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1.
In an attempt to model regular variations of the ionosphere, the least-squares harmonic estimation is applied to the time
series of the total electron contents (TEC) provided by the JPL analysis center. Multivariate and modulated harmonic estimation
spectra are introduced and estimated for the series to detect the regular and modulated dominant frequencies of the periodic
patterns. Two significant periodic patterns are the diurnal and annual signals with periods of 24/n hours and 365.25/n days (n = 1, 2, …), which are the Fourier series decomposition of the regular daily and yearly periodic variations of the ionosphere.
The spectrum shows a cluster of periods near 27 days, thereby indicating irregularities at this solar cycle period. A series
of peaks, with periods close to the diurnal signal and its harmonics, are evident in the spectrum. In fact, the daily signal
harmonics of ω
i
= 2πi are modulated with the annual signal harmonics of ω
j
= 2πj/365.25 as ω
ijM
= 2πi(1 ± j/365.25i). Among them, at low and midlatitudes, the largest variations belong to the diurnal signal modulated to the semiannual signal.
Some preliminary results on the modulated part are presented. The maximum ranges of the modulated daily signal are ±15 TECU
and ±6 TECU at high and low solar periods, respectively. A model consisting of purely harmonic functions plus modulated ones
is capable of studying known regular anomalies of the ionosphere, which is currently in progress. 相似文献
2.
S. M. Kudryavtsev 《Journal of Geodesy》1999,73(9):448-451
Modern models of the Earth's gravity field are developed in the IERS (International Earth Rotation Service) terrestrial reference
frame. In this frame the mean values for gravity coefficients of the second degree and first order, C
21(IERS) and S
21(IERS), by the current IERS Conventions are recommended to be calculated by using the observed polar motion parameters. Here, it
is proved that the formulae presently employed by the IERS Conventions to obtain these coefficients are insufficient to ensure
their values as given by the same source. The relevant error of the normalized mean values for C
21(IERS) and S
21(IERS) is 3×10−12, far above the adopted cutoff (10−13) for variations of these coefficients. Such an error in C
21 and S
21 can produce non-modeled perturbations in motion prediction of certain artificial Earth satellites of a magnitude comparable
to the accuracy of current tracking measurements.
Received: 14 September 1998 / Accepted: 20 May 1999 相似文献
3.
Wenbin Shen Jin Li Jiancheng Li Zhengtao Wang Jinsheng Ning Dingbo Chao 《地球空间信息科学学报》2008,11(4):273-278
Given the second radial derivative Vrr(P) |δs of the Earth's gravitational potential V(P) on the surface δS corresponding to the satellite altitude, by using the fictitious compress recovery method, a fictitious regular harmonic field rrVrr(P)^* and a fictitious second radial gradient field V:(P) in the domain outside an inner sphere Ki can be determined, which coincides with the real field V(P) in the domain outside the Earth. Vrr^*(P)could be further expressed as a uniformly convergent expansion series in the domain outside the inner sphere, because rrV(P)^* could be expressed as a uniformly convergent spherical harmonic expansion series due to its regularity and harmony in that domain. In another aspect, the fictitious field V^*(P) defined in the domain outside the inner sphere, which coincides with the real field V(P) in the domain outside the Earth, could be also expressed as a spherical harmonic expansion series. Then, the harmonic coefficients contained in the series expressing V^*(P) can be determined, and consequently the real field V(P) is recovered. Preliminary simulation calculations show that the second radial gradient field Vrr(P) could be recovered based only on the second radial derivative V(P)|δs given on the satellite boundary. Concerning the final recovery of the potential field V(P) based only on the boundary value Vrr (P)|δs, the simulation tests are still in process. 相似文献
4.
申文斌 《地球空间信息科学学报》2009,12(1):1-6
Given a continuous boundary value on the boundary of a "simply closed surface"S that encloses the whole Earth, a regular harmonic fictitious field V*(P) in the domain outside an inner sphere K i that lies inside the Earth could be determined, and it is proved that V*(P) coincides with the Earth’s real field V(P) in the whole domain outside the Earth. Since in the domain outside the inner sphere Ki and the fictitious regular harmonic function V*(P) could be expressed as a uniformly convergent spherical harm... 相似文献
5.
