Methodology of Testing Geopotential Models Specified in Different Tide Systems

It is proved that the Testing Geopotential Model (TGM) results in identical model distortions when TGM is performed in the mean, zero, and tide- free systems. The Molodensky quasigeoid height is invariant in relation to different tide systems, however, the Molodensky normal height, the ellipsoidal height, as well as, the actual geopotential, expressed in the above different tide systems, differ.     

Accuracy of Normal Heights Determined Using Improved Geopotential Models

The accuracy of determining the Molodensky normal heights using geopotential models has been investigated. On the basis of geopotential model JGM-3/OSU91A the Molodensky normal heights can be computed with an accuracy of about ±35 cm at the GPS sites in the central part of Europe. On the basis of JGM-3/OSU91A improved the accuracy becomes higher, about ±14 cm.     

On the Spectral Decomposition of Geopotential and Temperature Fields in the Stratosphere

The spectral structure of stratospheric fields (temperature and geopotential) is analyzed in terms of spherical harmonics in an effort to study the long-term behaviour of large-scale circulation patterns, as well as their connections to some extra-terrestrial effects. The daily meteorological data from the Free University Berlin (FUB) cover more or less the period 1976–1996 and are available for stratospheric levels of 50, 30 and 10 hPa. The analysis of the annual cycle of spherical harmonics is introduced, and changes of the principal wave components are compared with the changes in different sets of solar, geomagnetic and global circulation indices. This paper also deals with interannual variability with special emphasis on quasibiennial oscillations (QBO) and El Nino and Southern Oscillations (ENSO). Although this is a rather preliminary study, the decomposition of the stratospheric field into complex spherical harmonics seems to be a powerful technique in investigating and qualifying the response of the global atmospheric system to the changes in solar and geomagnetic activity, and in qualifying the relationships between large-scale circulation patterns and various oscillations such as QBO or ENSO, Using this technique, reasonable strong connections were found between wave numbers and interannual factors, and these connections were tentatively interpreted in terms of statistics. A very high degree of correlation was found for the four-trough shape of the polar vortex.     

Determination of Geopotential Differences between Local Vertical Datums and Realization of a World Height System

The methodology developed for connecting Local Vertical Datums (LVD) was applied to the Australian Height Datum (AHD) and the North American Vertical Datum (NAVD88). The geopotential values at AHD and NAVD88 were computed and the corresponding vertical offset of 974 mm with rms 51 mm was obtained between the zero reference surfaces defined by AHD and NAVD88. The solution is based on the four primary geodetic parameters, the GPS/levelling sites and the geopotential model EGM96. The Global Height System (or the Major Vertical Datum) can be defined by a geoidal geopotential value used in the solution as the reference value, or by the geopotential value of the LVD, e.g. NAVD88.     

Geopotential Reconstruction,Decomposition, Fast Computation,and Noise Cancellation by Harmonic Wavelets

Harmonic wavelets are introduced within the framework of the Sobolev-like Hilbert space H of potentials with square-integrable restrictions to the Earth's (mean) sphere _R . Basic tool is the construction of H-product kernels in terms of an (outer harmonics) orthonormal basis in H. Scaling function and wavelet are defined by means of so-called H-product kernels. Harmonic wavelets are shown to be building blocks that decorrelate geopotential data. A pyramid scheme enables fast computations. Multiscale signal-to-noise thresholding provides suitable denoising. Multiscale modelling of the Earth's anomalous potential from EGM96-model data is illustrated by use of bandlimited harmonic wavelets, i.e. Shannon and CP-wavelets.     

GRACE/GOCE扩展重力场模型确定我国1985高程基准重力位的精度分析

高精度高程基准重力位的确定往往依赖于高精度全球重力场模型,其对全球和区域高程基准的高精度统一非常关键,GRACE、GOCE卫星重力计划极大地提高了全球重力场模型中长波的精度.本文首先对GRACE/GOCE卫星重力场模型的内符合和外符合精度进行讨论分析,结果说明卫星重力模型的截断误差影响可达到分米级水平,在确定高程基准重力位时该影响不可忽略.利用EGM2008模型扩展GRACE/GOCE卫星重力场模型至2190阶,可有效减弱卫星重力模型的截断误差影响,但不同模型扩展时的最优拼接阶次不同,其中DIR-1、DIR-5模型对应的最优拼接阶次分别为180阶和220阶,以GPS水准数据检验,扩展模型在中国区域的精度均优于18 cm.最后,基于最优拼接阶次获得的扩展重力场模型对我国1985高程基准重力位进行了估计,DIR-5和TIM-5模型对应数值分别为62636853.47 m²·s^-2和62636853.49 m²·s^-2,精度均为1.51 m²·s^-2;发现在中国区域模型大地水准面与GPS/水准数据的差值存在微弱的系统性倾斜,东西向倾斜约为9 cm,南北向倾斜约为1.4 cm,考虑倾斜改正后基于DIR-5和TIM-5模型估计我国1985高程基准重力位的精度提高了0.16 m²·s^-2.

