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1.
Summary The components of the moments of the external force due to the gravitational effect of the Moon are derived, which causes disturbances in the motion of the Earth round its mass centre, taking into account the gravitational fields of both bodies in the form of a development in terms of harmonics upto degree n=4. This paper ties up with [3–5] and the notations are identical. 相似文献
2.
利用新疆地区北疆测网2015～2017年观测的共4期流动重力资料,分析研究区半年、1年尺度重力变化特征,并采用小波分解方法,对2017年8月9日精河MS6.6地震前重力变化异常进行分解,分离了不同深度的重力异常。结果表明,震中附近的精河地区从2015年开始一直处于重力负值变化,同时,震中周围的重力正值变化集中区逐步向震中地区迁移,地震发生前震中以南60km处出现重力变化零值线,并且零值线两侧的重力累积变化量达到70μGal。小波分解后,4阶细节图较好地反映了精河地震前的重力异常,其与地震孕育发生有较好的对应性。 相似文献
3.
Michele Caputo 《Pure and Applied Geophysics》1964,57(1):66-82
Summary Adopting thePizzetti-Somigliana method and using elliptic integrals we have obtained closed formulas for the space gravity field in which one of the equipotential surfaces is a triaxial ellipsoid. The same formulas are also obtained in first approximation of the equatorial flattening avoiding the use of the elliptic integrals. Using data from satellites and Earth gravity data the gravitational and geometric bulge of the Earth's equator are computed. On the basis of these results and on the basis of recent gravity data taken around the equator between the longitudes 50° to 100° E, 155° to 180° E, and 145° to 180° W, we question the advantage of using a triaxial gravity formula and a triaxial ellipsoid in geodesy. Closed formulas for the space field in which a biaxial ellipsoid is an equipotential surface are also derived in polar coordinates and its parameters are specialized to give the international gravity formula values on the international ellipsoid. The possibility to compute the Earth's dimensions from the present Earth gravity data is the discussed and the value ofMG=(3.98603×1020 cm3 sec–2) (M mass of the Earth,G gravitational constant) is computed. The agreement of this value with others computed from the mean distance Earth-Moon is discussed. The Legendre polinomials series expansion of the gravitational potential is also added. In this series the coefficients of the polinomials are closed formulas in terms of the flattening andMG.Publication Number 327, and Istituto di Geodesia e Geofisica of Università di Trieste. 相似文献
4.
A brief review of the existing methods of gravity reduction is given and a new method suitable for use on high speed digital computers is described. The method is based on the formula for the gravitational attraction of a frustum of a cone. The topographic contours are represented by polygons and the x and y coordinates of corners of the polygons constitute the input to the computer. The vertical component of the gravitational attraction is calculated by evaluating the cone formula for a number of vertical sections of the topography. Each vertical section is simplified by adopting a procedure of grouping and averaging for the distant points of the section. The effect of the earth's sphericity is taken into account by lowering the distant points of the sections by amounts determined by the curvature. The computations include the area close to the point at which the attraction is required and may be limited to an area defined by a circle centered at this point. The method is therefore compatible with the conventional zone chart methods. As an illustration of the method the gravitational attraction of Caryn Seamount in the Atlantic Ocean is computed. The total Bouguer correction and the Terrain correction are also computed for an area in northwestern South America and comparisons are made with hand computations by a zone chart method. As an example, for work at sea, the Bouguer corrections for an area near the Island of Mauritius in the Indian Ocean are computed and the effects of sphericity and three-dimensionality are calculated. The gravitational attraction of two-dimensional bodies can be computed in a very similar manner. The attraction of the Puerto Rico Trench model is computed and the results are compared with other methods. The effects of sphericity and assumptions involved in extending the models to infinity are discussed. 相似文献
5.
In Part I we focussed on a convergent representation of the gravitational potential generated bytopographic masses on top of the equipotential surface atMean Sea Level, thegeoid, and by those masses which compensate topography. Topographic masses have also been condensated, namely represented by a single layer. Part II extends the computation of the gravitational field of topographic-isostatic masses by a detailed analysis of itsforce field in terms ofvector-spherical harmonic functions. In addition, the discontinuous mass-condensated topographic gravitational force vector (head force) is given. Once we identify theMoho discontinuity asone interface of isostatically compensated topographical masses, we have computed the topographic potential and the gravitational potential which is generated by isostatically compensated masses atMean Sea Level, the geoid, and illustrated by various figures of geoidal undulations. In comparison to a data oriented global geoid computation ofJ. Engels (1991) the conclusion can be made that the assumption of aconstant crustal mass density, the basic condition for isostatic modeling, does not apply. Insteaddensity variations in the crust, e.g. betweenoceanic and continental crust densities, have to be introduced in order to match the global real geoid and its topographic-isostatic model. The performed analysis documents that thestandard isostatic models based upon aconstant crustal density areunreal. 相似文献
6.
