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1.
Summary Four parameters defining the Earth's tri-axial ellipsoid (E) have been derived on the basis of the condition that the gravity potential on E be constant and equal to the actual geopotential value (W0) on the geoid. The geocentric gravitational constant, the angular velocity of the Earth's rotation, the actual 2nd degree geopotential Stokes parameters and W0 are taken to be the primary geodetic constants defining E and its (normal) gravity field. 相似文献
2.
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
3.
Summary The integral mean values of gravity on the surface W=W
0
, obtained from satellite observations with the use of harmonic coefficients[3, 7] and from terrestrial gravity measurements[12], are compared. The squares and products of the harmonic coefficients were neglected, with the exception of [J
2
(0)
]
2
, which was taken into account. The Potsdam correction and the geocentric constant are being discussed. The paper ties up with[13–15] and the symbols used are the same. The given problem was treated, e.g., in[2, 4, 6, 8–10]; in the present paper the values of gravity are compared directly. 相似文献
4.
The TOPEX/POSEIDON (T/P) satellite altimeter data from January 1, 1993 to January 3, 2001 (cycles 11–305) was used for investigating the long-term variations of the geoidal geopotential W
0 and the geopotential scale factor R
0 = GM÷W
0 (GM is the adopted geocentric gravitational constant). The mean values over the whole period covered are W
0 = (62 636 856.161 ± 0.002) m2s-2, R
0 = (6 363 672.5448 ± 0.0002) m. The actual accuracy is limited by the altimeter calibration error (2–3 cm) and it is conservatively estimated to be about ± 0.5 m2s-2 (± 5 cm). The differences between the yearly mean sea surface (MSS) levels came out as follows: 1993–1994: –(1.2 ± 0.7) mm, 1994–1995: (0.5 ± 0.7) mm, 1995–1996: (0.5 ± 0.7) mm, 1996–1997: (0.1 ± 0.7) mm, 1997–1998: –(0.5 ± 0.7) mm, 1998–1999: (0.0 ± 0.7) mm and 1999–2000: (0.6 ± 0.7) mm. The corresponding rate of change in the MSS level (or R
0) during the whole period of 1993–2000 is (0.02 ± 0.07) mm÷y. The value W
0 was found to be quite stable, it depends only on the adopted GM, and the volume enclosed by surface W = W
0. W
0 can also uniquely define the reference (geoidal) surface that is required for a number of applications, including World Height System and General Relativity in precise time keeping and time definitions, that is why W
0 is considered to be suitable for adoption as a primary astrogeodetic parameter. Furthermore, W
0 provides a scale parameter for the Earth that is independent of the tidal reference system. After adopting a value for W
0, the semi-major axis a of the Earth's general ellipsoid can easily be derived. However, an a priori condition should be posed first. Two conditions have been examined, namely an ellipsoid with the corresponding geopotential which fits best W
0 in the least squares sense and an ellipsoid which has the global geopotential average equal to W
0. It is demonstrated that both a-values are practically equal to the value obtained by the Pizzetti's theory of the level ellipsoid: a = (6 378 136.7 ± 0.05) m. 相似文献
5.
The topic of the Earth's reference body, which has now been established as Pizzetti's level rotational ellipsoid, is analysed. Such a body is fully determined by four parameters: a, GM, J
2 and . At present, the largest discrepancy in determining these parameters occurs in the value of a, which may in future be replaced by the gravity potential of the mean sea level W
o, with respect to Brovar's condition.Pizzetti's four parameters of the reference body are determined by solving the Dirichlet boundary value problem. The Dirichlet problem has only a unique solution, which, however, can be expressed in infinitely many ways. It turns out that the most important part in the form of the solution is played by Lamé's conditions, which determine the type of ellipsoidal coordinates.The solutions given by Pizzetti, Molodensky and another variant are considered. The last variant leads to a simple formula for the potential of the reference ellipsoid, but the formulae for Lamé's coefficients are inconvenient. Of course, all the methods lead to identical solutions, but some of them are more convenient for the historical use of logarithms, whereas others are more appropriate for use in computers. 相似文献
6.
