局部地形改正的奇异积分研究

现有的地形改正积分核函数存在奇异现象,使得积分在奇异点处不连续.针对此问题,本文提出了采用高斯积分法与核函数项增加常数因子级数展开法来解决这一难题,并推导了高斯积分法处理奇异积分的公式及含可选小常数的地形改正的严密级数展开式.同时文中采用最新公布的3″×3″高分辨率的SRTM3地形数据代替传统的GTOPO30数据计算地形改正,结合实际算例确定了地形改正数的级数展开式的可选次项和最佳常数以及高斯积分法的最佳内外圈半径,并详细讨论了两种奇异积分处理方法和两种分辨率的地形数据对地形改正的影响.     

Gravimetric survey terrain correction using linear analytical approximation

Various methods for computing the terrain correction in a high‐precision gravity survey are currently available. The present paper suggests a new method that uses linear analytical terrain approximations. In this method, digital terrain models for the near‐station topographic masses are obtained by vectorizing scan images of large‐scaled topographic maps, and the terrain correction computation is carried out using a Fourier series approximation of discrete height values. Distant topography data are represented with the help of digital GTOPO30 and Shuttle Radar Topography Mission cartographic information. We formulate linear analytical approximations of terrain corrections for the whole region using harmonic functions as the basis of our computational algorithm. Stochastic modelling allows effective assessment of the accuracy of terrain correction computation. The Perm Krai case study has shown that our method makes full use of all the terrain data available from topographic maps and digital terrain models and delivers a digital terrain correction computed to a priori precision. Our computer methodology can be successfully applied for the terrain correction computation in different survey areas.     

基于球冠域的月球重力地形校正方法

利用卫星重力测量资料研究地球、月球与火星等星体的内部构造时,需要进行重力地形校正,计算全球布格重力异常,而在球坐标中实现地形校正计算是一种有效的途径.本文提出球坐标系中的球冠域地形校正计算方法,给出了该方法涉及的球坐标系之间坐标转换方法和球冠域内地形模型重构方法,并进行理论验证．作者利用嫦娥一号激光测高数据对月球重力进行地形校正,获得了月球全球布格重力异常,并与球坐标系中Tesseroid 单元体地形校正方法对比,分析了球冠域地形校正方法的计算精度、空间分辨率及其优缺点．     

DEM数据拼接对重力地形改正的影响及效果

数字高程模型(Digital Elevation Model,DEM)在中大比例尺重力地改中广泛应用,但对于数据处理中的多种插值算法的有效融合,并提高精度和处理速度,一直没有得到有效解决.基于 ArcGIS10、GeoIPAS3.0、Geosoft 的 DEM 拼接所用插值方法各异,插值精度各有差别,Suffer8在数...     

航空重力梯度测量之地形改正方法及讨论

本文简要介绍了航空重力梯度测量中地形改正的基本原理及其地改公式,并采用基于质量线和质量棱柱两种地形模型的数值积分公式进行了一些简单模拟试算.在研究航空重力梯度测量的精密地形改正方面,作者首次将考虑地球曲率影响的质量棱柱体模型用于梯度数据的地改.文章最后对所有结果做了一些必要统计分析.     

On the calculation of the gravity terrain corrections in Czechoslovakia

Summary A calculation of the gravity terrain corrections by computer is proposed.

---

¶rt;aam m¶rt; uuu mnauu nna unau uuum muu.

     

Testing the type of non-separability and some classes of space-time covariance function models

In statistical space-time modeling, the use of non-separable covariance functions is often more realistic than separable models. In the literature, various tests for separability may justify this choice. However, in case of rejection of the separability hypothesis, none of these tests include testing for the type of non-separability of space-time covariance functions. This is an important and further significant step for choosing a class of models. In this paper a method for testing positive and negative non-separability is given; moreover, an approach for testing some well known classes of space-time covariance function models has been proposed. The performance of the tests has been shown using real and simulated data.     

航空伽玛能谱数据地形改正方法对比研究及其应用

在地形高度变化较大的复杂地形区由于探测立本角难于近似满足2π条件,造成航空伽玛能谱测量数据高度改正结果失真,在山谷区立体角大于2π条件,改正结果偏高,在山峰区立体角小于2π条件,改正结果偏低,即地形的变化影响了高度改正的效果.本文对现有两类四种航空伽玛能谱测量数据地形改正方法进行理论分析和效果对比研究,优选出适用于航空...     

