复杂地形条件下航空伽玛能谱地形改正方法探讨

应用矩形辐射体航空伽玛辐射场理论,研究应用于复杂地形条件下的航空伽玛能谱资料的地形改正方法,并针对该方法进行验证. 本文利用航空物探测量过程中获得的DTM数据（达到了地形改正所需的地形起伏数据精度）,应用矩形辐射体航空伽玛辐射场理论,根据地面辐射体与航空伽玛场分布之间的正演关系,对航空伽玛能谱解释方法的原理进行了正演分析和反演推导. 探索出一种按影响角进行地形改正的方法. 该方法特点是适合于任意飞行方式(缓地形和水平飞行均可)和任意地形条件航空伽玛能谱的逐点地形改正. 结果表明该地形改正方法能够基本消除航空伽玛能谱测量中的地形起伏产生的影响,经地形修正后的航空伽玛能谱异常能较正确地反映地面辐射体的真实情况.     

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.     

基于一阶差分的岩溶管道充电法电位水平梯度异常分离方法

在隐伏岩溶探测中,为实现岩溶管道引起的充电法电位水平梯度局部异常与线性或低缓区域背景场的分离,突出局部微弱异常,本文根据半无限均匀大地中,良导电球体和无限长水平圆柱体充电电位水平梯度及其一次导数剖面曲线分布特征与规律,采用两点平滑法和一阶中心差分法推导出充电电位水平梯度一次导数的近视计算公式,建立了差分滤波函数F xi+1+12()h极小值点与线性或低缓区域背景场特征点的对应关系.在此基础上,提出了线性或低缓区域背景场的线性插值公式和拉格朗日插值公式,以及局部异常与线性或低缓区域背景场划分的作图法和解析法.差分滤波函数F xi+1+12()h对充电法电位水平梯度观测误差、地质噪声具有平滑和低通滤波作用,由此差分滤波函数F xi+1+12()h确定的实测充电法电位水平梯度线性或低缓区域背景场将更为合理,实现了充电法电位水平梯度局部异常与线性或低缓区域背景场的有效分离.利用该局部异常与线性或低缓区域背景场划分方法,实际处理了桂东北越城岭山脉东部岩溶区的洛潭水库实测充电电位水平梯度异常数据,提取了受强大区域背景场掩盖了的岩溶管道产生的微弱异常,突出了岩溶病态水库漏水通道、断裂构造分布等地质信息,为岩溶病态水库的除险加固工程供了有效的处理途径和工程靶区.地质钻探工程和地下水示踪试验均验证了所研发的基于一阶差分的充电法电位水平梯度局部异常与线性或低缓区域背景场分离方法的准确性、有效性和实用性.     

井地电位测量系统的三维正演

针对井地电位测量系统的正演数值模拟问题,首先介绍了该系统的正演基本理论,然后采用"镜像"法,推导了垂直有限长线电流源在无限大半均匀介质中任意深度时的正常电位解析式,并在此基础上,推导了相应的装置系数和混合边界条件公式.结合有限差分法,实现了正演模型的求解计算.数值模拟中,采用不同的正常电位公式,混合边界条件公式和装置系数公式,分别建立了均匀介质模型、高阻异常体模型和低阻异常体模型,并对异常体正演响应的异常特征和分布规律进行了对比分析.结果表明,所推导的公式模拟异常体电位响应更准确,为后续更精确的反演和解释现场测量数据奠定了基础.     

点源场井-地电位测量三维有限元模拟

井地电法是深部地质矿产勘查的重要方法之一,研究高效率、高精度、适用于起伏地形等复杂条件下的正演模拟算法具有理论和实际意义.本文研究了点源场井地电位测量的三维有限元正演模拟,采用与井轴一致倾斜的计算区域,使剖分单元随地形起伏,用预处理共轭梯度法求解线性方程组,利用行压缩存储和改进的行压缩存储方式来存储刚度矩阵和预处理矩阵,实现了起伏地形和倾斜井情形下的正演计算.此外,本文利用仿射坐标变换技术,给出了平行五面体单元精确的单元积分公式,这种处理技术同样可推广应用于其他平行多面体单元的单元分析,相比于采用等参变换和高斯数值积分,能极大地提高计算效率.文中构建了一些模型算例,其计算结果验证了程序的可靠性和高效性.     

