Local stability and estimation of uncertainty for solutions to inverse problems

 We present a method for studying local stability of a solution to an inverse problem and evaluate the uncertainty in determining true values of particular observables. The investigation is done under the assumption that only the Gaussian part of fluctuations about the local minimum of the cost (likelihood) function is essential. Our approach is based on the spectral analysis of the Hessian operator associated with the cost function at its extremal point, and we put forward an effective iterative algorithm suitable for numerical implementation in the case of a computationally large problem. Received: 16 May 2001 / Accepted: 22 October 2001     

1994年9月16日台湾海峡地震及其构造背景研究

采用宽频带Ｐ波波形资料，利用全局反演方法，推断了１９９４年９月１６日发生在台湾海峡的一次强烈地震的地震矩张量；并采用随机加权方法进行误差分析．结果表明，这次地震的矩张量解以双力偶成分为主，是断层面为ＥＷ走向的正倾错动．震源机制的张应力轴接近水平，ＳＮ走向；压应力轴几乎竖直．地震矩值为０．９８×１０１９Ｎｍ．震源过程的持续时间仅有４ｓ，震源时间函数显示了均匀的单一破裂事件．通过对台湾东南到吕宋岛以北地震带的震源性质分析，探讨了该地区产生ＳＮ向水平拉张应力状态的原因．     

震源最佳反演结果误差的随机加权估计

提出利用随机加权方法估计地震矩张量最佳反演结果的误差．这种方法不对误差来源作任何分布假设，只需重复产生一定数量的服从Ｄｉｒｉｃｈｌｅｔ分布的权向量．对于每个权向量，将其各分量分配到每条地震记录上，相应地确定一个震源参数解．对这些震源参数反演解进行基本的统计分析，便能估计出最佳解的方差、协方差和置信区间．还讨论了１９８６年台湾地震（Ｍｓ＝７．８）的震源矩张量中存在各向同性分量这一解答的可靠性．     

航空重力测量中垂直扰动加速度误差模型的建立与分析

根据GPS确定垂直扰动加速度的误差特性,建立了合适的垂直扰动加速度的误差模型。通过对计算结果的分析,提出了航空重力测量中,在重力通频带内,垂直扰动加速度误差可当作一种有色噪声来处理的新观点。并且根据误差模型,给出了滤波截止频率的相应取值以及GPS定位精度指标。     

Modified eigenfunction expansion methods for interaction of water waves with a semi-infinite elastic plate

The eigenfunction expansion method (will be referred to as error function method in this paper) of analysing reflection and transmission of ocean waves at a semi-infinite thin elastic plate [J Geophys Res 95 (1990) 11629; Phil Trans R Soc Lond A 347 (1994) 185] is modified and extended to cases with simply supported and built-in edges. The form of the error function in the eigenfunction expansion method of Fox and Squire [J Geophys Res 95 (1990) 11629] has been modified based on a dimensional analysis and also extended to plates with either a simply supported or a built-in edge. The modified error function does not include the so-called Lagrange multipliers used in the original method and therefore the modified solution is independent of the selection of the Lagrange multipliers. It is demonstrated that the modified error function method satisfies the relation of energy conservation very well for the three edge conditions examined. The relation of energy conservation for plates is derived for elastic plates with simply supported and built-in edges and it is found that the relation of energy conservation for a free edge is also held for simply supported and built-in edges.In addition, a minor modification has also been made to the eigenfunction method (will be called inner product method in this study) of Sahoo et al. [Proceedings of 10th International Offshore and Polar Engineering Conference 3 (2000) 594]. It will be shown that the modified inner product method becomes mathematically well defined. The modified coefficient matrixes for different edge conditions are diagonal and thus the linear simultaneous equations can be solved very easily. It is also demonstrated with examples that the extended error function method and the modified inner product method give identical results.     