This paper presents a survey of recent work on the gravimetric geoid. The gravity models considered are those published in the past few years by the Goddard Space Flight Center (GSFC), the Smithsonian Astrophysical Observatory (SAO) and the Ohio State University (OSU). Comparisons and analyses have been carried out through the ose of detailed gravimetric geoids which we have computed by combining the above-mentioned models with a set of 26 000, 1ox1o mean free air gravity anomalies. The accuracy of the detailed gravimetric geoid computed using the most recent Goddard Earth Model (GEM-6) in conjunction with the set 1ox1o mean free air gravity anomalies is assessed at 2 m on the continents of North America, Europe And Australia, 2 to 5 m in the North-East Pacific and North Atlantic areas and 5 to 10 m in other areas where surface gravity data are sparse. Rms differences between this detailed geoid and the detailed geoids computed using the other satellite gravity fields in conjunction with same set of surface data range from 3 to 7 m. The maximum differences in all cases occurred in the Southern Hemisphere where surface data and satellite observations are sparse. These differences exhibited wavelengths of approximately 30o to 50o in longitude. Detailed geoidal heights were also computed with models truncated to 12th degree and order as well as 8th degree and order. This truncation resulted in a reduction of the rms differences to a maximum of 5 m. Comparisons have been made with the astrogeodetic data of Rice (United States), Bomford (Europe), and Mather (Australia) and also with geoidal heights from satellite solutions for geocentric station coordinates in North America and the Caribbean. 相似文献
7.
Martin Dunst 《Pure and Applied Geophysics》1977,115(3):459-471
Considering the blocking problem as a baroclinic instability problem in a dispersive wave system with diabatic heating effects, it is of great interest to investigate the role of wavegroup velocityv
gr in blocking processes, becausev
gr controls the energy transfer in the wave field. Using a Newtonian Cooling —type of forcing with a phase differencek to the main field and taking the linearized version of a two-level model, the phase speedc
r, the group velocityv
gr and the growth ratekc
i have been obtained as analytical functions of the mean zonal windU, the thermal windU
T, the coefficient of diabatic heating x, the phase differencek and the wavelengthL. Now the hypothesis is introduced, that a blocking should be expected, ifv
gr has a maximum value in the vicinity ofL
o, for whichc
r vanishes and thee-folding timet=1/kc
i (kc
i>0) is smaller than 6 days (see condition (20) in the text). One finds, that for special parameter combinations (U
T, U, ), where 15 m/secU
T25m/sec,U=10m/sec, 0.8·10–51.5·10–5 [sec–1], certain valuesL
o with an appropriate phase differencek exist, which satisfy the conditions mentioned above (for values see Table 2). TherebyL
o varies within the range 8500 km <L
o<11000 km corresponding to the preferred planetary blocking wavenumber 2 in middle latitudes 50°<<70° N. 相似文献
8.
We have constructed Green's function to Stokes's boundary-value problem with the gravity data distributed over an ellipsoid of revolution. We show that the problem has a unique solution provided that the first eccentricity e0
of the ellipsoid of revolution is less than 0·65041. The ellipsoidal Stokes function describing the effect of ellipticity of the boundary is expressed in the
E-approximation as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Stokes function at the singular point = 0. We prove that the degree of singularity of the ellipsoidal Stokes function in the vicinity of its singular point is the same as that of the spherical Stokes function. 相似文献
9.
Summary The Banach theorem is applied to the Lagrange planetary equation for the semimajor axis of a geostationary satellite orbit to estimate the stability of near-geostationary satellite orbits. To achieve a graveyard (disposal) orbit, which will not interfere (=cross) the initial geostationary orbit, the geostationary semi-major axis ag have to be increased at least by 50 km. Numerical results for a variety of graveyard orbits show that the increase of ag by about 100 km will yield sufficiently stable orbits (accounting for the Earth's gravitational perturbations only) during the next 150 years.Dedicated to the 75th Birthday of Professor Academician Tibor Kolbenheyer 相似文献
10.
