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1.
FFT-based high-performance spherical harmonic transformation 总被引：6，自引：0，他引：6
Spherical harmonic transformation is of practical interest in geodesy for transformation of globally distributed quantities such as gravity between space and frequency domains. The increasing spatial resolution of the latest and forthcoming gravitational models pose true computational challenges for classical algorithms since serious numerical instabilities arise during the computation of the respective base functions of the spherical harmonic expansion. A possible solution is the evaluation of the associated Legendre functions in the Fourier domain where numerical instabilities can be circumvented by an independent frequency-wise scaling of numerical coefficients into a numerically suitable double precision range. It is then rather straightforward to commit global fast data transformation into the Fourier domain and to evaluate subsequently spherical harmonic coefficients. For the inverse, the computation of respective Fourier coefficients from a given spherical harmonic model is performed as an inverse Fast Fourier Transform into globally distributed data points. The two-step formulation turns out to be stable even for very high resolutions as well as efficient when using state-of-the-art shared memory/multi-core architectures. In principle, any functional of the geopotential can be computed in this way. To give an example for the overall performance of the algorithm, we transformed an equiangular 1 arcmin grid of terrain elevation data corresponding to spherical harmonic degree and order 10800. 相似文献
2.
The prism method for terrain corrections using digital computers 总被引：1，自引：0，他引：1
Dezső Nagy 《Pure and Applied Geophysics》1966,63(1):31-39
Summary In the prism method of making terrain corrections, the topography is approximated by a model consisting of right rectangular prisms. The vertical component of the gravitational attraction of each prism is calculated and the sum of these components gives the terrain correction.The prism method as programmed has no computational limitations. It can be used on all sizes of computers; it can be applied to a large area with any fine grid interval; it can be processed in a single run and yet provides complete flexibility for both research and routine computations. This has been achieved by breaking up larger areas into regions which fit into the computer memory. The contributions of these regions are automatically summed up for each station. While processing each region, various controls may be used at each station to exclude the contribution of a distant part of the area, to use approximate expressions farther from the station, to print out details around the station. There is also provision to refine the model by using smaller prisms around each computation point. Thus full use of elevation control can be made to calculate the terrain correction, the accuracy of which depends only on the quality of the input data.The prism method has been used to calculate terrain corrections for 130 stations in the New Quebec crater area. For five of these stations terrain corrections were also calculated by usingHammer's template. The two independent sets of values differ by less than four per cent. 相似文献
3.
4.
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. 相似文献
5.
地形改正是重力和电法勘探中用于消除测点周围地形起伏对观测结果影响的技术.由于地形形成自然电位异常的微观机理较为复杂,解析公式难以得到,可以采用最为直观的方法,寻找两者之间的拟合公式.根据研究,在自然电位梯度测量中,地形引起的自然电位异常分为两种:一是异常与地形起伏是镜像关系,这种情况占多数;另一种情况是异常与地形起伏为反镜像关系.多数地形起伏与异常存在线性关系、二次关系和指数关系,以线性关系为主.具体采用哪种拟合关系,可选取典型的地形和自然电位曲线,通过其变化规律进行判断;也可以采取试算的办法,通过改正效果的比较选择合适的拟合公式.本文选择鄂尔多斯盆地作为研究地点,提出了适用于自然电位梯度测量的地形改正方法.通过三种拟合公式改正效果的比较,得出线性拟合公式能更好地描述该测区内相对高差与自然电位改正量之间的关系.地形改正有效地消除了相对高差与自然电位之间的相关性,改正后的自然电位曲线能够较好地反映地下地质信息,自然电位等值线图异常更加突出.自然电位梯度测量中,地形起伏可影响异常形态,特别是起伏地形的面积与目标地质体的面积大小相当时,两者异常有可能难以区分,因此地形改正的研究具有重要的实用性. 相似文献
6.
Investigation of topographic reductions and aliasing effects on gravity and the geoid over Greece based on various digital terrain models 总被引：2，自引：0，他引：2
The reduction of gravity-field related quantities (e.g., gravity anomalies, geoid heights) due to the topography plays a crucial
role in both geodetic and geophysical applications, since in the former it is an intermediate step towards geoid prediction
and in the latter it reveals lateral as well as radial density contrasts and infers the geology of the area under study. The
computations are usually carried out by employing a DTM and/or a DBM, which describe the topography and bathymetry, respectively.