Based upon a data set of 25 points of the Baltic Sea Level Project, second campaign 1993.4, which are close to mareographic
stations, described by (1) GPS derived Cartesian coordinates in the World Geodetic Reference System 1984 and (2) orthometric
heights in the Finnish Height Datum N60, epoch 1993.4, we have computed the primary geodetic parameter W
0(1993.4) for the epoch 1993.4 according to the following model. The Cartesian coordinates of the GPS stations have been converted
into spheroidal coordinates. The gravity potential as the additive decomposition of the gravitational potential and the centrifugal
potential has been computed for any GPS station in spheroidal coordinates, namely for a global spheroidal model of the gravitational
potential field. For a global set of spheroidal harmonic coefficients a transformation of spherical harmonic coefficients
into spheroidal harmonic coefficients has been implemented and applied to the global spherical model OSU 91A up to degree/order
360/360. The gravity potential with respect to a global spheroidal model of degree/order 360/360 has been finally transformed
by means of the orthometric heights of the GPS stations with respect to the Finnish Height Datum N60, epoch 1993.4, in terms
of the spheroidal “free-air” potential reduction in order to produce the spheroidal W
0(1993.4) value. As a mean of those 25 W
0(1993.4) data as well as a root mean square error estimation we computed W
0(1993.4)=(6 263 685.58 ± 0.36) kgal × m. Finally a comparison of different W
0 data with respect to a spherical harmonic global model and spheroidal harmonic global model of Somigliana-Pizetti type (level
ellipsoid as a reference, degree/order 2/0) according to The Geodesist's Handbook 1992 has been made.
Received: 7 November 1996 / Accepted: 27 March 1997 相似文献
6.
Lorenzo Iorio 《Journal of Geodesy》2006,80(3):128-136
In this paper, we quantitatively discuss the impact of the current uncertainties in the even zonal harmonic coefficients J
l
of the Newtonian part of the terrestrial gravitational potential on the measurement of the general relativistic Lense–Thirring effect. We use a suitable linear combination of the nodes Ω of the laser-ranged LAGEOS and LAGEOS-II satellites. The one-sigma systematic error due to mismodelling of the J
l
coefficients ranges from ~ 4% for the EIGEN−GRACE02S gravity field model to ~ 9% for the GGM02S model. Another important source of systematic error of gravitational origin is represented by the secular variations j
l
of the even zonal harmonics. While the relativistic and J
l
signals are linear in time, the shift due to j
l
is quadratic. We quantitatively assess their impact on the measurement of the Lense–Thirring effect with numerical simulations obtaining a 10−20% one-sigma total error over 11 years for EIGEN-GRACE02S. Ciufolini and Pavlis (Nature 431:958–960, 2004) claim a total error of 5% at the one-sigma level. 相似文献
7.
The standard analytical approach which is applied for constructing geopotential models OSU86 and earlier ones, is based on
reducing the boundary value equation to a sphere enveloping the Earth and then solving it directly with respect to the potential
coefficients
n,m
. In an alternative procedure, developed by Jekeli and used for constructing the models OSU91 and EGM96, at first an ellipsoidal
harmonic series is developed for the geopotential and then its coefficients
n,m
e
are transformed to the unknown
n,m
. The second solution is more exact, but much more complicated. The standard procedure is modified and a new simple integral
formula is derived for evaluating the potential coefficients. The efficiency of the standard and new procedures is studied
numerically. In these solutions the same input data are used as for constructing high-degree parts of the EGM96 models. From
two sets of
n,m
(n≤360,|m|≤n), derived by the standard and new approaches, different spectral characteristics of the gravity anomaly and the geoid undulation
are estimated and then compared with similar characteristics evaluated by Jekeli's approach (`etalon' solution). The new solution
appears to be very close to Jekeli's, as opposed to the standard solution. The discrepancies between all the characteristics
of the new and `etalon' solutions are smaller than the corresponding discrepancies between two versions of the final geopotential
model EGM96, one of them (HDM190) constructed by the block-diagonal least squares (LS) adjustment and the other one (V068)
by using Jekeli's approach. On the basis of the derived analytical solution a new simple mathematical model is developed to
apply the LS technique for evaluating geopotential coefficients.
Received: 12 December 2000 / Accepted: 21 June 2001 相似文献
8.
Recurrence relations have been derived for truncation error coefficients of the extended Stokes' function and its partial
derivatives required in the computation of the disturbing gravity vector at any elevation above the earth's surface. The corresponding
formulae, the example of values of the truncation error coefficients for H=30.1 km and ψ0=30∘ and the estimations of truncation error are given in this article.
Received: 26 January 1996 / Accepted: 11 June 1997 相似文献
9.
