基于Taylor和Legendre多项式模型的截断阶数和边界效应研究（英文）

当利用Taylor多项式和Legender多项式建立区域地磁场模型时,会碰到两个问题:截断阶数的选取与边界效应的控制.现以常用的Taylor多项式模型和Legendre多项式模型为例,结合中国地区1970.0和2000.0年的地磁场实测数据,提出一种可解决以上两种问题的应用方案.为了进行综合比较和研究,还采用了最新的全球模型——IGRF11和CM4.结果显示通过计算两种模型的均方根偏差(RMSE)和AIC(AIC信息标准)值,并与IGRF11及CM4的均方偏差相比较,可以初步确定截断阶数的选取范围,比较各阶截断阶数的AIC值,可进一步获取合适的截断阶数.通过首次提出的"异常区域添加法"和"均匀添加法"逐步增加境外补充点,结果显示当不断增加补充点后,境外的磁异常的分布大为改善,并与IGRF11的分布高度一致.随着补充点的增加,极值点强度逐渐减弱并趋于稳定."均匀添加法"可更好地控制中国地区的地磁场边界效应.提出了一种可通过两个个步骤以确定最适截断阶数的方法,还提出了两个标准从而可初步确定补充点的数量,从而能够较好地控制边界效应.对于两种模型所反映的一些境外磁异常,可通过实地测量或是在磁异常周围增加测点而验证.     

基于CHAMP卫星与地面矢量数据联合建立中国地磁模型

首先对地面台站以及CHAMP卫星的矢量磁测数据进行预处理,结合12个子午工程台站最新的磁测数据,并利用第十二代国际地磁参考场模型(IGRF12)对不同数据归算至统一时间点,再结合第四代地磁场综合模型(CM4)计算并移除主磁场、磁层磁场、电离层磁场、感应磁场及较为微弱的环形场,最后通过球冠谐(SCH)模型联合建立了中国地区岩石圈磁场(地磁要素X、Y、Z和总强度F)的球冠谐模型(SCH2000),结合IGRF12得到了中国地磁模型(CGRF2000).建模同时考虑了测点数据海拔高度的影响,并讨论了截断阶数的选取以及边界效应的控制问题.通过比较均方偏差(RMS),认为8阶SCH2000模型可较好地反映中国地区岩石圈磁场,其分布与SCH1936、CM4以及Taylor多项式模型具有一定的相似性.从位置和强度来看,SCH2000模型所反映的岩石圈磁场更为准确,而与CM4存在一定差异,除了测点不同,截断阶数也是原因之一.通过验证,SCH2000模型各要素随高度的变化与CM4模型较为一致,所建立的CGRF2000与IGRF12模型的分布也较为相似.     

两种地磁场模型与地磁台站年均值一致性分析

研究了地磁场综合模型CM4和国际参考地磁场模型IGRF12与中国部分地磁台站年均值的一致性,并分析CM4与IGRF12模型之间的差异,结果表明,模型值与台站观测值的差值不随台站经纬度的改变而呈现规律性变化,两种模型值与台站观测值差值的两种变化形态相差较大;同一台站,同一地磁分量,两种地磁场模型的误差水平基本相当;同一地...     

基于第十三代国际地磁参考场模型在中国区域特征分析与研究

根据最新的第十三代国际地磁参考场模型（IGRF13）,计算了2015—2020年中国区域地磁场模型七要素长期变化速率,并在此基础上分析我国区域地磁场长期变化特征。通过分析计算我国28个地磁台的IGRF13模型值与实际地磁场的长期变化速率、差值及均方误差,结果显示：IGRF13模型所显示的地磁场长期变化与我国区域地磁场实际观测变化基本一致,但在局部区域也存在差异,IGRF13模型能够体现中国区域地磁场的特征。应用IGRF13模型数据时需要考虑局部区域与台站实际观测数据的误差。     

CM4模型数据与台站实测数据的对比研究

本文利用第四代地磁场综合模型(Comprehensive Model 4,CM4),计算了1982—2002年隆尧地磁台站的磁层源磁场及其感应场、电离层源磁场及其感应场的地磁北向分量X、东向分量Y、垂直分量Z,分析了各场源磁场随时间的变化特征。磁层源磁场及其感应场呈现出11年和27天的周期性变化,有些年的27天周期性变化显著,有些年则不太显著;电离层源磁场及其感应场具有明显的季节变化,不同年相同季节的变化形态一致但幅度不同;日变化分析显示,磁静日和磁扰日期间的模型数据与台站实测数据变化一致性较好,相关性较高。     