The forward computation of the gravitational and magnetic fields due to a 3D body with an arbitrary boundary and continually varying density or magnetization is an important problem in gravitational and magnetic prospecting. In order to solve the inverse problem for the arbitrary components of the gravitational and magnetic anomalies due to an arbitrary 3D body under complex conditions, including an uneven observation surface, the existence of background anomalies and very little or no a priori information, we used a spherical coordinate system to systematically investigate forward methods for such anomalies and developed a series of universal spherical harmonic expansions of gravitational and magnetic fields. For the case of a 3D body with an arbitrary boundary and continually varying magnetization, we have also given the surface integral expressions for the common spherical harmonic coefficients in the expansion of the magnetic field due to the body, and a very precise numerical integral algorithm to calculate them. Thus a simple and effective method of solving the forward problem for magnetic fields due to 3D bodies of this kind has been found, and in this way a foundation is laid for solving the inverse problem of these magnetic fields. In addition, by replacing the parameters and unit vectors in the spherical harmonic expansion of a magnetic field by gravitational parameters and a downward unit vector, we have also derived a forward method for the gravitational field (similar to that for the magnetic case) of a 3D body with an arbitrary boundary and continually varying density. 相似文献
7.
Summary Whereas observations of planets and solar satellites are more promising for detecting possible variations of Newtonian gravitational constant,G, with time the application of additional methods which are substantially different might be useful. It is discussed to what extent the tidal problems can be solved in connection with lunar orbit tracking for detectingG; further a relativeG-experiment at the earth surface is outlined. 相似文献
8.
The gravitational attraction produced by a geological body of irregular shape can be easily determined by dividing it into cubes of small size. The exact expression of the effect of a cube is very complicated, but it can be calculated by using an electronic computer. 4851 values of the gravitational attraction were determined for different positions of a cube with the side of 2l and the center in M(x0, y0, z0), for x0∈[0;20], y0∈[0;20] and z0∈[0;10]. Using these values, templates in double logarithmic representation were drawn, with x0 and z0 as parameters and y0 as abscissa, and with x0 and y0 as parameters and z0 in abscissa; this double set of templates permits a good interpolation for all cubes in the considered domain of M. The use of templates was tested to approximate the effect produced by a theoretical model of spherical shape and in a real case of a three-dimensional salt body of known shape based on a large number of boreholes. In both cases very good results were obtained. 相似文献
9.
Besides generating seismic waves, which eventually dissipate, an earthquake also generates a static displacement field everywhere within the Earth. This global displacement field rearranges the Earth’s mass thereby causing the Earth’s rotation and gravitational field to change. The size of this change depends upon the magnitude, focal mechanism, and location of the earthquake. The Sumatran earthquake of December 26, 2004 is the largest earthquake to have occurred since the 1960 Chilean earthquake. Using a spherical, layered Earth model, the coseismic effect of the Sumatran earthquake upon the Earth’s length-of-day, polar motion, and low-degree harmonic coefficients of the gravitational field are computed. Using a model of the earthquake source that is composed of five subevents having a total moment-magnitude M
w
of 9.3, it is found that this earthquake should have caused the length-of-day to decrease by 6.8 microseconds, the position of the Earth’s generalized figure axis to shift 2.32 milliarcseconds towards 127° E longitude, the Earth’s oblateness J
2 to decrease by 2.37 × 10−11 and the Earth’s pear-shapedness J
3 to decrease by 0.63 × 10−11. The predicted change in the length-of-day, position of the generalized figure axis, and J
3 are probably not detectable by current measurement systems. But the predicted change in oblateness is perhaps detectable if other effects, such as those of the atmosphere, oceans, and continental water storage, can be adequately removed from the observations. 相似文献
10.
