EGM2008重力场模型在兴城物探测量中的应用

以吉林大学兴城物探教学实习测网为例,基于EGM2008重力场模型,采用二次曲面、移动曲线、最小二乘配置、三次样条和反距离加权改正插值法,计算了不同GPS水准点密度情况下的水准面模型,并利用二等水准测量方法验证了计算精度,分析了该模型的适定性。结果表明,三次样条插值法的精度和稳定性最高,其次是移动曲线法和最小二乘配置法;二次曲面拟合的精度最低,反距离加权改正法稳定性最差。所有算法都表明,在研究区,当GPS水准点间隔20 km时,基于EGM2008模型确定的大地水准面精度在0.1 m以内;而采用单独GPS水准点的区域大地水准面模型能达到14cm,完全满足各种比例尺情况下的石油物探测量要求。     

地球物理勘探中几种二维插值方法的误差分析

为了研究采样和网格化方法对地球物理数据成图精度的影响,为野外数据采集布设提供一定的依据,采用数值模拟确定重力异常场场值,通过不同采样间距和不同插值方法计算重力异常绝对误差均方根值和节点处的绝对误差值,对比不同插值方法的误差,得到了如下认识：1）对于同一插值方法而言,存在小间距绝对误差均方根值小于大间距绝对误差均方根值的关系。2）对不同的插值方法而言:当采样间距小于最小异常地质体尺度时,绝对误差均方根值由小到大的顺序是径向基函数法、改进的谢别德法、克里金插值法、自然邻点法、反距离加权插值法、最近邻点法、最小曲率法,并且线性插值三角网法与自然邻点法具有几乎相同的数值;当采样间距大于最小异常地质体尺度时,绝对误差均方根值由小到大的顺序是径向基函数法、改进的谢别德法、克里金插值法、自然邻点法、最小曲率法、最近邻点法、反距离加权插值法,并且线性插值三角网法和自然邻点法具有几乎相同的数值。3）从绝对误差均方值看,径向基函数方法、改进的谢别德方法和克里金方法数值较小,其中径向基函数值绝对误差均方根值最小。4）从节点处绝对误差值来看,径向基函数方法、克里金方法、改进的谢别德方法相对其他插值方法具有更小的误差,不存在局部误差较小或较大的情况,是相对较好的插值方法,并且径向基函数方法是最好的。     

地球重力模型及中国大陆重力场的计算

融多颗卫星数据、地面重力值和其它资料一起的地球重力模型EGM 96 ,为研究中国大陆的重力场及相关问题提供了一个高精度 36 0阶的球谐系数。在分析EGM 96的基础上 ,计算并简单解释了中国大陆的自由空气异常和布格重力异常。计算所得重力场的精度和分辨率大大高于常用的1∶140 0 0 0 0 0自由空气异常图及布格重力图     

Interpolation with Splines in Tension: A Green''s Function Approach

Interpolation and gridding of data are procedures in the physical sciences and are accomplished typically using an averaging or finite difference scheme on an equidistant grid. Cubic splines are popular because of their smooth appearances; however, these functions can have undesirable oscillations between data points. Adding tension to the spline overcomes this deficiency. Here, we derive a technique for interpolation and gridding in one, two, and three dimensions using Green's functions for splines in tension and examine some of the properties of these functions. For moderate amounts of data, the Green's function technique is superior to conventional finite-difference methods because (1) both data values and directional gradients can be used to constrain the model surface, (2) noise can be suppressed easily by seeking a least-squares fit rather than exact interpolation, and (3) the model can be evaluated at arbitrary locations rather than only on a rectangular grid. We also show that the inclusion of tension greatly improves the stability of the method relative to gridding without tension. Moreover, the one-dimensional situation can be extended easily to handle parametric curve fitting in the plane and in space. Finally, we demonstrate the new method on both synthetic and real data and discuss the merits and drawbacks of the Green's function technique.     

Recent geoid computations for the Hellenic area

New geoid computations for the Hellenic area are carried out using (a) gravity anomalies for the land area available from old and new data bases, and gravity data for the sea area derived from altimetry and a recent digitization of sea gravity maps, and (b) a 1km × 1km digital terrain model. The EGM96 geopotential model is used as the reference field. In order to assess the quality of the computed geoid heights in the continental area comparisons were carried out with GPS/leveling heights and the recently available European Gravimetric Geoid EGG97. In the sea area the geoid heights were compared with sea surface heights of the recent and more accurate TOPEX/POSEIDON (T/P) altimetry mission. At the end of this article the improvement of the data bases is discussed and some plans for further development in the methodological schedule are pointed out.     

