。     

航空重力测量数据向下延拓中空间协方差函数特性研究

本文通过对航空重力测量数据的分析,建立起具有空间相关特性的空间协方差函数模型。利用所建立的模型,将航空重力测量试验数据采用最小二乘配置的方法向下延拓到地面,与地面已知重力数据进行比较。由比较结果,分析了空间协方差函数模型对航空重力测量数据向下延拓结果的影响,并表明所建立的空间协方差函数模型,满足协方差函数特性,且在局部区域使用能够达到满意的精度要求。     

卫星重力梯度向下延拓的频域最小二乘配置法

本文深入研究频域最小二乘配置法的基本原理及其在求解卫星重力梯度向下延拓问题中的应用。与一般空域最小二乘配置法相比，该方法具有高效稳定的特点，特别适合于大规模重力场数据处理，并为利用卫星重力梯度数据精化局部重力场提供了可供参考的方法。     

High-frequency parasitic modes of superconducting gravimeters

The superconducting gravimeter (SG) has a long-period instrumental noise called the parasitic mode at periods around 100 s, whose precise mechanism has not yet been identified. In this paper, another instrumental noise is detected at much higher frequencies by analyzing the high-rate gravity channel of two SGs in Japan. This is also a parasitic oscillation, characterized by frequencies on the order of 1 Hz and very high Q values. Detailed spectra indicate that the noise actually consists of two modes with small frequency separations. Based on a simple theory on the rotational motions of the superconducting sphere in the gravity sensor, the observed modes are tentatively identified as rotational oscillations of the sphere about two orthogonal axes in the horizontal plane. Interactions between the parasitic modes are investigated using the spectra acquired on an earthquake, to conclude that the low-frequency parasitic mode is likely to be a rotational motion of the sphere about the vertical axis.     

On estimating gravity anomalies— A comparison of least squares collocation with conventional least squares techniques

The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator are described.