     

不完全阶次球谐位系数模型的研究

利用局部重力资料确定不完全阶次位系数模型的方法进行研究．首先根据Molodensky边值问题的数学理论和函数展为级数式的一般原理,论述了方法在理论上的正确性;然后根据模型结构,提出了位系数补偿因子,并给出其确定的原则及计算公式;接着构制一个适合局部区域的不完全阶次的高阶位系数模型的方法进行探讨;最后对其精度进行检验．结果显示局部区域2160阶不完全阶次模型对实测垂线偏差二分量的恢复精度分别为±2．56s和±2．61s．     

不完全阶次球谐位系数模型的研究

利用局部重力资料确定不完全阶次位系数模型的方法进行研究．首先根据Molodensky边值问题的数学理论和函数展为级数式的一般原理,论述了方法在理论上的正确性;然后根据模型结构,提出了位系数补偿因子,并给出其确定的原则及计算公式;接着构制一个适合局部区域的不完全阶次的高阶位系数模型的方法进行探讨;最后对其精度进行检验．结果显示局部区域2160阶不完全阶次模型对实测垂线偏差二分量的恢复精度分别为±2．56s和±2．61s．     

Least-squares Minimization Approaches to Interpret Total Magnetic Anomalies Due to Spheres

We have developed three different least-squares approaches to determine successively: the depth, magnetic angle, and amplitude coefficient of a buried sphere from a total magnetic anomaly. By defining the anomaly value at the origin and the nearest zero-anomaly distance from the origin on the profile, the problem of depth determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(z)=0. Knowing the depth and applying the least-squares method, the magnetic angle and amplitude coefficient are determined using two simple linear equations. In this way, the depth, magnetic angle, and amplitude coefficient are determined individually from all observed total magnetic data. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal, West Africa. In all cases, the depth solutions are in good agreement with the actual ones.     

Zero initial partial derivatives of satellite orbits with respect to force parameters violate the physics of motion of celestial bodies

Satellite orbits have been routinely used to produce models of the Earth’s gravity field. In connection with such productions, the partial derivatives of a satellite orbit with respect to the force parameters to be determined, namely, the unknown harmonic coefficients of the gravitational model, have been first computed by setting the initial values of partial derivatives to zero. In this note, we first design some simple mathematical examples to show that setting the initial values of partial derivatives to zero is generally erroneous mathematically. We then prove that it is prohibited physically. In other words, setting the initial values of partial derivatives to zero violates the physics of motion of celestial bodies. Supported by a Grant-in-Aid for Scientific Research (Grant No. B19340129)     

Dynamic features of the Tianshan orogen deduced from satellitic gravity data

IntroductionGeopotential model, expressed by a spherical harmonic function, gives the global distribution of disturbed gravimetric potential. It is widely applied in the research of many disciplines of science, such as geodetics, geophysics, geodynamics, oceanography and space science. In geophysics, geopotential model shows the large-dimensional gravity variety, which is the reflection of anomalous density distribution in a large area or in the deep of the earth. Therefore, it is useful in th…     

Cohesive Crack Analysis of Toughness Increase Due to Confining Pressure

Apparent fracture toughness in Mode I of microcracking materials such as rocks under confining pressure is analyzed based on a cohesive crack model. In rocks, the apparent fracture toughness for crack propagation varies with the confining pressure. This study provides analytical solutions for the apparent fracture toughness using a cohesive crack model, which is a model for the fracture process zone. The problem analyzed in this study is a fluid-driven fracture of a two-dimensional crack with a cohesive zone under confining pressure. The size of the cohesive zone is assumed to be negligibly small in comparison to the crack length. The analyses are performed for two types of cohesive stress distribution, namely the constant cohesive stress (Dugdale model) and the linearly decreasing cohesive stress. Furthermore, the problem for a more general cohesive stress distribution is analyzed based on the fracture energy concept. The analytical solutions are confirmed by comparing them with the results of numerical computations performed using the body force method. The analytical solution suggests a substantial increase in the apparent fracture toughness due to increased confining pressures, even if the size of the fracture process zone is small.     