A set of acceleration source spectra is constructed using the observed parameters of the specific barrier model of Papageorgiou and Aki. The spectra show a significant departure from the 2-model at the high frequency range. Specifically, the high frequency spectral amplitudes of seismic excitation are higher as compared to the level predicted by the 2-model. This is also supported by other observational evidence. The high frequency amplitudes of acceleration scale proportionally to the square root of the rupture areaS, to the rupture spreading velocityv, and to the local strain drop (/) (=strain drop in between barriers). The local strain drop in between barriers is not related in a simple way to the global strain drop, which is the strain drop estimated by assuming that it is uniform over the entire rupture area. Consequently, the similarity law does not apply. Using the source spectra which we constructed, we derive expressions for high frequency amplitudes of acceleration such asa
rms anda
max. Close to the fault both are independent of fault dimensions and scale as (/µ)(f)1/2, while away from the fault plane they scale asW
1/2(/µ)(f)1/2, whereW is the width of the fault and f is the effective bandwidth of the spectra. 相似文献
11.
R. S. Sidhu 《Pure and Applied Geophysics》1970,80(1):48-70
Summary The frequency equation of Rayleigh waves propagating over the free surface of an isotropic, perfectly elastic, heterogeneous semi-infinite medium with material properties varying as =
0
e
az
, =
0
e
az
, =
0
e
az
(a>0) has been obtained. Solution of the frequency equation in closed form is obtained in two cases (i) =0, (ii) =, and the Rayleigh wave dispersion curves for phase and group velocities drawn. In both the cases the medium yields single Rayleigh modes which cannot propagate below certain cut-off frequencies. It is found that in case (i), <c<c
0 and 0.87500 <c
g
<c
0, and in case (ii), 1.03082 <c<c
1 and 0.90850 <c
g
<c
1, wherec andc
g
denote phase nad group velocities respectively, is the constant shear wave velocity of the mediumc
0 andc
1 are the corresponding Rayleigh wave velocities of the homogeneous medium of the same Poisson's ratio. The motion of the surface particles is found to be retrograde elliptical as in the homogeneous case, but the ratic of the major and minor axes now becomes frequency dependent and is plotted against frequency. In both the cases (i) and (ii), the ratio starts at a lower value at the cut-off frequency and approaches the corresponding value of the homogeneous medium at high frequencies. 相似文献
12.
Summary The paper presents, in a condensed form, the fundamentals of global atmospheric energetics that have a bearing on the linear theory of compensation of non-equilibrium states in the Earth's atmosphere. The author introduces a new coordinate system with the vertical coordinate *=Z*/T*, which suits global atmospheric energetice.The relation between the energetics of the atmospheric system as a whole and the mean energetics level (MEL) is shown. Contrary to what has been assumed so far, it is proved that this level is neither an isopycnic level nor a physical surface, where */t=0 applies everywhere.List of Symbols Used
x, y, z
space coordinates in thez-system
-
x, y,
space coordinates in the -system
-
t
time
-
p, T,
pressure, thermodynamic temperature and air density
-
p*, T*,
pressure, temperature, density and geopotential on the mean energy level
-
g
acceleration of the Earth's gravity
-
c
p
,c
v
,R
specific temperature under constant pressure, volume and specific gas constant
-
= c
p
/c
v
Poisson's constant
-
E
k
,E
v
,E
p
kinetic, internal and potential energies of the atmospheric system
-
r'(x,y)
correction function to inhomogeneous atmosphere
-
v, v
n
magnitude of motion velocity, magnitude of the normal component of velocity
-
O, S, S
0
volume of the whole atmospheric system, surface limiting volumeO and the Earth's surface
-
Z
S
height of surfaceS
-
arbitrary scalar quantity
-
H
,
horizontal differential operators in thez- andp-systems
Dedicated to Corresponding Member Vojtch Vítek, Director of the Institute of Physics of the Atmosphere of the Czechoslovak Academy of Sciences, at the occasion of his sixtieth birthday. 相似文献
13.