井-地充电法圈定矿体边界异常特征研究

采用有限单元法对井-地充电法进行了数值模拟,通过对水平、倾斜等不同形态板状矿体在不同地电条件下井-地充电法异常的计算和讨论,研究了矿体的空间分布与电位梯度分布之间规律,并提出深宽比和深峰比的概念以讨论异常形态与地下地质体间的对应关系.计算结果表明:电位梯度峰值位置和矿体边界位置有一定的对应关系,利用电位梯度等值线形态及其峰值位置可有效获得矿体走向、倾向和边界等信息.     

水域地形改正方法研究

在区域重力调查工作中,地形改正误差对重力异常总精度影响较大,是提高布格异常总精度的关键因素.在以往的区域重力工作中,遇到河、湖等水体时,因为条件所限,通常将水域视为与地形改正密度相同的物质,对岸边点不进行水体改正,无形中对重力异常的精度产生了影响.随着技术进步,对地形改正精度要求越来越高,故,需要进行精细的地形改正.水体作为特殊的地表覆盖物,具有较大规模时,成为不容忽略的影响因子.根据本文评估计算,平均水深达20m、水面宽度达2km时,水体对测点的影响已经接近或超过现行规范的精度要求.所以,当遇到水深大于20m的青海湖、水深达到100m的纳木错等大型湖泊时,传统的、忽略水体影响的工作方法已不能满足精度要求,需要消除水体对测点产生的影响.本文给出了用计算机进行水体改正的具体方法:用DEM数据和水体深度资料,采用共用点法计算出进行了水体改正的地形改正值和水体改正值.并用模型数据进行了水体改正计算,根据计算结果对水体改正值进行了定性分析,得出结论:1)水体改正方法正确、简便,可应用于重力调查工作;2)当水体的平均厚度达到20m以上时,在区域重力工作中,必须考虑进行水体改正;3)水体改正值与测点距水体的距离、测点周边水体面积大小、水体边界形状、测点海拔高程和水底地形等因素有关.即,在以下情况下水体对测点的影响值增大:测点距水体距离减小、测点周边水体面积增大、测点位置突入水域越多、测点高程越接近水面高程、水底地形越陡.     

重力场与构造应力场内在关系的理论研究

根据地球动力学原理,提出了重力异常变化量向构造应力场应力降转化的理论模型,推导了简明的应力降值及其方位角的实用计算公式。考虑到研究的是动态场,涉及到的时间范围短,在做理论分析时,可以忽略地形改正和莫霍面深度起伏改正,从而,能够应用重力测量研究监测区域的动态应力场特征。根据应力分析方法,阐明了重力场和应力场的异常变化与孕震过存在密切关系。     

三维起伏地形条件下航空瞬变电磁响应特征研究

航空瞬变电磁法以其速度快、成本低、通行性好等的优势能够有效的应用于地质地形条件复杂的地区.目前对于航空瞬变电磁法的研究主要基于平坦地形的理想情况,对于地形效应的研究相对较少,然而实际应用中地形不可避免,若忽略地形影响将对资料解释造成较大的误差,从而制约航空电磁方法的进一步发展.本文基于交错网格的时域有限差分方法对三维起伏地形条件下航空瞬变电磁进行正演模拟,在保证算法准确性的前提下给出大量模型算例.以经典地形模型为例,利用所给方法计算三维正演响应,结果显示起伏对于航空瞬变电磁数据有着显著的影响且影响主要集中在早期.而后,以实际地质资料为基础,构建起伏地形条件下包含多个异常体的三维复杂模型,计算了复杂模型的航空瞬变电磁响应,并给出三维全域视电阻率曲线,从而对地形效应的影响有了更加直观的认知.最后,通过大量模型讨论了地形的尺寸参数、电性参数、飞行轨迹与飞行高度等因素变化对于航空瞬变电磁数据的影响情况,并得出有价值的结论.     