Interpolation with Splines in Tension: A Green's Function Approach

Interpolation and gridding of data are procedures in the physical sciences and are accomplished typically using an averaging or finite difference scheme on an equidistant grid. Cubic splines are popular because of their smooth appearances; however, these functions can have undesirable oscillations between data points. Adding tension to the spline overcomes this deficiency. Here, we derive a technique for interpolation and gridding in one, two, and three dimensions using Green's functions for splines in tension and examine some of the properties of these functions. For moderate amounts of data, the Green's function technique is superior to conventional finite-difference methods because (1) both data values and directional gradients can be used to constrain the model surface, (2) noise can be suppressed easily by seeking a least-squares fit rather than exact interpolation, and (3) the model can be evaluated at arbitrary locations rather than only on a rectangular grid. We also show that the inclusion of tension greatly improves the stability of the method relative to gridding without tension. Moreover, the one-dimensional situation can be extended easily to handle parametric curve fitting in the plane and in space. Finally, we demonstrate the new method on both synthetic and real data and discuss the merits and drawbacks of the Green's function technique.     

快速样条函数插值网格化法

网格化是物化探数据处理的重要环节。本文采用首次提出的快速样条函数插值方法对二维离散数据进行曲面插值，进而作网格化计算。算例表明，本文网格化方法精度高、计算速度快。     

EGY-HGM2016: an improved hybrid local geoid model for Egypt based on the combination of GOCE-based geopotential model with gravimetric and GNSS/levelling measurements

An improved hybrid gravimetric geoid model for Egypt, EGY-HGM2016, has been recently computed implementing the least-squares collocation (LSC) method through the remove-compute-restore (RCR) procedure. The computation of EGY-HGM2016 involves different datasets in terms of gravity anomalies determined from the GOCE (gravity field and steady-state ocean circulation explorer)-based global geopotential model (SPW-R4) up to d/o 200 and EGM2008 from d/o 201 to 720 combined with terrestrial gravity datasets in terms of 2140 gravity field anomalies and about 121,480 marine surface gravity anomalies. In addition, orthometric heights from 17 GPS/levelling measurements have been considered during the modelling process to improve the determination of the hybrid gravimetric geoid over the Egyptian region. The EGY-HGM2016 model estimated over Egypt provides geoid heights that are ranging from 7.677 to 21.095 m with a standard deviation (st. dev.) of about 2.534 m in the northwest of the country excluding the involvement of the orthometric heights from GPS/levelling measurements. When the later dataset is considered during the implementation of LSC process, hybrid residual height anomalies ranging from ?1.5 to +0.9 m, with a mean of 0.22 m and a st. dev. of 0.17 m, are obtained. Comparison of the predicted hybrid gravimetric geoid with the corresponding ones obtained from EGM2008, GOCE-based SPW R4 model, and GPS/levelling reveals considerable improvements of our EGY-HGM2016 model over Egypt.     

Utilisation of Fast Fourier Transform and Least-squares Modification of Stokes formula to compile a gravimetric geoid model over Khartoum State: Sudan

We use Fast Fourier Transform (FFT) and least-squares modification (LSM) of Stokes formula to compute the geoid over Khartoum State in Sudan. The two methods (FFT and LSM) have been utilised to test their efficiency with respect to EGM08 and the local GPS-levelling data. The FFT method has many advantages, it is fast and it reduces the computational complexity. The modification of Stokes formula is widely used in geoid modelling; however, its implementation based on point-wise summation requires a considerable amount of time. In FFT, we combine the terrestrial gravity data and the global geopotential model (GGM) by means of a remove-compute-restore procedure and we successfully apply the modification of the Stokes formula in the least-squares sense. FFT and LSM geoid solutions are evaluated against EGM2008 and the GPS-levelling data. The analysis of the undulation differences shows that the LSM solution is more compatible with EGM08 and GPS-levelling data. The discrepancies of the differences are removed using a 4-parameter model, the standard deviation (STD) of the undulation differences of LSM decreased from 0.41 to 0.37 m and from 0.48 to 0.39 m for FFT solution. There is no significant impact to the LSM geoid when adding the additive corrections, while the FFT geoid solution is slightly improved when terrain correction is applied.     

http://www.sciencedirect.com/science/article/pii/S1674987113000510

In this paper,we analyze lithospheric density distribution of China and surrounding regions on the basis of 300300gravity data and 1 1 P-wave velocity data.Firstly,we used the empirical equation between the density and the P-wave velocity difference as the base of the initial model of the Asian lithospheric density.Secondly,we calculated the gravity anomaly,caused by the Moho discontinuity and the sedimentary layer discontinuity,by the Parker formula.Thirdly,the gravity anomaly of the spherical harmonics with 2e40 order for the anomalous body below the lithosphere is calculated based on the model of EGM96.Finally,by using Algebra Reconstruction Techniques(ART),the inversion of 300300residual lithospheric Bouguer gravity anomaly caused by the lithosphere yields a rather detailed structural model.The results show that the lithospheric density distribution of China and surrounding regions has a certain connection with the tectonic structure.The density is relatively high in the Philippine Sea plate,Japan Sea,the Indian plate,the Kazakhstan shield and the Western Siberia plain,whereas the Tibetan Plateau has low-density characteristics.The minimum value of density lies in the north of Philippines,in the Taiwan province and in the Ryukyu island arc.     