海洋沉积物质14C测年的若干问题

本文根据海洋沉积物质测年中的一些具体实例,结合国际上的研究动态,探讨了测年中表观年龄与储存效应及污染程度的关系。它从储存年龄的客观性角度强调了校正的必要性,并且对不同的海洋物质在测年中的可靠性做了探究,尤其就无机样品的误差形成原因及途径进行了分析,指出“死碳”的混入及碳酸盐物质缓慢的生长速率是主要的误差来源。     

Estimating the internal pressure gradient errors in a σ-coordinate ocean model for the Nordic Seas

Internal pressure gradient estimation is problematic in σ-coordinate ocean models and models based on more generalised topography following coordinate systems. Artificial pressure gradients in these models may create artificial flow. In recent literature, several methods for reducing the errors in the estimated internal pressure gradients are suggested. A basin with a bell-shaped seamount in the middle has often been applied as a test case. To supplement the findings from these more idealised experiments, the internal pressure gradient errors in a σ-coordinate ocean model for the Nordic Seas are discussed in the present paper. Three methods for estimating internal pressure gradients are applied in these experiments. The sensitivity of the results to the subtraction of background stratification and to the horizontal viscosity are also investigated. For the extended Nordic Seas case, basin scale modes dominate after a few days of simulation. The errors in the transports across some sections may be larger than 1 Sv (1 Sv = 10⁶ m³ s^− 1) in these studies with 16-km grid resolution. The order of magnitude of the errors in the transports of Atlantic water into the Nordic Seas is approximately 0.5 Sv or between 5 and 10 % of recent transport estimates based on measurements. The results do not indicate that the errors are generally reduced if the background stratification is subtracted when estimating internal pressure gradients in terrain following models. However, the results from the experiments initialised with the background stratification show that the erroneous flows may be reduced considerably by using more recent techniques for estimating internal pressure gradients, especially for higher values of horizontal viscosity.     

近半个世纪中国区域历史气温网格数据集的建立

气候序列长度不一致以及由此导致的空间抽样误差在气候变化检测研究中常常产生影响,因此往往需要把全球或者区域尺度气候数据转化为格点气候数据集。文中分别采用修改后的一级差分方法和普通Kriging方法,把中国大陆(共约728个站,不含港、澳、台地区)气象台站1951年1月—2004年12月经过质量控制和均一化的历史气温数据转化为2.5°×2.5°经纬度网格化数据集。对比分析表明:应用上述两种方法,(1)格点化带来的空间抽样误差较小;(2)格点化后的格点气温序列和站点序列相关程度很高;(3)不同的方法建立的格点数据集在序列的相关性、距平场的相似性描述方面均非常一致。二者的相关性和相似性也表明文中所建立的格点数据集是比较合理的。最后利用格点化后的气温数据集,分别采取距平平均方法和一级差分方法,对近54年中国气温变化趋势进行了更为准确的估计。不同的计算方法对中国区域气温增暖幅度的研究表明,整个中国区域内近50年气温表现出一致的增暖特点,其中以北方地区(西北、东北)气温增暖幅度最大,个别地区达到近0.6℃/(10a),而最低的长江中、上游地区,年均气温增暖幅度较小,还不到0.1℃/(10a),全国平均的年平均气温近54年来增暖速率约为0.23—0.25℃/(10a),这和其他专家得出的结论是基本一致的,而由于文中对数据集进行了较为系统的质量控制,使得估计结果更为精确、可信。     

用NOAA/AVHRR探测地表反射率和NDVI的订正及误差分析

NOAA/ AVHRR反射率和标准化差值植被指数 (NDVI) 资料在气象、水文等领域都有广泛的应用。但因为地表双向反射和大气对可见光和近红外辐射的影响, 即使在地表没有变化的情况下, 卫星探测到的反射率和NDVI也有很大的变化。在除云处理和NOAA-14/AVHRR衰减校准的基础上, 利用6S模式对NOAA-14/AVHRR可见光和近红外反射率及NDVI资料进行了大气订正, 并利用Roujean和Rahman模式在大气订正后进行了双向反射订正。大气订正使可见光反射率减小3.34(反射率单位), 近红外反射率增加3.43(反射率单位), NDVI增加了0.22, 分别占各自平均值的78.2%, 15.9%, 35.5%。双向反射订正对NDVI的绝对值影响不大, 但消除了反射率和NDVI的不规则变化, 订正后能够较好地反映森林植被的物候效应。对各订正参数进行了误差分析, 结果表明订正对太阳和卫星天顶角的误差最敏感。     

大比例尺数字测图的精度分析及其二次改正

通过对数字化测图的误差成因分析，在作业过程中布设适当的检查点，对检查点的误差进行定性和定量的分析与计算，在数字测图中加入误差改正，从而提高数字化测图的精度。