Errors in these DTMs/DBMs will introduce errors in the computed topographic effects, while poor spatial resolution of the
topography and bathymetry models will result in aliasing effects to both gravity anomalies and geoid heights, both influencing
the accuracy of the estimated solutions. The scope of this work is twofold. First, a validation and accuracy assessment of
the SRTM 3″ (90 m) DTM over Greece is performed through comparisons with existing global models as well as with the Greek
450 m national DTMs. Whenever a misrepresentation of the topography is identified in the SRTM data, it is “corrected” using
the local 450 m DTM. This process resulted in an improved SRTM DTM called SRTMGr, which was then used to determine terrain
effects to gravity field quantities. From the fine-resolution SRTMGr DTMs, coarser models of 15″, 30″, 1′, 2′ and 5′ have
been determined in order to investigate aliasing effects on both gravity anomalies and geoid heights by computing terrain
effects at variable spatial resolutions. From the results acquired in two test areas, it was concluded that SRTMGr provides
similar results to the local DTM making the use of other older global DTMs obsolete. The study for terrain aliasing effects
proved that when high-resolution and accuracy gravity and geoid models are needed, then the highest possible resolution DTM
should be employed to compute the respective terrain effects. Based on the results acquired from two the test areas a corrected
SRTMGr DTM has been compiled for the entire Greek territory towards the development of a new gravimetric geoid model. Results
from that analysis are presented based on the well-known remove-compute-restore method, employing land and marine gravity
data, EGM08 as a reference geopotential model and the SRTMGr DTM for the computation of the RTM effects. 相似文献
7.
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． 相似文献
8.
For airborne gravity gradiometry in rugged terrain, helicopters offer a significant advantage over fixed-wing aircraft: their ability to maintain much lower ground clearances. Crucially, this provides both better signal-to-noise and better spatial resolution than is possible with a fixed-wing survey in the same terrain. Comparing surveys over gentle terrain at Margaret Lake, Canada, and over rugged terrain at Mount Aso, Japan, demonstrates that there is some loss of spatial resolution in the more rugged terrain. The slightly higher altitudes forced by rugged terrain make the requirements for terrain correction easier than for gentle terrain. Transforming the curvature gradients measured by the Falcon gravity gradiometer into gravity and the complete set of tensor components is done by a Fourier method over gentle terrain and an equivalent source method for rugged terrain. The Fourier method is perfectly stable and uses iterative padding to improve the accuracy of the longer wavelengths. The equivalent source method relies on a smooth model inversion, and the source distribution must be designed to suit the survey design. 相似文献
9.
Ali Kiliçoğlu Ahmet Direnç Hasan Yildiz Murat Bölme Bahadir Aktuğ Mehmet Simav Onur Lenk 《Studia Geophysica et Geodaetica》2011,55(4):557-578
Turkish regional geoid models have been developed by employing a reference earth gravitational model, surface gravity observations
and digital terrain models. The gravimetric geoid models provide a ready transformation from ellipsoidal heights to the orthometric
heights through the use of GPS/leveling geoid heights determined through the national geodetic networks. The recent gravimetric
models for Turkish territory were computed depending on OSU91 (TG-91) and EGM96 (TG-03) earth gravitational models. The release
of the Earth Gravitational Model 2008 (EGM08), the collection of new surface gravity observations, the advanced satellite
altimetry-derived gravity over the sea, and the availability of the high resolution digital terrain model have encouraged
us to compute a new geoid model for Turkey. We used the Remove-Restore procedure based on EGM08 and applied Residual Terrain
Model (RTM) reduction of the surface gravity data. Fast Fourier Transformation (FFT) was then used to obtain the residual
quasigeoid from the reduced gravity. We restored the individual contributions of EGM08 and RTM to the whole quasi-geoid height
(TQG-09). Since the Helmert orthometric height system is adopted in Turkey, the quasi-geoid model (TQG-09) was then converted
to the geoid model (TG-09) by making use of Bouguer gravity anomalies and digital terrain model. After all we combined a gravimetric
geoid model with GPS/leveling geoid heights in order to obtain a hybrid geoid model (THG-09) (or a transformation surface)
to be used in GPS applications. The RMS of the post-fit residuals after the combination was found to be ± 0.95 cm, which represents
the internal precision of the final combination. And finally, we tested the hybrid geoid model with GPS/leveling data, which
were not used in the combination, to assess the external accuracy. Results show that the external accuracy of the THG-09 model
is ± 8.4 cm, a precision previously not achieved in Turkey until this study. 相似文献
10.