Hugo Mandelbaum 《Pure and Applied Geophysics》1968,71(1):66-117
Summary Four hourly current-and wind observations during the years 1924–1927 at the German lightvessels Norderney, Elbe 1, and Aussen-Eider were subjected to harmonic analysis with emphasis on the influence of the wind on the residual as well as on the tidal current. The tidal current is strongest at Elbe 1 and weakest at Aussen-Eider. The half-monthly inequality of the current is strongly influenced by a 2 tidal component. Wind influences the velocity, phase and duration of ebb-and flow current in a systematic way at Norderney and Elbe 1. Deviations from the mean tidal current are caused mainly by the change in wind direction rather than by wind velocity. The mean residual current is weak at the three stations. But wind driven currents have a velocity up to 5 times as great as the mean residual current and reverse their direction with the wind. The annual variation of the mean residual current, however, is caused only to a small part by the annual wind variation.Abbreviations used in this paper Gr. M. Tr.
Greenwich moon transit, i.e. Greenwich civil time of the upper or lower transit of the moon through the meridian of Greenwich
-
C
n
computed tidal current at M1/2Hn
-
C
n
m
computed mean tidal current at M1/2Hn
-
M
n
Moon-half hour mean, i.e. mean of all current velocities observed during M1/2Hn
- M.A.
Moon age of an observation, true Greenwich time of Gr.M.Tr. directly preceeding the time of observation, expressed in 12 integral numbers, each representing M.A. falling in 12 different hourly intervals
- M1/2H
Moon-half hour, 1/2 of the interval between one moon transit and the next, i.e. 1/24 of 12h25m
-
R
n
o
,R
n
'
,R
n
"
residual current computed by harmonic analysis ofn M1/2H means of the mean current, the current at weak winds, and the current at strong winds respectively
- d.o.f.
degrees of freedom
-
standard deviation ofC
n fromM
n
- *
mean standard deviation ofC
n fromM
n for analysis with weighted means
- A
o
Standard error of the residual currentA
o
- AB
standard error of the harmonic coefficientsA
1,B
1,A
2,B
2,...
- S
2
Phase of the current componentS
2 相似文献
14.
15.
Mariya I. Yurkina 《Studia Geophysica et Geodaetica》1996,40(1):9-13
Summary On the basis of the fundamental relations of the Molodensky's Earth's figure theory (1945), admitting the inequality of the
gravity potentials at the Major Vertical Datum W0 and on the surface of the reference level ellipsoid U0, and taken into account that potential W0 enters into equations directly, it is recomended, W0 should be adopted as a primary geodetic constant. Parameters of the best fitting ellipsoid are not needed for the solution
of geodetic problems and for the investigation of the Earth's gravity field. The reason for requiring the reference and actual
fields be close is only that the boundary-value problem can be solved in the linear approximation.
Dedicated to the Memory of M.S. Molodensky
Contribution to the I.A.G. Special Commission SC3 Fundamental Constants (SCFC). 相似文献
16.
The sea surface cannot be used as reference for Major Vertical Datum definition because its deviations from the ideal equipotential surface are very large compared to rms in the observed quantities. The quasigeoid is not quite suitable as the surface representing the most accurate Earth's model without some additional conditions, because it depends on the reference field. The normal Earth's model represented by the rotational level ellipsoid can be defined by the geocentric gravitational constant, the difference in the principal Earth's inertia moments, by the angular velocity of the Earth's rotation and by the semimajor axis or by the potential (U
0
) on the surface of the level ellipsoid. After determining the geopotential at the gauge stations defining Vertical Datums, gravity anomalies and heights should be transformed into the unique vertical system (Major Vertical Datum). This makes it possible to apply Brovar's (1995) idea of determining the reference ellipsoid by minimizing the integral, introduced by Riemann as the Dirichlet principle, to reach a minimum rms anomalous gravity field. Since the semimajor axis depends on tidal effects, potential U
0
should be adopted as the fourth primary fundamental geodetic constant. The equipotential surface, the actual geopotential of which is equal to U
0
, can be adopted as reference for realizing the Major Vertical Datum. 相似文献
17.
Prof. Dr. W. Heiskanen 《Pure and Applied Geophysics》1950,18(1):99-102
Summary By means of the increased gravity measurements it is possible to compute gravimetrically the undulationsN of the geoid with regard to the used reference ellipsoid as well as the «absolute» deflection of the vertical components
g
and
g
. The quantities
g
and
g
enable us to transfer the astronomically observed coordinates of any points from the geoid to the reference ellipsoid and in this way compute without any triangulations the distances along the reference ellipsoid. And still more. With the aid ofN,
g
and
g
we can obtain a general Geodetic World System and convert the existing many systems to it.—The geoid study is no more any academical pastime, it can solve the most important problems of the practical geodesy. 相似文献
18.