基于数字高程模型的南天山地貌特征研究

基于STRM-DEM((90 m)数据,利用ArcGIS空间分析模块,通过人工判定法、最大高差法以及最大高差与面积比法联合对比,获取研究区最佳分析窗口为31×31,面积约为7. 78 km~2,根据获取的最佳窗口提取出西南天山地区地形高程(最大高程、最小高程、平均高程)和地形起伏度。分析认为:西南天山山势陡峻,总体呈中东部高、西部低的地貌特征,且以高地形起伏度为主,沿西南天山走向方向,高山区地形起伏度自东向西逐渐降低;高海拔地区呈北东—南西向展布规律,反映了该地区遭受了南北向强烈挤压隆升作用;并通过条带状地形剖面分析研究区夷平面地貌特征,认为西南天山地区发育4级层状地貌面,反映了该地区的多次构造运动。     

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．     

印支运动以来中国海陆地势演化及阶梯地貌特征

地势是地面高低起伏的形势,是地球内营力和外营力共同作用的结果,是地壳内部结构、构造及其发展在地表的反映.空间重力异常与地形、地貌密切相关,反映地壳内部结构和构造的变化.均衡原理认为高山下面地壳厚,平原下面地壳薄,即地势的起伏同莫霍面的起伏呈镜像关系.中国海陆地质地球物理系列图编制了大地构造格架图和大地构造格架演化图等专题图件,对中国海陆各主要块体的时空演化进行研究,研究了中国海陆地势的"跷跷板"演化过程.本文根据中国海陆1:500万空间重力异常图和莫霍面深度图分析了海陆地貌特征,按照构造地貌的分类原则,将中国海域和陆域作为一个整体进行地貌分类,在中国大陆地势呈三个地貌阶梯的基础上,总结出中国海陆地貌总体特征为西高东低,呈五级阶梯分布.     

Geomorphological inheritance for loess landform evolution in a severe soil erosion region of Loess Plateau of China based on digital elevation models

The influence of pre-quaternary underlying terrain on the formation of loess landforms, i.e., the geomorphological inheritance issue, is a focus in studies of loess landforms. On the basis of multi-source information, we used GIS spatial analysis methods to construct a simulated digital elevation model of a pre-quaternary paleotopographic surface in a severe soil erosion area of the Loess Plateau. To reveal the spatial relationship between underlying paleotopography and modern terrain, an XY scatter diagram, hypsometric curve, gradient and concavity of terrain profiles are used in the experiments. The experiments show that the altitude, gradient and concavity results have significant linear positive correlation between both terrains, which shows a relatively strong landform inheritance relationship, particularly in the intact and complete loess deposit areas. Despite the current surface appearing somewhat changed from the original shape of the underlying terrain under different erosion forces, we reveal that the modern terrain generally smoothes the topographic relief of underlying terrain in the loess deposition process. Our results deepen understanding of the characteristics of geomorphological inheritance in the formation and evolution of loess landforms.     