Study of geoid–quasigeoid separation obtained from terrestrial gravity data and two geopotential models

In this article, separation between the geoid and the quasigeoid was calculated using ground gravity data and the data extracted from two Global Geopotential Models (GGMs). The calculated results were compared together. To do so, the authors used the terrestrial gravity data in a vast region of Iran, comprising 8,245 stations which are kindly put in our disposal by the National Cartographic Center of Iran, as well as two GGMs, namely EGM96 and EGM2008 for comparison. The calculation of the separation for GGMs was performed by iteration method. The results showed that the geoid–quasigeoid separations obtained from the terrestrial data versus the orthometric heights are nonlinear in mountainous areas, whereas they are almost linear in flat regions due to decreasing the values of the topographic potential of the masses between the earth surface and the geoid. On the other hand, in case of GGMs, a positive correlation was observed between the separations and the orthometric heights in both mountainous and flat areas. As the difference between the separations extracted by two methods in mountainous areas—especially in the regions with ragged topography—differs strongly, it is recommended to use the dense gravity and height networks for accurate determination of the geoid–quasigeoid separation in these regions. Finally, we can conclude that the mean values of separation by two global geopotential models (EGM96 and EGM2008) are 21.87 and 21.23 cm, respectively, values which did not differ strongly, whereas this mean value obtained from ground gravity data is 16.10 cm, which differs from the GGMs’ results with approximately 5 cm.     

复杂条件二维重力场及重力张量场空间波数域正演方法

随着传感器技术的发展,重力场与重力张量场测量技术发展迅速,为实现地下密度分布精细反演提供了数据保障。正演是反演的基础,解决任意密度分布复杂地质体重力场与重力张量正演高效、高精度计算问题,是实现重力高效、精细反演、人机交互反演解释的关键。针对起伏地形和任意密度分布这种复杂条件下二维重力场及重力张量场高效高精度正演问题,这里提出了一种空间波数混合域正演算法,其关键环节包括:①结合新的矩形二度体组合模型波数域表达式和一维Gauss-FFT算法,提出了一种任意密度分布和起伏地形下重力场及重力张量高效、高精度正演算法;②采用新的二维正演算法,计算观测最高点和最低点之间多个不同高度水平网格重力场及重力张量,结合三次样条插值方法,实现了起伏地形上重力场及重力张量场高效、高精度正演。模型算例结果表明,新方法具有高效、高精度的显著特点。     

Different ways to handle topography in practical geoid determination

In this paper two different methods of how to handle topography in geoid determination is investigated. First method employs the Residual Terrain Model (RTM) remove-restore technique and yields the quasigeoid, whereas the second method is the classical Helmert condensation method, yielding the geoid. Both methods were used with the Earth Gravity Model (1996) (EGM96) geopotential model as reference, and results are compared to precise Global Positioning System (GPS) levelling networks in Scandinavia, especially an accurate GPS data set from the very rugged Sognefjord region, where the topography was represented by either a detailed (100 m) or a coarse (1000 m) digital terrain model. The inclusion of bathymetry in the terrain model was also investigated.Even if two different methods were used, they produced almost identical results at the 5 cm level in the mountains, but small systematic differences exist. Results show the importance of comparing the right types of geoid (classical geoid or quasigeoid), since differences in residuals are significant.     

一种实用的等值线型数据网格化方法

数据网格化通常包括三大类:测线型数据网格化、等值线型数据网格化和离散点型数据网格化。文中研究的等值线型数据分块存储、网格点八方位搜索插值的网格化方法较好地解决了平面等值线型数字化数据的网格化计算问题,其计算数据量大,实用性强,精度高,计算速度快。     

基于ABC-GRNN组合模型的露天矿边坡变形预测

准确预测露天矿边坡变形是有效实现边坡临灾预警的重要保证,针对传统边坡变形预测方法无法表征和综合分析边坡变形受多种因素的影响,提出一种露天矿边坡变形的人工蜂群(ABC)算法优化广义回归网络(GRNN)组合预测模型(ABC-GRNN)。在此预测模型中,综合考虑了影响露天矿边坡变形的5个因素：开采扰动、降雨量、降雨持续时间、温度以及湿度。以山西中煤平朔安家岭露天矿为例,通过遗传算法改进BP神经网络(GA-BPNN)、支持向量机(SVM)等人工智能算法与实测变形数据进行预测效果对比分析。结果表明：ABC算法能够快速帮助GRNN寻优获取合适的传递参数,并对变形进行有效的预测。ABC-GRNN组合预测模型,将预测结果的平均绝对误差292.9 mm、平均绝对百分比误差0.691 3%及均方根误差338.9 mm分别降低到25 mm、0.043 3%和29.5 mm,说明该模型具有更高的预测精度;ABC-GRNN模型比其他模型收敛速度快,只经过7步的迭代,即可得到最小的均方误差。与其他预测模型相比较,本文模型的预测精度更高、泛化能力更强、收敛速度更快,有较高的实用价值。     

