位场数据网格化的反插值法

位场不规则分布数据的网格化是位场数据分析处理的首要问题.本文借鉴反插值法的原理，提出利用基于预条件共轭梯度的反插值法实现位场数据的网格化.其中，插值算子采用高斯权系数，滤波算子采用Laplacian算子，预条件算子采用滤波算子的逆.通过理论模型和实际航磁数据的网格化试验分析，验证了本文的反插值法适合地球物理位场特征，网格化速度快，精度高，效果好.     

地质统计学在气象要素场插值的实例研究

对两种气象要素场数据分别用距离平方反比法、三次B样条和克里格（Kriging）法插值计算.比较了三种方法结果的差异和当计算场满足不同类型克里格数学假设前提下,普通克里格法（OK）与泛克里格法（UK）插值结果的异同.结果表明：克里格法的误差普遍偏小,且在插值区域峰值处克里格法的最大绝对误差和残差方差均可能较样条的小,说明只要充分了解研究区域特点,恰当选用参数,克里格法有可能得到优于样条的结果,而距离平方反比法和克里格法用全场数据插值不如使用局部数据插值的精度高,则表明内插计算具有局域性.同时还发现,虽然插值场是否满足克里格法假设对插值结果存在影响,但这种影响有时并不重要,它依赖于插值场的性质.     

格林样条插值算法及其应用

新近发展起来了一种基于双调和算子格林函数计算的数据插值方法——格林样条插值法,这是用中心点位于各观测数据点的多个格林函数进行加权叠加而解析地计算出插值曲面(曲线)的全局插值方法.本文介绍了该方法的基本原理、插值方法和实用程序的发展概况及使用中可能出现的问题.利用格林样条插值法和另两种常用插值法处理了某地布格重力异常的实测数据,对比插值结果说明,格林样条法在抑制虚假异常、稳定显示局部异常和消除奇异边缘效应等方面,具有一定的优越性.     

反插值法实现地球物理数据快速网格化

本文借鉴反演理论，采用反插值法实现地球物理数据的快速网格化.首先由已知点与未知网格点的反距离拓扑关系建立反演方程，用已知点值直接计算出其所在网格的未知网格点值，再利用Laplacian算子滤波，使得模型光滑，且能量最小化.利用预条件共轭梯度法求解网格化方程组，并结合螺旋坐标系思想和Wilson\|Burg谱分解法，将二维数据的滤波处理转换到一维空间进行处理，实现二维数据快速滤波.另外，引入了阻尼约束，保证求解稳定、迭代收敛.最后，应用该方法对合成数据和实际资料进行了试验.     

基于固定位置插值累加法的重力异常等值线图分析

相较于重力异常等值线图绘制中常用的同点差值插值法,使用了一种新重力异常等值线图的制图方法,称之为固定位置插值累加法。分别应用模拟数据及河北省2018至2021年度相对重力实测数据,使用同点差值插值法与固定位置插值累加法绘制了重力异常等值线图,并对结果进行了对比,结果表明固定位置插值累加法在使用测点数据次数和等值线密度方面有所改进。此外,参考河北省南部2018年6月至2019年10月震例,计算得出此两种方法震中与重力异常零等值线的距离。结果表明：使用固定位置插值累加法较同点差值插值法缩短了震中与震前重力异常零等值线间的距离。     

基于虚拟日变台进行地磁矢量数据日变通化方法

流动地震地磁矢量观测是一种获取地震前兆异常的方法,试验研究和观测实例表明,地震孕育引起的地磁场异常变化量级较小,因此在观测、数据处理过程中都要尽可能消除误差提高精度.本文主要从地磁矢量数据日变通化精度方面开展讨论,首先使用反距离加权插值法由泰安、武汉、崇明、杭州4个地磁台观测资料计算出蒙城地磁台相应的虚拟地磁数据,其磁偏角、水平分量、垂直分量三个要素与真实观测值的相关系数分别高达0.9987、0.9946和0.9806,验证了反距离加权插值方法对地磁观测数据空间插值的有效性.其次,选择东部和西部测区分别使用反距离加权插值方法建立各地磁矢量测点位置的虚拟日变台并用其进行通化,实例计算结果表明,该方法可有效提高日变通化精度,对于地磁台站稀疏地区更具实际应用价值.     