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. 相似文献
11.
A recently proposed method for the computation of the gravitational effect due to the topographic masses defined by a Digital Elevation Model (DEM) involves the representation of the surface relief by means of parts of bilinear surfaces. The so-called bilinear method delivers eventually the mathematical model for the gravitational attraction of a right rectangular prism, whose top is modeled by a bilinear surface. Scope of the paper is to assess the new method by conducting numerical tests using both real and synthetic data. The performance of the bilinear method is evaluated in terms of its computational efficiency as well as its precision by comparing it with other analytical methods available for the practical evaluation of gravitational terrain effects. The techniques considered for the assessment of the bilinear approximation are the vastly applied right rectangular prism method and the polyhedral modeling, a less popular but extremely flexible approach based on the closed expression for the gravity field of an arbitrarily shaped mass distribution defined by planar faces. The different geometric modeling of the topographic relief produces discrepancies to the gravitational attraction of up to several mGal. Thus the choice for the geometric representation of the terrain plays a fundamental role to the numerical computation of potential field quantities especially in the critical region surrounding the computation point. 相似文献
12.
F. Perlant 《Surveys in Geophysics》2000,21(2-3):201-207
More and more applications can benefit from having 3Dinformation or 3D terrain knowledge. After describingthe general principles of digital terrain modeling, weconcentrate on the matching step used in thestereoscopic process. Limitations encouraged us toextend the approach to multiple views, in order toautomate further the digital terrain modeling.But other ways are also possible to produce 3D terraininformation such as using different imagery (videosequences or SAR imagery) or topographic maps. Finally,when dealing with the DTM (Digital Terrain Model) orDEM (Digital Elevation Model) produced, one often hasto cope with fusion and mosaicking problems. 相似文献
13.
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. 相似文献
14.
D. J. WOODWARD 《Geophysical Prospecting》1975,23(3):526-532
Formulae for the gravitational attraction, at a point, of vertical triangular prisms with oblique ends are presented. They are suited to computation on an electronic computer and are useful for determining the thickness of sediments in a sedimentary basin by iterative means. 相似文献
15.
Hydrogeomorphic models allow parsimonious, fast and effective floodplain extent mapping using topographic data as the main input. Hydrogeomorphic approaches enforce the principle that floodplains are well-distinguished and unique landscape features within river corridors. We investigated the sensitivity of a hydrogeomorphic floodplain delineation algorithm, based on a hydrological power law, relating flow depth to contributing area, digital terrain model (DTM) resolution and river network hierarchy. In addition, we compared the results to other common floodplain mapping methods using standard flood-hazard maps as a reference. Taking the Arno River Basin, Italy, as a case study, our results show a dependency between the optimal power law parameters and DTM resolution, with larger parameter values required to reach optimal consistency with flood-hazard maps as DTM resolution increased. Floodplain mapping performance was also found to depend on stream order. We further tested the model consistency at a larger scale to evaluate its performance with respect to inundation maps in Hungary, Italy, Spain and the UK. Our study suggests that pre-defined power law parameters can be assumed, considering DTM resolution and stream order, supporting the use of the presented hydrogeomorphic model for large-scale floodplain mapping in ungauged basins where reference flood-hazard maps are not available. 相似文献
16.
Modeling of dam-break flooding in an urban residential area in southern California is presented. Modeling is performed using BreZo, an unstructured grid, Godunov-type, finite volume model that solves the shallow-water equations. The model uses terrain data from a 1.5 m Light Detection and Ranging (LiDAR) Digital Terrain Model (DTM) and contour data depicting the reservoir and breach geometry. A spatially distributed Manning coefficient based on a landcover classification derived from digital orthophotos and vector data (e.g., parcel outlines) is also used, and the interception of flow by storm drains is modeled with sink terms in the 2D continuity equation. The model is validated with flood extent and stream flow measurements, and a sensitivity analysis is completed to identify the necessary level of data and model complexity for accuracy purposes. Results show street depressions in the land surface should be resolved by the computational mesh for flood extent and stream flow accuracy. A ca. 5 m resolution mesh that spans streets by approximately 3 cells achieves a good balance between accuracy and computational effort. Results also show that heterogeneous resistance is important for stream flow accuracy, and the interception of overland flow by storm sewers is important for flood extent accuracy. The sensitivity of predictions to several additional factors such as the reservoir level, breach geometry and DTM source (LiDAR, National Elevation Data, Shuttle Radar Topography Mission Data) is also reported. 相似文献
17.