重力异常场空间-波数混合域三维数值模拟

重力勘探中复杂条件下的三维正演计算量大存储要求高,使得这种条件下重力勘探高效、精细正反演变得困难.针对这一问题,提出一种空间-波数混合域数值模拟方法,该方法将空间域引力位积分进行水平方向二维傅里叶变换,将三维空间域卷积问题转换为多个不同波数之间相互独立的空间垂向一维积分问题,一维积分垂向可离散为多个单元积分之和,每个单元采用二次形函数表征密度变化,可得出单元积分的解析表达式.该方法计算量和存储需求少,算法高度并行;保留垂向为空间域,优势之一在于可根据实际情况合理调整单元疏密程度,准确模拟任意复杂地形和密度异常体的重力异常,兼顾计算精度与计算效率;优势之二在于用形函数拟合求得积分的解析解,计算精度和效率高;充分利用一维形函数积分的高效和高精度,不同波数之间一维积分高度并行性及快速傅里叶变换的高效性,实现重力异常场三维数值模拟.设计棱柱体模型,通过数值解和解析解对比验证了该方法的正确性、适用性和高效性.针对任意复杂地形条件下的重力场及其张量的模拟问题,提出一种快速算法,对其有效性进行了验证.探究标准FFT法的截断效应对计算精度的影响,对比分析Gauss-FFT法和标准FFT扩边法两种方法的计算精度和效率,总结了二者的选取策略,结果表明选用标准FFT扩边法计算效率更高.实际地形的数值模拟表明本文算法适用于任意复杂地形的高效计算.     

Improving the computation of the gravitational terrain effect close to ground stations in the GTE software

The precise computation of the vertical gravitational attraction of the topographic masses (terrain correction) is still being studied both for geodetic and geophysical applications. In fact, it is essential in high precision geoid estimation by means of the well-known remove-compute-restore technique, which is used to isolate the gravitational effects of anomalous masses in exploration geophysics. The terrain correction can be evaluated exploiting a Digital Terrain Model (DTM) in different ways, such as classical numerical integration, prisms, tesseroids, polyhedrons, and/or Fast Fourier Transform techniques. The increasing resolution of recently developed DTMs, the increasing number of observation points, and the increasing accuracy of gravity data represent, nowadays, major challenges for the terrain correction computation. Classical point mass approximation and prism based-algorithms are indeed too slow, while Fourier-based algorithms are usually too much approximate when compared to the required accuracy. In this work, we improve the Gravity Terrain Effects (GTE) algorithm, the innovative tool that exploits a combined prism-Fast Fourier Transform approach especially developed for airborne gravimetry, to compute the terrain correction on the surface of the DTM (i.e. corresponding to the ground stations and/or its vicinity). This required development of a proper adjustment of the algorithms implemented within the GTE software and also to define and implement a procedure to overcome the problems of the computation of the gravitational effects due to the actual slope of the terrain close to the stations. The latter problem is thoroughly discussed and solved by testing different solutions like concentric cylindrical rings, triangulated polyhedrons, or ultra-high resolution squared prisms. Finally, numerical tests to prove the temporal efficiency and the computational performances of the improved GTE software to compute terrain correction for ground stations are also presented.     

Effects of terrain smoothing on topographic shielding correction factors for cosmogenic nuclide‐derived estimates of basin‐averaged denudation rates

Estimation of spatially averaged denudation rates from cosmogenic nuclide concentrations in sediments depends on the surface production rates, the scaling methods of cosmic ray intensities, and the correction algorithms for skyline, snow and vegetation shielding used to calculate terrestrial cosmogenic nuclide production. While the calculation of surface nuclide production and application of latitude, altitude and palaeointensity scaling algorithms are subjects of active research, the importance of additional correction for shielding by topographic obstructions, snow and vegetation is the subject of ongoing debate. The derivation of an additional correction factor for skyline shielding for large areas is still problematic. One important issue that has yet to be addressed is the effect of the accuracy and resolution of terrain representation by a digital elevation model (DEM) on topographic shielding correction factors. Topographic metrics scale with the resolution of the elevation data, and terrain smoothing has a potentially large effect on the correction of terrestrial cosmogenic nuclide production rates for skyline shielding. For rough, high‐relief landscapes, the effect of terrain smoothing can easily exceed analytical errors, and should be taken into account. Here we demonstrate the effect of terrain smoothing on topographic shielding correction factors for various topographic settings, and introduce an empirical model for the estimation of topographic shielding factors based on landscape metrics. Copyright © 2008 John Wiley and Sons, Ltd.     