基于互联网信息快速估计汶川地震有感范围

通过搜索和分析互联网上有关汶川地震的信息得出,汶川地震后3h为有感信息密集发布时段,信息总量为4 515条。分析信息的发布时间、地域和有感强度分布特征,对信息按照无感、有感和强有感进行分类,提取分布于199个地区的2 289条有感信息作为数据源进行有感范围的空间插值拟合处理。空间插值选用反距离权插值、径向基函数插值和克里格插值3种方法,通过对不同插值结果的比较分析发现,克里格插值方法在一定的插值模型和参数下对有感范围的拟合效果与汶川地震实际影响范围基本吻合,尤其是强有感范围基本反映了地震灾区范围。该项研究为震后快速获取地震有感范围提供了有效途径,同时也为地震灾害速判提供了动态修正依据,为地震应急提供第一时间的灾情信息。     

三维空间内近地表激发井深设计插件的开发与应用

通过探讨三维空间内激发井深设计过程中的网格化方法、空间属性插值等关键技术,针对地震采集施工设计的应用需求,结合对比目前在野外采集施工设计中常用的近地表激发井深设计软件Surfer和油藏建模软件Earth Vision,设计了符合野外激发井深设计需求的软件流程,论证了适应井深设计要求的空间插值算法(反距离加权法和普通克里金),并通过对测线交叉异常点的自动剔除等质量控制手段,消除异常点产生的影响因子,提高了插值精度,编写了相应的核心算法模块,自主研发了一套基于VS2005 C++结合Qt4与OpenGL技术的软件产品,通过大量的实际资料数据验证与测试,在野外生产中投入应用.     

基于GIS技术的三维同震位移场构建

重特大地震引起的同震位移场对分析研究发震构造起着至关重要的作用,其空间表现形式直接影响到应急辅助决策的准确性和效率。考虑到二维同震位移场模型在内容表达和视觉效果上均存在一定的局限性,将利用汶川MS8.0级地震所获取的GPS同震位移数据,基于ArcGIS平台的ArcScene和ArcGlobe模块,先后进行数据插值处理和基本高度设置,以构建三维同震位移场模型。为使得所构建模型达到更好效果,将利用多种数据插值法进行分析对比。鉴于原始数据点密集度较低、覆盖范围集中且分布均匀,选用反距离加权法进行插值。分析比对已有研究成果,表明:模型在位移整体趋势以及极值呈现等方面均与现有成果相符合;三维同震位移场模型表达内容更加丰富、直观,视觉效果更加清晰、显著,更有助于发震机制研究以及震情、灾情的分析与决策。     

基于新型能量插值法精确建立GRACE-only地球重力场模型

本文基于新型能量插值法,利用美国喷气推进实验室(JPL)公布的2008年的GRACE-Level-1B实测数据,反演了120阶GRACE地球重力场.首先,由于GPS轨道测量精度相对较低,通过将K波段测距仪高精度的星间距离观测量插值引入双星动能差中,进而建立了新型能量插值卫星观测方程.其次,详细对比分析了2点、4点、6点和8点能量插值观测方程对地球重力场反演精度的影响.研究结果表明:基于最优的信噪比,6点能量插值公式有利于提高120阶GRACE地球重力场的反演精度.最后,基于美国、欧洲和澳大利亚的GPS/水准观测数据检验了本文新建立的WHIGG-GEGM03S地球重力场模型的正确性和有效性.     

An alternative method for estimating densification point velocity based on back propagation artificial neural networks

The establishment of Turkish National Fundamental GPS Network (TNFGN) was completed in 2001 and Large Scale Map and Map Information Production Regulation (LSMMIPR) came into force in 2005 in parallel with the establishment of TNFGN and the increase in the use of GPS applications. TNFGN has been designed as first order GPS network and it comprises second-, third- and fourth-order GPS densification networks. LSMMIPR has required determining the positions of first-, second- and third-order GPS densification (C1, C2 and C3) points with the reference epoch besides the measurement epoch. Therefore, it is necessary to estimate the velocity vectors of the densification points. In practise, the velocity vectors of C1, C2 and C3 points are estimated from TNFGN points or higher-order densification points velocity vectors by interpolation methods but LSMMIPR did not specify the interpolation method for this procedure. The objective of this study is to use a back propagation artificial neural network (BPANN) that has been more widely applied in engineering among all other neural network models for estimating the velocity of the densification point as an alternative to the interpolation methods. BPANN and selected ten interpolation methods are evaluated over a test area, in terms of root mean square error (RMSE). The results showed that the employment of BPANN estimated the densification point velocity (V_X,Y,Z) with a better accuracy (±5.0 mm, ±4.0 mm, ±3.9 mm, respectively) than the interpolation methods in the test area and indicated that BPANN can be a useful tool for estimating point velocity in the densification networks as a real alternative to the interpolation methods.     