Parameters of the gravity field harmonics outside the geoid are sought in solving the Stokes boundary-value problem while
harmonics outside the Earth in solving the Molodensky boundary-value problem. The gravitational field generated by the atmosphere
is subtracted from the Earth’s gravity field in solving either the Stokes or Molodensky problem. The computation of the atmospheric
effect on the ground gravity anomaly is of a particular interest in this study. In this paper in particular the effect of
atmospheric masses is discussed for the Stokes problem. In this case the effect comprises two components, specifically the
direct and secondary indirect atmospheric effects. The numerical investigation is conducted at the territory of Canada. Numerical
results reveal that the complete effect of atmosphere on the ground gravity anomaly varies between 1.75 and 1.81 mGal. The
error propagation indicates that precise determination of the atmospheric effect on the gravity anomaly depends mainly on
the accuracy of the atmospheric mass density distribution model used for the computation. 相似文献
18.
A high resolution geophysical survey was carried out on the Pont De Coq, a medieval stone arch bridge located in Normandy (France) in 2011 and 2012. Two complementary methods are used: Electrical Resistivity Tomography (ERT) and Ground PenetratingRadar (GPR). They allow to evaluate the structural state of the bridge and to characterize the subsurface around and beneath the bridge. An excellent correlation is obtained between the geophysical methods and the geological data obtained around the bridge. In order to improve the restitution of the geophysical data, an advanced photogrammetric method is performed, providing a high resolution 3D Digital Terrain Model (DTM) of the Pont de Coq. The advanced photogrammetry enhances the presentation of the GPR and ERT data. This approach is an easy-to-use, rapid and cost-effective tool for stakeholders. Finally, it is a promising and original method for improved interpretations of future geophysical surveys. 相似文献
19.
Could surface roughness be a poor proxy for landslide age? Results from the Swabian Alb,Germany 
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下载免费PDF全文 The potential of surface roughness to quantify geomorphological landforms and processes has been enhanced with the availability of high‐resolution digital terrain models (DTM). Recent studies that attempt to identify landslide features with surface roughness have suggested that this measure of topographic heterogeneity may also be applied to estimate the relative age of landslides. This is a provisional study that explores the potential of this relationship by assessing the ability of surface roughness to act as a proxy for relative landslide age. The surface roughness for a set of 12 dated landslides in the Swabian Alb that occurred between 1789 and 1985 was calculated from a 1 m2 spatial resolution LiDAR DTM with three algorithms: root‐mean‐square‐height (RMSH), standard deviation of slope (SDS), and direction cosine eigenvalue ratios (DCE). Scale‐dependence was analysed by calculating surface roughness for a range of moving window sizes (3 × 3, 5 × 5, 9 × 9 and 15 × 15), and surface roughness for each landslide was summarized by the median and upper quartile. Only weak correlations (best Spearman's rho 0.58) were present between landslide age and surface roughness. This correlation becomes weaker with increasing moving window size. Given weak observed associations and discussed challenges pertaining to the complexities of landslide morphology change over time, we currently find that surface roughness alone may not be justifiable to act as a proxy for landslide age for our study region. Furthermore, we recommend future studies should focus on addressing possible natural and anthropogenic factors such as land use change that may alter surface roughness. These studies may focus on one of the three roughness measures used here as they are strongly correlated. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
20.
Adaptability of the ocean and earth tidal models based on global observations of the superconducting gravimeters 总被引：1，自引：0，他引：1
As the gravity field is the most primary and direct physical quantity reflecting the density variation of the Earth’s interior and its geodynamic properties under various environmental changes and as the knowledge of the fine structure of the Earth’s interior and its geo-dynamics has a strong impact on space research, grav-ity observations become more and more important in Earth sciences. Therefore based on a global network of superconducting gravimeters (SGs), the Global Geo-dynamic Proje… 相似文献