Quantification of peatland water storage capacity using the water table fluctuation method 
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下载免费PDF全文 Peat specific yield (SY) is an important parameter involved in many peatland hydrological functions such as flood attenuation, baseflow contribution to rivers, and maintaining groundwater levels in surficial aquifers. However, general knowledge on peatland water storage capacity is still very limited, due in part to the technical difficulties related to in situ measurements. The objectives of this study were to quantify vertical SY variations of water tables in peatlands using the water table fluctuation (WTF) method and to better understand the factors controlling peatland water storage capacity. The method was tested in five ombrotrophic peatlands located in the St. Lawrence Lowlands (southern Québec, Canada). In each peatland, water table wells were installed at three locations (up‐gradient, mid‐gradient, and down‐gradient). Near each well, a 1‐m long peat core (8 cm × 8 cm) was sampled, and subsamples were used to determine SY with standard gravitational drainage method. A larger peat sample (25 cm × 60 cm × 40 cm) was also collected in one peatland to estimate SY using a laboratory drainage method. In all sites, the mean water table depth ranged from 9 to 49 cm below the peat surface, with annual fluctuations varying between 15 and 29 cm for all locations. The WTF method produced similar results to the gravitational drainage experiments, with values ranging between 0.13 and 0.99 for the WTF method and between 0.01 and 0.95 for the gravitational drainage experiments. SY was found to rapidly decrease with depth within 20 cm, independently of the within‐site location and the mean annual water table depth. Dominant factors explaining SY variations were identified using analysis of variance. The most important factor was peatland site, followed by peat depth and seasonality. Variations in storage capacity considering site and seasonality followed regional effective growing degree days and evapotranspiration patterns. This work provides new data on spatial variations of peatland water storage capacity using an easily implemented method that requires only water table measurements and precipitation data. 相似文献
11.
The purpose of GPS-satellite-to-satellite tracking (GPS-SST) is to determine the gravitational potential at the earth's surface from measured ranges (geometrical distances) between a low-flying satellite and the high-flying satellites of the Global Positioning System (GPS). In this paper, GPS-satellite-to-satellite tracking is reformulated as the problem of determining the gravitational potential of the earth from given gradients at satellite altitude. The uniqueness and stability of the solution are investigated. The essential tool is to split the gradient field into a normal part (i.e. the first-order radial derivative) and a tangential part (i.e. the surface gradient). Uniqueness is proved for polar, circular orbits corresponding to both types of data (first radial derivative and/or surface gradient). In both cases gravity recovery based on satellite-to-satellite tracking turns out to be an exponentially ill-posed problem. Regularization in terms of spherical wavelets is proposed as an appropriate solution method, based on the knowledge of the singular system. Finally, the extension of this method is generalized to a nonspherical earth and a non-spherical orbital surface, based on combined terrestrial and satellite data. 相似文献
12.
Summary The paper is dealing with the separation problem of weak intensity anomalies from the perturbation background. By means of the Shannon's form and based on the values estabilished for a measured gravitational field, g, the mean quantity of information sent forth at the source — perturbating body — is calculated in order to intercept the g set. This quantity takes a maximum value above the perturbating body, while for the remainder a deadening of the perturbations is obtained. 相似文献
13.
Abstract Small amplitude oscillations of a uniformly rotating, density stratified, Boussinesq, non-dissipative fluid are examined. A mathematical model is constructed to describe timedependent motions which are small deviations from an initial state that is motionless with respect to the rotating frame of reference. The basic stable density distribution is allowed to be an arbitrary prescribed function of the gravitational potential. The problem is considered for a wide class of gravitational fields. General properties of the eigenvalues and eigenfunctions of square integrable oscillations are demonstrated, and a bound is obtained for the magnitude of the frequencies. The modal solutions are classified as to type. The eigenfunctions for the pressure field are shown to satisfy a second-order partial differential equation of mixed type, and the equation is obtained for the critical surfaces which delineate the elliptic and hyperbolic regions. The nature of the problem is examined in detail for certain specific gravitational fields, e.g., a radially symmetric field. Where appropriate, results are compared with those of other investigations of waves in a rotating fluid of spherical configuration and the novel aspects of the present treatment are emphasized. Explicit modal solutions are obtained in the specific example of a fluid contained in a rigid cylinder, stratified in the presence of vertical gravity, with the buoyancy frequency N being an arbitrary prescribed function of depth. 相似文献
14.