2022年青海门源6.9级地震前岩石圈磁场异常变化分析

基于青海及甘肃部分地区2020—2021年2期流动地磁测点的观测资料,获得该地区的岩石圈磁场异常变化,通过研究岩石圈磁场各个分量的变化特征,系统分析2022年1月8日青海门源6.9级地震前岩石圈磁场的异常变化特征。结果表明：(1)门源地震前,震中区域岩石圈磁场各个分量具有较为明显的异常显示。具体表现为：震中区域附近岩石圈磁场变化的水平矢量具有方向转向及幅值弱化的异常变化现象;垂直矢量方向出现明显的南向、北向对冲的异常现象;磁偏角在震中附近具有“0”变线和高梯级带分布;总强度和垂直分量在震中附近具有“0”变线分布,并发生弯曲。(2)依据压磁效应分析,冷龙岭断裂北部岩石圈磁场增大,应力变化主要以释放为主,应力变化应处于较低水平;冷龙岭断裂南部岩石圈磁场强度减小,应力变化主要以积累为主,应力变化应处于较高水平。门源地震前,冷龙岭断裂构造应力调整引起的压磁效应可能是造成震中区域岩石圈磁场异常变化的主要原因。     

Effect of transect location,transect spacing and interpolation methods on river bathymetry accuracy

Digital elevation models (DEMs) of river channel bathymetries are developed by interpolating elevations between data collected at discrete points or along transects. The accuracy of interpolated bathymetries depends on measurement error, the density and distribution of point data, and the interpolation method. Whereas point measurement errors can be minimized by selecting the most efficient equipment, the effect of data density and interpolation method on river bathymetry is relatively unknown. Thus, this study focuses on transect‐based collection methods and investigates the effects of transect location, the spacing between transects, and interpolation methods on the accuracy of interpolated bathymetry. This is accomplished by comparing four control bathymetries generated from accurate and high resolution, sub‐meter scale data to bathymetries interpolated from transect data extracted from the control bathymetries using two transect locating methods and four interpolation methods. The transect locating methods are a morphologically‐spaced and an equally‐spaced model. The four interpolation methods are Ordinary Kriging, Delaunay Triangulation, and Simple Linear, which are applied in curvilinear coordinates (Delaunay Triangulation is also applied in Cartesian coordinates), and Natural Neighbor only in Cartesian Coordinates. The bathymetric data were obtained from morphologically simple and complex reaches of a large (average bankfull width = 90 m) and a small (average bankfull width = 17 m) river. The accuracy of the developed DEMs is assessed using statistical analysis of the differences between the control and interpolated bathymetries and hydraulic parameters assessed from bankfull water surface elevations. Results indicate that DEM accuracy is not influenced by the choice of transect location method (with same averaged cross‐section spacing) or a specific interpolation method, but rather by the coordinate system for which the interpolation method is applied and the spacing between transects. They also show negligible differences between the mean depths and surface areas calculated from bathymetries with dense or coarse spacing. Copyright © 2016 John Wiley & Sons, Ltd.     

时空Kriging算法在区域地磁场插值中的应用及改进

本文以区域地磁场为应用背景,研究了时间域信息对地磁场插值效果的影响.用时空Kriging算法进行插值时,在时空Kriging变差函数的拟合过程中,将角度信息引入向量距离,定义了新的向量距离形式,提出了改进的时空Kriging算法,并对权重的选取进行讨论.对经度87.2°E—126.6°E,纬度19.0°N—49.6°N范围内的32个台站时均值地磁场数据进行插值实验.在添加了时间信息之后,插值结果在兼顾经度方向和纬度方向变化的同时,边值问题也得以缓解,明显优于传统方法.交叉验证结果表明,随着时间域信息和向量角度的加入,Kriging算法的性能得到改进,地磁场的插值精度依次提高.对比实验中,改进Kriging算法的精度最高、性能最稳定,MAE集中在1nT左右,MSE集中在[0,5]的范围内.     