基于CM4模型的中国大陆地区地磁场时空分布特征分析

本文利用第四代地磁场综合模型（Comprehensive Model 4,CM4）,计算了1982-2001年中国大陆地区同一经度链和同一纬度链上地磁台站的磁层源磁场及其感应场、电离层源磁场及其感应场的地磁北向分量X、东向分量Y、垂直分量Z的模型值,分析了各场源磁场随时间和空间的变化特征。结果表明:在时间上,经度链和纬度链台站的磁层源磁场及其感应场均呈现出11年和27天周期性变化。电离层源磁场及其感应场具有明显的季节变化,不同年份相同季节变化形态一致但幅度不同。在空间分布上,经度链和纬度链台站磁层源磁场及其感应场的年变化幅度呈现出不同变化特征,电离层源磁场及其感应场在经度链上变化特征不同,而纬度链台站的数值基本一致。日变化分析显示,磁静日和磁扰日期间,模型数据与台站实测数据变化一致性较好,相关性较高。     

墨西哥及邻近地区地壳磁异常场研究

基于墨西哥国内49个地磁测点的3分量数据,利用全球模型CM4,区域模型Taylor多项式及曲面Spline 模型计算并分析了地壳磁异常场,并在境外均匀选取了16个CM4模型的地壳场值作为补充点以控制边界效应.为了进一步比较验证,还选用了最新的EMM2010模型.结果显示将实测值减去CM4地核场的差值所得到的磁异常分布与直接基于测点的CM4磁异常分布在分布形态和强度都有较大的差别,而与基于实测值的Spline网格值减去CM4地核场网格值后非常类似.总强度F在境内以负值居多,强度随纬度的升高其强度由大变小再变大;水平分量H在境内以正值居多,强度随纬度的升高而强度变大;磁偏角D分量除了西北部分区域外,其它区域都为正值,强度随经度的升高而变大.基于现代高精度的CM4及EMM2010模型绘制了墨西哥地区的磁异常网格值进行比较,两者间存在的差异主要由截断阶数与所使用卫星数据的不同所致.通过实测值结合Taylor多项式和曲面Spline两种区域模型研究磁异常,认为若进行地磁场异常的理论研究,可采用现有的高精度全球模型绘制的磁异常图,若进行实际的工程应用,可从实际的测点出发,结合常用的区域模型进行应用,曲面Spline模型较适于模拟区域地区的地壳磁异常.     

一种改善区域地磁场模型边界效应的方法

针对目前建立区域地磁场模型截断阶数受限,地磁图精度偏低等缺陷,研究了运用Taylor多项式拟合法建立区域地磁场模型所存在的边界效应问题.从理论上深入分析了产生边界效应误差的根源,提出了采用边界插值约束的Taylor多项式拟合法,在改善区域地磁模型边界效应的同时,提高了模型拟合的截断阶数,进而绘制出较高精度的区域地磁场图,同时对该技术和现有补充国际地磁参考场值方法进行了比较分析,最后进行了仿真试验.试验证明,该技术具有优于补充国际地磁参考值的方法,能克服现有区域地磁场模型的边界效应问题,提高了区域地磁场模型的拟合精度.     

地磁场模型和冠谐分析

地磁场是由内源场(地核场和地壳场)和外源场(电离层场和磁层场)组成的,地磁场模型是表示地磁场时空分布的数学表达式.本文简述了地磁场全球模型和区域模型的计算方法和应用;评述了冠谐分析方法及其在地磁学中的应用;介绍了地磁场模型误差的主要来源.     

最新国际地磁参考场模型IGRF11研究

详细阐述了国际地磁参考场模型IGRF11的建模原理、 数据来源、 球谐系数及误差来源等. 以NOAA/NGDC候选地磁场模型为例, 分析了数据的选取原则和校正方法. 在MATLAB环境下, 研制了该模型的可视化软件, 为制备地磁仿真基准图提供了最有可能和最为便捷的途径, 能有效使用国际公开数据, 减少外场地磁实测工作量和成本, 对地磁导航工程化具有重要的价值. 对模型检验值和实测值与模型计算值进行比较, 结果表明, 软件计算结果是正确的、 可靠的; 对IGRF11与WMM2010模型的异同点进行比较, 结果表明, WMM2010的模型精度要高于IGRF11, 具有更为广阔的适用范围. 最后, 从模型长期变化估算角度入手, 分析了引起IGRF11模型计算精度低的原因.      

Contribution to the knowledge of the magmatic evolution by the study of the variation of the coefficient of viscosity

The determination of the coefficient of viscosity of eruptive products gives useful elements to the knowledge of possible variations of composition and physical conditions of the magmas.     

Pictorial Series of the Manifestations of the Dynamics of the Earth

Studia Geophysica et Geodaetica -     

Magnetic stratigraphy of the Ordovician in the lower reach of the Kotuy River: the age of the Bysy-Yuryakh stratum and the rate of geomagnetic reversals on the eve of the superchron