Low-degree earth deformation from reprocessed GPS observations 总被引:3,自引:1,他引:2
Mathias Fritsche R. Dietrich A. Rülke M. Rothacher P. Steigenberger 《GPS Solutions》2010,14(2):165-175
Surface mass variations of low spherical harmonic degree are derived from residual displacements of continuously tracking
global positioning system (GPS) sites. Reprocessed GPS observations of 14 years are adjusted to obtain surface load coefficients
up to degree n
max = 6 together with station positions and velocities from a rigorous parameter combination. Amplitude and phase estimates of
the degree-1 annual variations are partly in good agreement with previously published results, but also show interannual differences
of up to 2 mm and about 30 days, respectively. The results of this paper reveal significant impacts from different GPS observation
modeling approaches on estimated degree-1 coefficients. We obtain displacements of the center of figure (CF) relative to the
center of mass (CM), Δr
CF–CM, that differ by about 10 mm in maximum when compared to those of the commonly used coordinate residual approach. Neglected
higher-order ionospheric terms are found to induce artificial seasonal and long-term variations especially for the z-component of Δr
CF–CM. Daily degree-1 estimates are examined in the frequency domain to assess alias contributions from model deficiencies with
regard to satellite orbits. Finally, we directly compare our estimated low-degree surface load coefficients with recent results
that involve data from the Gravity Recovery and Climate Experiment (GRACE) satellite mission. 相似文献
10.
Y. M. Wang 《Journal of Geodesy》1989,63(4):359-370
The formulas for the determination of the coefficients of the spherical harmonic expansion of the disturbing potential of
the earth are defined for data given on a sphere. In order to determine the spherical harmonic coefficients, the gravity anomalies
have to be analytically downward continued from the earth's surface to a sphere—at least to the ellipsoid. The goal of this
paper is to continue the gravity anomalies from the earth's surface downward to the ellipsoid using recent elevation models.
The basic method for the downward continuation is the gradient solution (theg
1 term). The terrain correction has also been computed because of the role it can play as a correction term when calculating
harmonic coefficients from surface gravity data.
Theg
1 term and the terrain correction were expanded into the spherical harmonics up to180
th
order. The corrections (theg
1 term and the terrain correction) have the order of about 2% of theRMS value of degree variance of the disturbing potential per degree. The influences of theg
1 term and the terrain correction on the geoid take the order of 1 meter (RMS value of corrections of the geoid undulation) and on the deflections of the vertical is of the order 0.1″ (RMS value of correction of the deflections of the vertical). 相似文献
11.
The derivatives of the Earth gravitational potential are considered in the global Cartesian Earth-fixed reference frame. Spherical
harmonic series are constructed for the potential derivatives of the first and second orders on the basis of a general expression
of Cunningham (Celest Mech 2:207–216, 1970) for arbitrary order derivatives of a spherical harmonic. A common structure of
the series for the potential and its first- and second-order derivatives allows to develop a general procedure for constructing
similar series for the potential derivatives of arbitrary orders. The coefficients of the derivatives are defined by means
of recurrence relations in which a coefficient of a certain order derivative is a linear function of two coefficients of a
preceding order derivative. The coefficients of the second-order derivatives are also presented as explicit functions of three
coefficients of the potential. On the basis of the geopotential model EGM2008, the spherical harmonic coefficients are calculated
for the first-, second-, and some third-order derivatives of the disturbing potential T, representing the full potential V, after eliminating from it the zero- and first-degree harmonics. The coefficients of two lowest degrees in the series for
the derivatives of T are presented. The corresponding degree variances are estimated. The obtained results can be applied for solving various
problems of satellite geodesy and celestial mechanics. 相似文献
12.
ZHONG Yexun LI Zhanyuan HUANG Hu 《地球空间信息科学学报》2006,9(2):147-150
IntroductionThe map is a basic form of geographic informationvisualization[1]. To provide space attributes or geo-graphic orders is the basic function of a map. Incartography, according to the different measure ofphenomenal quantitative attribute, four fo… 相似文献
13.
Z. Martinec 《Journal of Geodesy》1998,72(7-8):460-472
Green's function for the boundary-value problem of Stokes's type with ellipsoidal corrections in the boundary condition for
anomalous gravity is constructed in a closed form. The `spherical-ellipsoidal' Stokes function describing the effect of two
ellipsoidal correcting terms occurring in the boundary condition for anomalous gravity is expressed in O(e
2
0)-approximation as a finite sum of elementary functions analytically representing the behaviour of the integration kernel
at the singular point ψ=0. We show that the `spherical-ellipsoidal' Stokes function has only a logarithmic singularity in
the vicinity of its singular point. The constructed Green function enables us to avoid applying an iterative approach to solve
Stokes's boundary-value problem with ellipsoidal correction terms involved in the boundary condition for anomalous gravity.
