用边界单元法模拟二维地形对大地电磁场的影响

本文用边界单元法模拟二维地形对大地电磁场的影响.首先用格林公式将二维大地电磁的边值问题转变成积分方程,然后用边界单元法解积分方程,得到地形上的大地电磁场和它的法向导数,由此可计算电阻率.与有限单元法相比,本方法剖分后的地形与实际地形的拟合程度高,向计算机输入原始数据的工作简单,可以在微机上计算地形引起的视电阻率.本方法适合于在野外生产现场进行大地电磁法的地形改正.计算表明,地形对H_x型波的影响比对E_x型波严重得多;随着周期的增长,地形对H_x型波的影响变得稳定.     

海洋重力勘探中的完全布格校正

海洋重力测量由于海底地形的复杂性,需要在简单布格校正的基础上加入海底地形校正,从而使理论地球模型更好的符合实际的地球椭球体.本文总结了完全布格校正的理论,从空间域和频率域的角度对中间层和地形校正的方法作了介绍,并引入了一种综合的方法且将之运用到了实际的工作中,并取得了很好的效果.     

A rapid method for simulating three-dimensional fluvial terrain

A rapid, computer-based method of simulating ‘geomorphologically-sensible’ three-dimensional terrain data by modelling landform morphology is presented. For some engineering applications such an approach, even in a simple form, is preferable to the synthesis of terrain data by purely stochastic methods, and additionally can be useful where real data sets are difficult to obtain. The approach adopted utilizes a computer program which models landscape evolution by establishing a stream network on a tilted surface, with accompanying fluvial downcutting and slope adjustment. This is achieved by an iterative mechanism that combines deterministic and stochastic processes with geomorphological theory. The end-product is a matrix of high-resolution altitude data that has been used as the terrain model for a vehicle simulation exercise.     

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．     

复杂地形条件下四面体剖分电阻率三维有限元数值模拟

地形起伏对电阻率影响非常大,复杂地形条件下的电阻率异常解释一直受到很多的关注.本文提出了一种四面体网格交叉剖分方法,剖分的网格相互交错,使剖分的网格具有多样性,能较好地模拟复杂地形情况下的地电模型.同时,从点电源场满足的方程出发,本文推导了三维复杂地形条件下有限元数值模拟算法,并编制了计算程序.算例表明,本方法行之有效,计算精度高.     

The prism method for terrain corrections using digital computers

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.     

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.     

Heli-borne gravity gradiometry in rugged terrain

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.     

Comparing seismic susceptibility models of the Himalayan terrain

The ongoing intra-continental collision between the Indian and Eurasian plates along the Himalayas has resulted in many damaging earthquakes with severe damages to man-made structures and natural landscapes due to ground shaking and ground failure, which in turn depends on geomorphological, geological and geophysical variables. Seismic susceptibility models are developed for Gangtok City by combining all the three variables using both knowledge-driven and data-driven methods on facet and grid cell terrain units. Finally, the results are critically evaluated by validation with the earthquake intensity data recorded during earthquake events. First-stage modelling attempt using different knowledge-driven methods on different terrain units shows bi-modal data distribution with low predictability due to extremely rugged topography with wide altitudinal variations within short distances. Second-stage modelling of separated population by using the same methodologies increases model predictability in which one model method describes the higher topographic levels better and the other model method is found to be better for lower topographic levels. Seismic susceptibility of the area is best described by composite models, combining different best methods of fine classification for lower and higher topographic levels having the same mapping/terrain units. Comparison of the composite models shows that the terrain unit does not play a significant role but the type of models selected determines the best possible seismic susceptibility map of the area.     

川滇区域高频地震动地形效应初探

历次强震表明:局域起伏地形对由高频地震动起决定作用的震害存在显著影响。忽略场地浅表土层的影响,凸起地形场地震害高于凹陷地形。然而,由于地形效应影响因素的复杂多样以及公认地形效应表征模型的缺失,已有的宽频带地震动模拟与预测方法并未考虑高频地震动地形效应,这可能导致对地震动时程及参数的错误估计。为此,本文利用当前较具代表性的地形效应量化表征模型,初步分析了川滇区域高频地震动的地形效应。首先,给出了基于量化表征模型的区域高频地震动地形效应计算分析方案;其次,完整地阐述了该方案在川滇地区的应用,并结合漾濞地震震害考察结果初步验证了川滇高频地震动地形效应分析结果的可靠性;最后,讨论了分析结果的局限并给出其应用于宽频带地震动模拟与预测方法中的初步建议。     

Modelling the 2D terrain effect on MT by the boundary-element method

The boundary-element method is used to model the 2D terrain effect on the magnetotelluric (MT) field. Firstly, the boundary-value problem of a 2D magnetotelluric field is transformed into an integral equation problem by using Green's theorem. Then the boundary-element method is used to solve the integral equation and to obtain the MT field and its normal derivative on the terrain. From these values, the apparent resistivity can be calculated. Compared with the finite-element method, the boundary-element method is simpler in element division and the initial data preparation. The configuration of a terrain divided by the boundary-element method is more consistent with the practical terrain. The method proposed in this paper can be run on a microcomputer, so that it can be used in the field.     

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.     

A priori models and inversion of gravity gradient data in hilly terrain

The increased popularity of airborne measurements of the gravity gradient tensor for resource studies and geological mapping has resulted in a new awareness of the importance of terrain effects. In these measurements, the terrain effect often overwhelms that of the underlying crust and it becomes important to formulate a strategy for taking it into account when presenting the data and when inverting the data into density models. Using newly acquired data from Northern Sweden, we first attempted to estimate a variable terrain density model by inverting the data using a terrain model with a laterally varying density. Using data weights related to the topography variations, we find the best estimate of the lateral variation of the terrain density. We translate this model into a full three-dimensional model such that all columns have the same vertical centre of mass as estimated from inspecting the radially averaged power spectrum of the area. This then defines a reference model for subsequent three-dimensional inversion of the gravity gradient tensor dataset. We tested this approach first on synthetic data calculated from the measured topography including two density anomalies before we applied it to the measured data. The result is a model in which the surface density variations are propagated downwards in a systematic manner now in better agreement with measured densities of rock samples in the area.     