On terrain corrections in terrestrial heat flow

The theory of heat-flow variation over a Lees-type hill is well known for evaluating terrain effects on terrestrial heat flow. However, a hill cannot be converted into a valley by simply changing the sign of one of the terrain-defining parameters, nor can several Lees' hills be superposed to simulate a series of hills and valleys for correcting a terrain-induced disturbance of heat flow. The proper derivations for a Lees-type valley are presented and the superposition is compared with analytic solutions for two parallel semi-cylindrical valleys and two semi-spherical basins embedded in an otherwise planar ground. Generally, heat flux climaxes over central valleys or basins, and dips toward their margins where rapid change in topography occurs. Variation of heat flux induced by a three-dimensional terrain is relatively large, as compared to two-dimensional features, but its areal extent is relatively limited. The two-dimensional effects also extend relatively deeper. In applying two-dimensional algorithms to a three-dimensional terrain, the correction may be over- or underestimated depending on the distance from a borehole to prominent terrain features in the surrounding area.     

On ensemble representation of the observation-error covariance in the Ensemble Kalman Filter

Evensen (2003) presents a modification of the Ensemble Kalman Filter (EnKF), in which the observation-error and background-error covariance matrices are both represented by ensembles, in contrast to the usual practice, where only the background error is so represented. It is shown that this modification can cause the ensemble to collapse to a single member, in the common situation where the number of observations is more than twice the number of ensemble members, and to be rank-deficient when the number of observations is greater than or equal to the ensemble size. It is also shown that some further modifications to the scheme, presented by Evensen as offering numerical efficiencies, can prevent this collapse. However, these latter modifications are shown in some simple numerical examples to require tuning to produce acceptable results, which are nevertheless inferior to those of the standard EnKF.Acknowledgements The author acknowledges useful discussions with Peter Steinle, and other participants at the EnKF workshop held in BMRC in November, 2003.     

On the consistency of the indirect lognormal correction

The indirect lognormal correction is a change-of-support model commonly used in geostatistical applications when dealing with additive variables, for which the upscaling amounts to arithmetic averaging. It was designed as a generalization of the lognormal correction that states the permanence of lognormality, but so far its internal consistency has not been proven in the general case. After a recall of the theoretical conditions that change-of-support models must honor, the concept of conventional income is introduced and used to establish the mathematical consistency of the indirect lognormal correction. However, the suitability of this model is questionable in many situations, in particular when the support effect is important or when the point-support distribution presents a zero effect, is not continuous or not positively skewed.Tel.: +56-2-672-3504, +56-2-678-4498     

On the effects of triangulated terrain resolution on distributed hydrologic model response

Distributed hydrologic models based on triangulated irregular networks (TIN) provide a means for computational efficiency in small to large‐scale watershed modelling through an adaptive, multiple resolution representation of complex basin topography. Despite previous research with TIN‐based hydrology models, the effect of triangulated terrain resolution on basin hydrologic response has received surprisingly little attention. Evaluating the impact of adaptive gridding on hydrologic response is important for determining the level of detail required in a terrain model. In this study, we address the spatial sensitivity of the TIN‐based Real‐time Integrated Basin Simulator (tRIBS) in order to assess the variability in the basin‐averaged and distributed hydrologic response (water balance, runoff mechanisms, surface saturation, groundwater dynamics) with respect to changes in topographic resolution. Prior to hydrologic simulations, we describe the generation of TIN models that effectively capture topographic and hydrographic variability from grid digital elevation models. In addition, we discuss the sampling methods and performance metrics utilized in the spatial aggregation of triangulated terrain models. For a 64 km² catchment in northeastern Oklahoma, we conduct a multiple resolution validation experiment by utilizing the tRIBS model over a wide range of spatial aggregation levels. Hydrologic performance is assessed as a function of the terrain resolution, with the variability in basin response attributed to variations in the coupled surface–subsurface dynamics. In particular, resolving the near‐stream, variable source area is found to be a key determinant of model behaviour as it controls the dynamic saturation pattern and its effect on rainfall partitioning. A relationship between the hydrologic sensitivity to resolution and the spatial aggregation of terrain attributes is presented as an effective means for selecting the model resolution. Finally, the study highlights the important effects of terrain resolution on distributed hydrologic model response and provides insight into the multiple resolution calibration and validation of TIN‐based hydrology models. Copyright © 2005 John Wiley & Sons, Ltd.     