卫星重力资料揭示的新疆天山地区构造动力学状态

利用最新的地球重力场模型,计算了新疆及邻近地区的自由空气重力异常、大地水准面扰动异常、地壳和上地幔平均密度异常以及地幔对流引起的岩石层底界面粘滞应力场分布．根据计算结果,对新疆天山地区的构造动力学特征进行了分析和推断,认为天山处于地幔对流形成的挤压沉降环境中,在南北不对称的挤压应力作用下快速隆升,挤压应力场中心在天山以南．这种应力场特征有利于塔里木板块向天山之下俯冲的观点．天山南北两侧的准噶尔盆地南缘和塔里木盆地北缘,是地壳内质量缺失区,是由于南北两侧地壳向天山下挤压而弯曲造成的．中国天山东段的深部密度分布特征与中段和西段的不同,可能是地幔对流分布的东西向差异造成的．     

区域高阶重力场模型与青藏地区局部位系数模型

根据当今全球模型研究的Ｍｏｌｏｄｅｎｓｋｙ理论,推导了相应的区域高阶重力场模型系数修正公式．考虑了球近似边值条件引起的各种偏差,使用了椭球坐标系,按椭球调和展开．并利用中国青藏地区地面重力资料对原始全球模型ＯＳＵ９１Ａ１Ｆ的高阶部分系数进行修正,获得该地区的局部重力场模型ＱＺ９３Ｇ（完整到３６０阶）,它对实测平均重力异常的恢复精度为±１１．８×１０－５ｍ／ｓ２．     

Interpretation of general geophysical patterns in Iran based on GRACE gradient component analysis

Only with satellites it is possible to cover the entire Earth densely with gravity field related measurements of uniform quality within a short period of time. However, due to the altitude of the satellite orbits, the signals of individual local masses are strongly damped. Based on the approach of Petrovskaya and Vershkov we determine the gravity gradient tensor directly from the spherical harmonic coefficients of the recent EIGEN-GL04C combined model of the GRACE satellite mission. Satellite gradiometry can be used as a complementary tool to gravity and geoid information in interpreting the general geophysical and geodynamical features of the Earth. Due to the high altitude of the satellite, the effects of the topography and the internal masses of the Earth are strongly damped. However, the gradiometer data, which are nothing else than the second order spatial derivatives of the gravity potential, efficiently counteract signal attenuation at the low and medium frequencies. In this article we review the procedure for estimating the gravity gradient components directly from spherical harmonics coefficients. Then we apply this method as a case study for the interpretation of possible geophysical or geodynamical patterns in Iran. We found strong correlations between the cross-components of the gravity gradient tensor and the components of the deflection of vertical, and we show that this result agrees with theory. Also, strong correlations of the gravity anomaly, geoid model and a digital elevation model were found with the diagonal elements of the gradient tensor.     

区域高阶重力场模型与青藏地区局部位系数模型

根据当今全球模型研究的Ｍｏｌｏｄｅｎｓｋｙ理论，推导了相应的区域高阶重力场模型系数修正公式．考虑了球近似边值条件引起的各种偏差，使用了椭球坐标系，按椭球调和展开．并利用中国青藏地区地面重力资料对原始全球模型ＯＳＵ９１Ａ１Ｆ的高阶部分系数进行修正，获得该地区的局部重力场模型ＱＺ９３Ｇ（完整到３６０阶），它对实测平均重力异常的恢复精度为±１１．８×１０^－５ｍ／ｓ^２．     

大地水准面异常在湖南地区的地球物理解释

以湖南地区为例,利用超高阶地球重力位模型EGM2008计算了研究区的重力大地水准面,并采用棱柱体公式和球体公式相结合的方法分别进行了完全地形改正和Airy-Heiskanen局部均衡改正,得到布格大地水准面和均衡大地水准面.对三种大地水准面进行不同波长分量的分离处理,得到包含不同深度异常信息的剩余大地水准面,并结合其他地球物理资料对研究区进行了详细的地球物理解释.结果表明,剩余重力大地水准面可以有效地反映出研究区内的深部构造特征,如深大断裂带分布、构造块体位置、上地幔密度横向分布等,但对地壳内异常结构反映不明显;研究区岩石圈密度变化相对平缓,厚度由东向西增加;根据剩余均衡大地水准面及研究区Airy局部均衡莫霍面,可以大致推测出研究区的莫霍面起伏形态以及均衡状态,可作为一种有用的参考信息.     

原地应力对钻孔应变耦合系数的影响分析

利用4层介质耦合钻孔模型,研究该模型中耦合介质弹性参数变化对钻孔应变耦合系数的影响。计算结果表明:在钻孔耦合介质中,弹性层等效弹性模量变化对面应变耦合系数的影响大于对差应变的影响,与观测结果对比,分析发现面应变耦合系数观测值存在明显非均匀性,而且其大小与台站的背景应力场存在对应关系。     

地基液化导致沉箱码头破坏及地基加固方法的非线性数值分析

地震作用引发的地基液化,往往导致沉箱基础的破坏。本文基于Biot两相饱和多孔介质动力耦合理论,采用FE-FD耦合数值分析方法,对液化海床沉箱基础的地震反应进行非线性有效应力分析。在数值分析过程中,建立了以土骨架位移和超静孔隙水压力表达的us-pw动力固结方程和循环弹塑性本构模型,该方法能够很好地模拟地震作用下沉箱码头的动力特性及液化破坏的影响。通过数值模拟计算,分析了采用碎石桩进行置换砂区域的防液化加固方法,并就碎石桩处理区域的选择提出了建议。