In this study we assume that a gravitational curvature tensor, i.e. a tensor of third-order directional derivatives of the Earth’s gravitational potential, is observable at satellite altitudes. Such a tensor is composed of ten different components, i.e. gravitational curvatures, which may be combined into vertical–vertical–vertical, vertical–vertical–horizontal, vertical–horizontal–horizontal and horizontal–horizontal-horizontal gravitational curvatures. Firstly, we study spectral properties of the gravitational curvatures. Secondly, we derive new quadrature formulas for the spherical harmonic analysis of the four gravitational curvatures and provide their corresponding analytical error models. Thirdly, requirements for an instrument that would eventually observe gravitational curvatures by differential accelerometry are investigated. The results reveal that measuring third-order directional derivatives of the gravitational potential imposes very high requirements on the accuracy of deployed accelerometers which are beyond the limits of currently available sensors. For example, for orbital parameters and performance similar to those of the GOCE mission, observing third-order directional derivatives requires accelerometers with the noise level of \({\sim}10^{-17}\,\hbox {m}\,\hbox {s}^{-2}\) Hz\(^{-1/2}\). 相似文献
15.
In this paper, on the basis of intensity data from 85 earthquakes occurred in China, the method of resolving overdetermined
equations by using the damped least squares method is applied to inversing for the mean value of 1 s. S wave quality factor,
the spreading factor and the S-wave acceleration at the foci of earthquakes in 7 regions of China. The relation between S-wave
acceleration at the foci of earthquakes and magnitude is discussed. As an example, 2-DQ
S distribution in Taiwan Province is obtained by inversion. It is found that there exists some corresponding relation between
this distribution and Bouguer gravitational anomaly and seismicity.
Preliminary analysis and discussion on results of the inversion, and estimation of error inQ
S are made.
The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 202–211, 1991.
The English version of this paper is improved by Professor Yushou Xie. 相似文献
16.
Michael R. Leeder 《地球表面变化过程与地形》1979,4(3):291-295
A test is proposed for Bagnold's postulate that the normal weight stress due to moving ‘bedload’ is balanced by a solid transmitted stress due to the rate of change of momentum produced by grain impacts on unit area of the stationary bed. The test involves derivation of an expression for normal momentum transfer due to saltating grains at moderate transport stages when grain-to-grain collisions and partial suspension during saltation may be ignored. A dimensionless number, Φ, (a grain Froude Number) is derived, given by ū2/g where ū is the mean grain forward velocity, g is the gravitational acceleration and L? is the length of a single saltation ‘jump’. Equilibrium demands that Φ be unity during bedload transport involving saltating grains if Bagnold's postulate is correct. Experimental data shows Φ < 1, the discrepancy between theory and experiment being due to the existence of lift forces acting upon bedload grains. Bagnold's postulate is correct for concentrated dispersions of grains, as in grain flows, when fluid lift forces may be neglected due to high particle concentration. 相似文献
17.
18.
利用北天山地区2016～2019年观测的4期流动重力观测资料,分析研究一年尺度的重力场动态变化特征,并利用小波分析方法,将不同场源深度的重力异常进行分离。通过功率谱分析,获取各阶小波重力细节对应的场源深度。研究结果表明,2017年8月9日精河MS6.6地震前,震中位于负值集中区,四阶小波重力细节显示震中附近出现明显的四象限分布;2020年1月16日库车MS5.6地震前,震中位于负值区,小波重力细节整体量值较小;功率谱估算的场源近似深度与2次地震的震源深度相近。 相似文献
19.
Burša Milan Raděj Karel Šima Zdislav True Scott A. Vatrt Viliam 《Studia Geophysica et Geodaetica》1997,41(3):203-216
The geopotential scale factor R
o
= GM/W
o
(the GM geocentric gravitational constant adopted) and/or geoidal potential Wo have been determined on the basis of the first year's (Oct 92 – Dec 93) ERS-1/TOPEX/POSEIDON altimeter data and of the POCM 4B sea surface topography model: R
o
°=(6 363 672.58°±0.05) m, W
o
°=(62 636 855.8°±0.05)m
2
s
–2
. The 2°–°3 cm uncertainty in the altimeter calibration limits the actual accuracy of the solution. Monitoring dW
o
/dt has been projected. 相似文献
20.
The occurrence of spread-F at Trivandrum (8.5^N, 77^E, dip 0.5^N) has been investigated on a seasonal basis in sunspot maximum and minimum years in terms of the growth rate of irregularities by the generalized collisional Rayleigh-Taylor (GRT) instability mechanism which includes the gravitational and cross-field instability terms. The occurrence statistics of spread-F at Trivandrum have been obtained using quarter hourly ionograms. The nocturnal variations of the growth rate of irregularities by the GRT mechanism have been estimated for different seasons in sunspot maximum and minimum years at Trivandrum using h’F values and vertical drift velocities obtained from ionograms. It is found that the seasonal variation of spread-F occurrence at Trivandrum can, in general, be accounted for on the basis of the GRT mechanism. 相似文献