Effects of Interpolation Errors on the Analysis of DEMs

A suite of methods to interpolate a digital elevation model from a ground survey was evaluated with respect to precision and ability to maintain the shape of the original height data. This shape reliability was evaluated by comparing the spatial patterns of secondary terrain parameters derived from the interpolated elevation data. The best interpolation method for this study area was found to be a spline interpolation, which is somewhat contradictory to findings in the literature. The error and uncertainty found in the results for terrain analysis and modelling tools is important and sometimes distressingly high, even for some frequently used local or context operations on altitude. Positional operations, in which the output is determined more by the position in the topographic structure, seem to give more reliable results. Therefore, the results obtained by terrain analysis and spatial modelling need careful interpretation. © 1997 John Wiley & Sons, Ltd.     

时域瞬变电磁法三维有限差分正演技术研究

瞬变电磁法应用广泛,三维数值模拟是研究复杂地质模型异常响应规律的重要技术手段之一,也是反演的基础.目前瞬变电磁数值模拟的不足主要有两个方面:第一,场源是在地表水平、浅层介质均匀的条件下计算的,限制了应用范围;第二,地下边界采用Dirichlet边界条件,导致计算空间很大,耗时较长.针对上述问题,在三维正演时,场源采用有限长细导线模型,在Maxwell有源差分方程中直接加入电流密度进行计算.在地表面加入空气层,避免了复杂的向上延拓计算,也可以对地形影响下的响应规律进行分析.在空气边界和地下边界均采用CPML吸收边界条件,并改进了CPML的参数分布,能够吸收空气介质和大地介质中的低频电磁波而反射误差极小,在满足计算精度的条件下可以有效减小节点数量.对循环迭代方法进行优化,将计算域、CPML区域和场源的空间循环统一转化为矩阵方式,加快了计算速度,但是空间消耗增大了约4~5倍.采用三维有限差分正演算法对均匀半空间模型、层状模型和地形模型进行了计算,并与解析解进行了对比验证.     

起伏地形下CSAMT二维正反演研究与应用

CSAMT在山区金属矿勘查中,采用各种滤波和相位积分之类的处理方法,校正因地形起伏和局部电性不均匀引起的静态效应,往往难保奏效,开发消除静态效应的新方法是提高CSAMT资料处理与解释水平和方法应用效果的重要研究课题. 本文以如何消除地形影响为重点,对起伏地形下CSAMT二维大地三维源地电模型,采用加权余弦数值积分法,进行波数域电磁场二维有限单元法正演. 为模拟复杂地形地电模型,选取交叉对称网格三角形剖分法,实现了在国内常用赤道电偶极装置的CSAMT二维正演计算;在二维正演的基础上,开发了基于奥克姆反演法的CSAMT二维反演技术,研制出一套起伏地形下CSAMT二维正反演处理与解释方法技术系统. 通过理论模型试算和实测数据处理证实,本系统能有效地削减起伏地形影响. 在找矿应用中,该系统反演的电阻率断面,极大地消除了起伏地形影响和静态效应,突显出清晰的控矿构造和矿体的异常,取得了重要成效.     

日本琵琶湖流域大气边界层的三维数值模拟

本文在地形坐标下引入一种水平导数差分近似方法,建立一个适合日本琵琶湖复杂地形、满足静力平衡条件的三维非定常大气边界层数值模式。在弱的背景风场下,模式加入了琵琶湖流域的实际地形,计算结果表明:模式运行十分稳定,且占机内存小,节省计算时间,同时模式还做了流域地形、湖泊本身存在与否等因子对边界层风场影响的数值试验。在强的背景风场下,模式加入了经过适当平滑的琵琶湖流域地形,得出了一些有益的看法。     

Analytical trajectory model of air pollution

Summary The basic principles of the method of calculating air pollution in a complex terrain are presented. The method is based on a trajectory air pollution model. The formula for the distribution of pollutant concentration in a puff is obtained by solving a simple turbulent diffusion equation analytically. An example of the model's application is given.     

Assessment of the hydraulic slope flow approach using a mesoscale model

The simplified hydraulic two-layer model for a katabatic flow is analysed using the outputs from a high-resolution mesoscale simulation. A stably stratified night is simulated for the Duero basin, a complex terrain area located in the northern Spanish plateau, with large vertical and horizontal spatial resolution. Well-defined katabatic flows on the basin slopes are generated by the simulation, that are relatively stationary and quasi-bidimensional for some areas in the central part of the night. The bulk quantities used in the two-layer approach as well as the different terms in the equations are computed from the three-dimensional information provided by the mesoscale simulation. This method allows to inspect how well the simplified approach represents the katabatic flow generated by the mesoscale model. The study shows that the hydraulic model allows for a comprehensive analysis of the basic mechanisms of the slope flows but is not able to close the budget equations, since the residuals are large.     

Numerical modeling of 3-D terrain effect on MT field

Using the boundary element method, the numerical modeling problem of three-dimensional terrain effect on magnetotelluric (MT) field is solved. This modeling technique can be run on PC in the case of adopting special net division. The result of modeling test for 2-D terrain by this modeling technique is basically coincident with that by 2-D modeling technique, but there is a great difference between the results of 3-D and 2-D modeling for 3-D terrain. Project supported by the National Natural Science Foundation of China.