On a class of non-stationary, compactly supported spatial covariance functions

Globally supported covariance functions are generally associated with dense covariance matrices, meaning severe numerical problems in solution feasibility. These problems can be alleviated by considering methods yielding sparse covariance matrices. Indeed, having many zero entries in the covariance matrix can both greatly reduce computer storage requirements and the number of floating point operations needed in computation. Compactly supported covariance functions considerably reduce the computational burden of kriging, and allow the use of computationally efficient sparse matrix techniques, thus becoming a core aspect in spatial prediction when dealing with massive data sets. However, most of the work done in the context of compactly supported covariance functions has been carried out in the stationary context. This assumption is not generally met in practical and real problems, and there has been a growing recognition of the need for non-stationary spatial covariance functions in a variety of disciplines. In this paper we present a new class of non-stationary, compactly supported spatial covariance functions, which adapts a class of convolution-based flexible models to non-stationary situations. Some particular examples, computational issues, and connections with existing models are considered.     

New anisotropic covariance models and estimation of anisotropic parameters based on the covariance tensor identity

 Many heterogeneous media and environmental processes are statistically anisotropic. In this paper we focus on range anisotropy, that is, stochastic processes with variograms that have direction dependent correlation lengths and direction independent sill. We distinguish between two classes of anisotropic covariance models: Class (A) models are reducible to isotropic after rotation and rescaling operations. Class (B) models can be separated into a product of one-dimensional functions oriented along the principal axes. We propose a new Class (A) model with multiscale properties that has applications in subsurface hydrology. We also present a family of Class (B) models based on non-Euclidean distance metrics that are generated by superellipsoidal functions. Next, we propose a new method for determining the orientation of the principal axes and the degree of anisotropy, i.e., the ratio(s) of the correlation lengths. This information reduces the degrees of freedom of anisotropic variograms and thus simplifies the estimation procedure. In particular, Class (A) models are reduced to isotropic and Class (B) models to one-dimensional functions. Our method is based on an explicit relation between the second-rank slope tensor (SRST), which can be estimated from the data, and the covariance tensor. The procedure is conceptually simple and numerically efficient. It is more accurate for regular (on-grid) data distributions, but it can also be used for sparse (off-grid) spatial distributions. In the case of non-differentiable random fields the method can be extended using generalized derivatives. We illustrate its implementation with numerical simulations.     

钻孔体应变观测资料的实地校正

以钻孔体应变为例,利用潮汐因子对钻孔体应变观测资料进行校正。结果表明,由于各台所处的构造条件、地形条件、钻孔条件不同,各台的校正系数也不同。校正系数隨时间变化比较稳定,变异程度系数最大约为4.1%最小仅有0.1%,表明校正结果相当好。文中给出了部分钻孔体应变台站观测资料的校正系数。该方法有计算简便、结果可靠、实用性较强等优点。     

On correction of loss of mass during Thellier experiments

Determination of geomagnetic paleointensity by the Thellier method compares the decay of natural remanent magnetisation with the gain of a laboratory induced thermoremanent magnetisation. If fragile samples lose some amount of their material after each heating step, the Thellier experiment will be systematically disturbed and paleointensity will be over-estimated. For a lost of 5% of the sample’s mass an over-estimate of 10% in paleointensity is observed. This can easily be corrected by a normalisation to the initial mass of the unheated sample. This is necessary for any fragile materials such as baked clays or when a specimen breaks into pieces during the Thellier experiment.     

Correlation and covariance of runoff

The application of objective methods for interpolation of stochastic fields is based on the assumption of homogeneity with respect to the correlation function, i.e. only the relative distance between two points is of importance. This is not the case for runoff data which is demonstrated in this paper. Taking into consideration the structure of the river network and the related drainage basin supporting areas theoretical expressions are derived for the correlation function for flow along a river from its outlet and upstream. The results are exact for a rectangular drainage basin. For more complex basin geometry a grid approximation is suggested. The found relations are demonstrated on a real world example with a good agreement between the theoretically calculated correlation functions and empirical data.     

On the correction of gravity tides observation and the indication analysis of gravity anomaly

The problems of correcting gravity tidal observations and indicating of the gravity anomalies used in earthquake prediction in China are systematically studied in this paper. The correcting problems of the rheological model of the instrument, inertia of the earth and the effects of the ocean loading, air pressure, underground water on gravity tidal recording data are also discussed in details, the related results are also given in the paper. The problem of the indicating non-tidal information in stational gravity data is dicussed. The properties of the several different data processing filters are compared in theoretical point of view.