Initial coagulation rates of colloidal hematite (-Fe2O3) particles (diameter less than 0.1 µm) were measured experimentally in well-defined laboratory systems at constant temperature. The relative stability ratio,W, was obtained at various ionic strengths in NaCl medium and at pH values in the range from 3 to 12. ExperimentalW values ranged from 1 to 104 in various systems. The results delineate the roles ofspecific andgeneralized coagulation mechanisms for iron oxides. Among the specifically-interacting species (G
ads
0
>G
coul
0
) studied were phosphate, monomeric organic acids of various structures, and polymeric organic acids. The critical coagulation-restabilization concentrations of specifically-interacting anions (from 10–7 to 10–4 molar) can be compared with the general effects of non-specific electrolyte coagulants (10–3 to 10–1 molar). The laboratory results are interpreted with the help of a Surface Complex Formation/Diffuse Layer Model (SCF/DLM) which describes variations of interfacial charge and potential resulting from variations of coagulating species in solution. Comparison of these laboratory experiments with observations on iron behavior in estuarine and lake waters aids in understanding iron removal mechanisms and coagulation time scales in natural systems. 相似文献
19.
The Narmada-Son lineament (NSL) forms a major tectonic feature on the Indian subcontinent. The importance of this lineament lies in its evolution as well as its tectonic history. The lineament seems to have been active since Precambrian times. In order to understand the history of its evolution, it is necessary to know what igenous activity has been taking place along this lineament, and how the Deccan trap volcanics, which cover large areas along this lineament, have erupted.For the study of this problem an analysis of the aeromagnetic anomaly map lying between 76°15 to 77°30E and 21°45 to 22°50N has been carried out. Four different profiles (B
1
B
1,B
2
B
2,B
3
B
3 andB
4
B
4) have been drawn in N-S direction over this area and interpreted in terms of the intrusive bodies present within or below the surface of Deccan trap exposures. Inversion and forward modelling techniques have been adopted for interpretation purposes. An analysis of frequency spectra along the profiles has also been carried out to estimate the average depth of the different magnetic bodies. These results have been correlated with the available geological information. It has been found that most of the small wavelength anomalies are caused by dyke-like bodies within or below the Deccan trap at a depth of less than 0.5 km. 相似文献
20.
Seismic anisotropy of shales 总被引：3，自引：0，他引：3
C.M. Sayers 《Geophysical Prospecting》2005,53(5):667-676
Shales are a major component of sedimentary basins, and they play a decisive role in fluid flow and seismic‐wave propagation because of their low permeability and anisotropic microstructure. Shale anisotropy needs to be quantified to obtain reliable information on reservoir fluid, lithology and pore pressure from seismic data, and to understand time‐to‐depth conversion errors and non‐hyperbolic moveout. A single anisotropy parameter, Thomsen's δ parameter, is sufficient to explain the difference between the small‐offset normal‐moveout velocity and vertical velocity, and to interpret the small‐offset AVO response. The sign of this parameter is poorly understood, with both positive and negative values having been reported in the literature. δ is sensitive to the compliance of the contact regions between clay particles and to the degree of disorder in the orientation of clay particles. If the ratio of the normal to shear compliance of the contact regions exceeds a critical value, the presence of these regions acts to increase δ, and a change in the sign of δ, from the negative values characteristic of clay minerals to the positive values commonly reported for shales, may occur. Misalignment of the clay particles can also lead to a positive value of δ. For transverse isotropy, the elastic anisotropy parameters can be written in terms of the coefficients W200 and W400 in an expansion of the clay‐particle orientation distribution function in generalized Legendre functions. For a given value of W200, decreasing W400 leads to an increase in δ, while for fixed W400, δ increases with increasing W200. Perfect alignment of clay particles with normals along the symmetry axis corresponds to the maximum values of W200 and W400, given by and . A comparison of the predictions of the theory with laboratory measurements shows that most shales lie in a region of the (W200, W400)‐plane defined by W400/W200≤Wmax400/Wmax200 . 相似文献