地面重力数据结合GPS/水准数据精化兴城物探实验区大地水准面

区域大地水准面的确定是GPS测量常需解决的问题。目前确定大地水准面的方法主要包括重力法、GPS水准几何法及组合法,其中组合法因其精度和可靠性都较高,常用于计算高精度区域大地水准面。高精度的大地水准面模型是组合法确定区域大地水准面的关键。在我国,EGM2008全球重力场模型精度和分辨率均高于此前的所有模型,研究基于该模型的组合法大地水准面精化具有重要的实践意义。笔者以吉林大学兴城教学实习基地物探实验区为例,基于实测重力数据、EGM2008重力场模型和GPS水准数据,采用组合法精化了区域大地水准面,比较了组合法大地水准面模型和无重力实测数据的几何法大地水准面模型的精度差异,分析了该方法在物探测量中的适用性。结果表明,实验区组合法大地水准面模型精度最高达到1.2 cm,并且误差分布区间较小,总体上精度和可靠性高于对比的几何方法,并且组合法和几何法获取的两种大地水准面模型均能满足大比例尺物探测量要求。EGM2008模型精度较高,故平坦地区使用组合法时,高密度的实测重力数据可能带来高频扰动,有可能降低EGM2008重力场模型本身的精度,所以重力数据采集过程中要顾及重力点的密度和空间分布。本文方法更适用于地形复杂的地区。     

均衡重力异常计算方法

本文提出了采用埃利均衡补偿模式计算5ˊ×5ˊ平均均衡重力异常的一种方认。计算是使用5ˊ×5ˊ平均高程值,将A～O带分为近、中、远三个区:近区用1ˊ40〞×1ˊ40〞的柱体,中区用5ˊ×5ˊ的柱体,远区用15ˊ×15ˊ的柱体,分别采用矩形柱体、质线和质点的正演公式计算地形一均衡校正值。从华南某地区的均衡重力异常图可以看出,根据均衡重力异常可以消除由地壳厚度变化而产生的区域场,突出局部异常场。     

油藏数值模拟中地质模型的建模流程与方法

围绕油藏数值模拟过程中三维地质模型的建模技术进行了分析与探讨,详细介绍了基于角点网格模型的建模方法,给出了相应的实现步骤。其主要流程是:首先根据断层数据构造断层模型,在断层模型的基础上构建骨架模型;然后在骨架模型约束下采用地层恢复技术实现含断层的地层模型;最后基于结构模型插值物性参数完成属性模型。以塔河油田缝洞型油藏为例,对建模流程和技术的可行性进行验证,结果表明,其建模结果与专业地质建模软件Petrel相符。     

Using Newton's law and geophysical bounds on mass density contrast to ensure consistency between gravity and height data

In this paper we advocate the use of Newton's law of gravitational attraction to ensure perfect consistency between gravity and height data. Starting with the absolute gravity on the topography we decompose this signal into a number of quantities associated with physics of the system. To model gravitational attraction from topography we use DTM and Newton's law of gravitational attraction. A residual part of the gravity signal is interpreted as inconsistency between gravity and heights. In the paper we discuss a method by which such inconsistency (at least in principle) can be decomposed into a “gravity error” and a “terrain error”. In practice such separation is not possible because the two types of error are nearly 100% correlated. The inconsistency can be interpreted as a measure of ambiguity of the gravity-terrain models which are consistent with a set of measured/interpolated data. We discuss the influence of such ambiguity on the accuracy of the geoid for the investigated area of Jutland, Denmark.     

逐点激发井深设计网格化方法的选取

随着地震勘探的不断深入,地震资料采集要求主频足够高,频带足够宽,能量足够强,而逐点激发井深设计有助于获得满意的地震信号,要设计合理的井深,网格化方法的选取非常重要。这里首先介绍了Surfer软件中十二种网格化方法原理特征,以及在逐点井深设计上的应用;然后运用Surfer软件中不同的插值方法,对BIN12工区岩性数据进行网格的效果对比与网格的密度探讨,选取了最佳的网格化方法;最后针对几种网格化方法进行井深对比试验,通过资料分析,说明了设计的井深合理,选取网格化方法的效果较好。