Mean Free-Air Gravity Anomalies in the Mountains

Mean free-air gravity anomalies are often needed in geodesy for gravity field modelling. Two possible ways of compiling the mean free-air gravity anomalies are discussed. One way is via simple Bouguer gravity anomalies and the second and more time consuming way is via refined Bouguer gravity anomalies. In flat areas the differences between using any of the two ways should not be significant. In the mountains however, every effect introducing a high dependency, such as e.g. terrain effect, can negatively affect the interpolation process. In fact, a numerical experiment conducted in one part of Rocky Mountains revealed large and systematic differences. The effect of these differences on the geoid model is more then two meters in the test area. Our investigation shows that this bias is caused by the location of gravity measurement points, chosen mostly on hill-tops. At such points, the terrain correction to gravity is systematically larger than the mean value of the correction. Therefore, it is not possible to prevent the mean free-air gravity anomalies obtained from simple Bouguer gravity anomalies from having a systematic bias. One can see this bias as a result of the aliasing effect because the simple Bouguer gravity anomalies in the mountains contain a higher frequency signal (terrain effect) that is, according to sampling theorem, impossible to reconstruct by sparse measured gravity data, see e.g. (Goos et al., 2003). Therefore, the more rigorous way of computing the mean free-air gravity anomalies is via refined Bouguer gravity anomalies.     

Dimension and entropy in the soil-covered landscape

Both the Hausdorff dimension and the K-entropy supply a measure of the irregularity of the landspace surface. The relationship between the two measures is investigated over a variety of terrains in Britain and a method of calculating the entropy is checked against an independent estimate of the dimension with reasonable agreement. The calculation of the K-entropy requires that the landscape surface be represented by an homogenous ergodic random field. This condition is satisfied by the tendency of soil-covered terrains to progressively approximate to a form well represented by a Gaussian field. Gaussian random fields can either be very smooth, possessing derivatives of all orders at every point or they are highly irregular and non-differentiable everywhere. Within the regular conceptualization the Rice-Kac theory is used to predict the numbers of crossing points and the extent of excursion sets. These predictions are tested against an example terrain from the High Weald of East Sussex with very good agreement, apart from predictions of local maxima. A worked example of the calculation of the K-entropy is given as an appendix. The potential role of information theory in geomorphology extends beyond the use made of entropy in this investigation. In particular ergodic theory has important practical and theoretical implications.     

Spatial variations of terrain and their impacts on landscape patterns in the transition zone from mountains to plains—A case study of Qihe River Basin in the Taihang Mountains

Terrain plays a key role in landscape pattern formation, particularly in the transition zones from mountains to plains. Exploring the relationships between terrain characteristics and landscape types in terrain-complex areas can help reveal the mechanisms underlying the relationships. In this study, Qihe River Basin, situated in the transition zone from the Taihang Mountains to the North-China Plain, was selected as a case study area. First, the spatial variations in the relief amplitudes (i.e., high-amplitude terrain undulations) were analyzed. Second, the effects of relief amplitudes on the landscape patterns were indepth investigated from the perspectives of both landscape types and landscape indices. Finally, a logistic regression model was employed to examine the relationships between the landscape patterns and the influencing factors (natural and human) at different relief amplitudes. The results show that with increasing relief amplitude, anthropogenic landscapes gradually give in to natural landscapes. Specifically, human factors normally dominate the gentle areas (e.g., flat areas) in influencing the distribution of landscape types, and natural factors normally dominate the highly-undulating areas (e.g., moderate relief areas). As for the intermediately undulating areas (i.e., medium relief amplitudes), a combined influence of natural and human factors result in the highest varieties of landscape types. The results also show that in micro-relief areas and small relief areas where natural factors and human factors are more or less equally active, landscape types are affected by a combination of natural and human factors. The combination leads to a high fragmentation and a high diversity of landscape patterns. It seems that appropriate human interferences in these areas can be conducive to enhancing landscape diversity and that inappropriate human interferences can aggravate the problems of landscape fragmentation.