Until recently, the existing data prevented the geophysicists from accurately dating the Bysy-Yuryakh stratum, which outcrops in the middle reach of the Kotuy River, constraining the time of its formation to a wide interval from the end of the Late Cambrian to the beginning of the Silurian. The obtained paleomagnetic data unambiguously correlate the Bysy-Yuryakh stratum to the Nyaian regional stage and constrain its formation, at least a considerable part of it, by the Tremadocian. This result perfectly agrees with the data on the Bysy-Yuryakh conodonts studied in this work and yields a spectacular example of the successful application of paleomagnetic studies in solving important tasks of stratigraphy and, correspondingly, petroleum geology. Within the Bysy-Yuryakh stratum, we revealed a large normal-polarity interval corresponding to the long (>1 Ma) period when the geomagnetic reversals were absent. This result, in combination with the data for the Tremadocian and Middle–Upper Cambrian sequences of the other regions, indicates that (1) the rate of occurrence of the geomagnetic reversals on the eve of the Ordovician Moyero superchron of reversed polarity was at most one reversal per Ma; (2) the superchron does not switch on instantaneously but is preceded by a certain gradual change in the operation conditions of the dynamo mechanism which, inter alia, manifests itself by the reduction of the frequency of geomagnetic reversals with the approach of the superchron. This finding supports the views according to which a process preparing the establishment of the superchrons takes place at the core–mantle boundary.     

Evolution of the Source of the Active Region of the Sun

Geomagnetism and Aeronomy - The magnetic evolution of the active region of the Sun at the level of the photosphere has been studied. Magnetic synoptic maps of the 2007 Kitt Peak Observatory were...     

On the solution of the reverse problem of geodesics with the help of the chord

Резюме Дается вывод формул для вычислений длины хорды, длины и азимутов нормаляных сечений и длины геодезической линии эллипсоида. Применяются тригонометрические функции данных величин и постоянные принятого ргфгргнц-эллипсоида, что является целесообразным при использовании вычислителQjных машин, особенно автоматов. Рабочие формулы рекомендуются в форме (8–11).

---

---

Dedicated to Professor František Fiala on His 85th Birthday

---

Address: Veveři 95, Brno.     

On the gravimetric undulations of the geoid and the deflections of the vertical

Summary The author mentions the aims of the World-wide gravity project he established in the Ohio State University in Columbus, in 1950. He outlines the practical procedure of the gravimetric computations of the undulationsN and the vertical deflection components and and emphasizes that only by the global international cooperation and additional gravity observations at sea carried out during the last decade it has been possible to gather to Columbus the needed gravity material. Since there exist still large gravimetrically unsurveyed areas it is of vital significance to study what gravity anomalies are best to be used for these regions. The given figures concerning the accuracy of theN, and , estimated theoretically and obtained in practice, indicate that in the gravimetrically well surveyed parts of the world like in Europe and the United States we can get gravimetrically on basis of existing gravity material theN-values with accuracy of about 5–10 meters, and and with the accuracy of about 1. The geoid undulationsN are already computed in Columbus for more than 6000 points of the northern hemisphere. The sample maps show the interesting geoid of Europe and vicinity between the latitudes 60° and 30° and longitude 5° W and 30° E, drafted on basis of more than 1000N-values computed at the corners of 1°×1° squares. It is interesting to realize that the geoid undulations in all this area are positive, the extreme values being between 40 and 50 meters. The geophysical significance of the geoid maps of this kind is pointed out.     

The effect of the pollution of the ground layer of the atmosphere on the albedo

Summary A simple model is proposed suitable for studying the effect of the ground layer of the atmosphere, polluted by aerosol, on the albedo. This model is founded on solving the equation of transfer of radiative energy. The numerical results are discussed, particular attention being paid to the analysis of errors due to neglecting the multiple reflection of solar radiation on the aerosol particles. A method which would also include the multiple reflection is proposed, and the conditions under which the presence of the aerosol is responsible for an increase or decrease of the solar radiation balance on the Earth's surface, are analysed.     

On the determination of the non-linearity of the gravimeter scale

Summary The results of two different methods of the determination of the non-linearity of the gravimeter scale are compared; the economy is discussed as well.     

On the maintenance of the axisymmetric part of the flow in the atmosphere

Summary The maintenance of the axisymmetric component of the flow in the atmosphere is investigated by means of a steady-state, quasi-geostrophic formulation of the meteorological equations. It is shown that the meridional variations in the time-averaged axisymmetric variables can be expressed as the sum of three contributions, one being due to the eddy heat transport, another to the eddy momentum transport, and a third to the convective-radiative equilibrium temperature which enters the problem through the specification of a Newtonian form of diabatic heating. The contributions by the large scale eddies are evaluated through the use of observed values for the eddy heat and momentum transports.The contributions from each of the three forcing mechanisms to the temperature and zonal wind fields are invstigated individually and found to be of about equal importance. The sum of the three contributions are also presented for the temperature, the zonal wind, the stream function associated with the mean meridional circulation and the corresponding vertical motion. Although the results fail to reproduce the main observed features of the lower stratosphere, they are found to be in good agreement with observations in the middle latitude troposphere. At any pressure level, for example, the computed mean zonal wind has a jet-like profile and the axis of the jet is found to slope to the south with height, as observed in the atmosphere.Based in part on a thesis submitted by the first author as partial fulfillment of the requirements for the Ph.D. degree at the University of Michigan. — Publication No. 194 from the Department of Meteorology and Oceanography, The University of Michigan.