地震同震形变场失相干恢复方法研究

在合成孔径雷达干涉测量中,干涉相干是局部干涉条纹质量的重要评价标准,但是由于各种失相干源的影响,会出现失相干现象,而这可能会丢失重要的形变数据。本文首先利用ENVISAT ASAR的两景影像获得了2009年意大利拉奎拉M_W6.3地震的带有失相干现象的同震形变场,对数据预处理后再使用移动窗口克里金法对拉奎拉地震的同震形变场进行插值处理,恢复了形变图的失相干区域,之后进一步通过正反演获得同震形变场,并与上一步的插值结果进行对比分析。结果显示,插值结果与反演结果在极震区吻合得很好,验证了移动窗口克里金插值法恢复失相干的可靠性,说明插值法可以成为实现地震同震形变场失相干恢复的一种途径。      

Modelling the Velocity Field in a Regular Grid in the Area of Poland on the Basis of the Velocities of European Permanent Stations

The paper presents the results of testing the various methods of permanent stations’ velocity residua interpolation in a regular grid, which constitutes a continuous model of the velocity field in the territory of Poland. Three packages of software were used in the research from the point of view of interpolation: GMT (The Generic Mapping Tools), Surfer and ArcGIS. The following methods were tested in the softwares: the Nearest Neighbor, Triangulation (TIN), Spline Interpolation, Surface, Inverse Distance to a Power, Minimum Curvature and Kriging. The presented research used the absolute velocities’ values expressed in the ITRF2005 reference frame and the intraplate velocities related to the NUVEL model of over 300 permanent reference stations of the EPN and ASG-EUPOS networks covering the area of Europe. Interpolation for the area of Poland was done using data from the whole area of Europe to make the results at the borders of the interpolation area reliable. As a result of this research, an optimum method of such data interpolation was developed. All the mentioned methods were tested for being local or global, for the possibility to compute errors of the interpolated values, for explicitness and fidelity of the interpolation functions or the smoothing mode. In the authors’ opinion, the best data interpolation method is Kriging with the linear semivariogram model run in the Surfer programme because it allows for the computation of errors in the interpolated values and it is a global method (it distorts the results in the least way). Alternately, it is acceptable to use the Minimum Curvature method. Empirical analysis of the interpolation results obtained by means of the two methods showed that the results are identical. The tests were conducted using the intraplate velocities of the European sites. Statistics in the form of computing the minimum, maximum and mean values of the interpolated North and East components of the velocity residuum were prepared for all the tested methods, and each of the resulting continuous velocity fields was visualized by means of the GMT programme. The interpolated components of the velocities and their residua are presented in the form of tables and bar diagrams.     

Modeling and Mapping High Water Table for a Coastal Region in Florida using Lidar DEM Data

Predicting and mapping high water table elevation in coastal landscapes is critical for both science application projects like inundation risk analysis and engineering projects like pond design and maintenance. Previous studies of water table mapping focused on the application of geostatistical methods, which cannot predict values beyond an observation spatial domain or generate an ideal pattern for regions with sparse measurements. In this study, we evaluated the multiple linear regression (MLR) and support vector machine (SVM) techniques for high water table prediction and mapping using fine spatial resolution lidar-derived Digital Elevation Model (DEM) data, and designed an application protocol of these two techniques for high water table mapping in a coastal landscape where groundwater, tide, and surface water are related. Testing results showed that SVM largely improved the high water table prediction with a mean absolute error (MAE) of 1.22 feet and root mean square error (RMSE) of 2.22 feet compared to the application of the ordinary Kriging method which could not generate a reasonable water table. MLR was also promising with a MAE of around 2 feet and RMSE of around 3 feet. The study suggests that both MLR and SVM are valuable alternatives to estimate high water table elevation in Florida. Fine resolution lidar DEMs are beneficial for high water table prediction and mapping.     

Topographic accuracy assessment of bare earth lidar-derived unstructured meshes

This study is focused on the integration of bare earth lidar (Light Detection and Ranging) data into unstructured (triangular) finite element meshes and the implications on simulating storm surge inundation using a shallow water equations model. A methodology is developed to compute root mean square error (RMSE) and the 95th percentile of vertical elevation errors using four different interpolation methods (linear, inverse distance weighted, natural neighbor, and cell averaging) to resample bare earth lidar and lidar-derived digital elevation models (DEMs) onto unstructured meshes at different resolutions. The results are consolidated into a table of optimal interpolation methods that minimize the vertical elevation error of an unstructured mesh for a given mesh node density. The cell area averaging method performed most accurate when DEM grid cells within 0.25 times the ratio of local element size and DEM cell size were averaged. The methodology is applied to simulate inundation extent and maximum water levels in southern Mississippi due to Hurricane Katrina, which illustrates that local changes in topography such as adjusting element size and interpolation method drastically alter simulated storm surge locally and non-locally. The methods and results presented have utility and implications to any modeling application that uses bare earth lidar.