A new Green-function approach is more convenient from the numerical point of view since the solution of the boundary-value
problem is determined in one step by computing a Stokes-type integral. The question of the convergence of an iterative scheme
recommended so far to solve this boundary-value problem is thus irrelevant.
Received: 5 June 1997 / Accepted: 20 February 1998 相似文献
14.
Accuracy of GPS-derived relative positions as a function of interstation distance and observing-session duration 总被引:6,自引:0,他引:6
Ten days of GPS data from 1998 were processed to determine how the accuracy of a derived three-dimensional relative position
vector between GPS antennas depends on the chord distance (denoted L) between these antennas and on the duration of the GPS observing session (denoted T). It was found that the dependence of accuracy on L is negligibly small when (a) using the `final' GPS satellite orbits disseminated by the International GPS Service, (b) fixing
integer ambiguities, (c) estimating appropriate neutral-atmosphere-delay parameters, (d) 26 km ≤ L ≤ 300 km, and (e) 4 h ≤T ≤ 24 h. Under these same conditions, the standard error for the relative position in the north–south dimension (denoted S
n
and expressed in mm) is adequately approximated by the equation S
n
=k
n
/T
0.5 with k
n
=9.5 ± 2.1 mm · h0.5 and T expressed in hours. Similarly, the standard errors for the relative position in the east–west and in the up-down dimensions
are adequately approximated by the equations S
e
=k
e
/T
0.5 and S
u
=k
u
/T
0.5, respectively, with k
e
=9.9 ± 3.1 mm · h0.5 and k
u
=36.5 ± 9.1 mm · h0.5.
Received: 5 February 2001 / Accepted: 14 May 2001 相似文献
15.
GOCE gravitational gradients along the orbit 总被引:6,自引:3,他引:3
Johannes Bouman Sophie Fiorot Martin Fuchs Thomas Gruber Ernst Schrama Christian Tscherning Martin Veicherts Pieter Visser 《Journal of Geodesy》2011,85(11):791-805
GOCE is ESA’s gravity field mission and the first satellite ever that measures gravitational gradients in space, that is,
the second spatial derivatives of the Earth’s gravitational potential. The goal is to determine the Earth’s mean gravitational
field with unprecedented accuracy at spatial resolutions down to 100 km. GOCE carries a gravity gradiometer that allows deriving
the gravitational gradients with very high precision to achieve this goal. There are two types of GOCE Level 2 gravitational
gradients (GGs) along the orbit: the gravitational gradients in the gradiometer reference frame (GRF) and the gravitational
gradients in the local north oriented frame (LNOF) derived from the GGs in the GRF by point-wise rotation. Because the V
XX
, V
YY
, V
ZZ
and V
XZ
are much more accurate than V
XY
and V
YZ
, and because the error of the accurate GGs increases for low frequencies, the rotation requires that part of the measured
GG signal is replaced by model signal. However, the actual quality of the gradients in GRF and LNOF needs to be assessed.
We analysed the outliers in the GGs, validated the GGs in the GRF using independent gravity field information and compared
their assessed error with the requirements. In addition, we compared the GGs in the LNOF with state-of-the-art global gravity
field models and determined the model contribution to the rotated GGs. We found that the percentage of detected outliers is
below 0.1% for all GGs, and external gravity data confirm that the GG scale factors do not differ from one down to the 10−3 level. Furthermore, we found that the error of V
XX
and V
YY
is approximately at the level of the requirement on the gravitational gradient trace, whereas the V
ZZ
error is a factor of 2–3 above the requirement for higher frequencies. We show that the model contribution in the rotated
GGs is 2–35% dependent on the gravitational gradient. Finally, we found that GOCE gravitational gradients and gradients derived
from EIGEN-5C and EGM2008 are consistent over the oceans, but that over the continents the consistency may be less, especially
in areas with poor terrestrial gravity data. All in all, our analyses show that the quality of the GOCE gravitational gradients
is good and that with this type of data valuable new gravity field information is obtained. 相似文献
16.
Determination of the free core nutation period from tidal gravity observations of the GGP superconducting gravimeter network 总被引:1,自引:1,他引:1
This study is based on 25 long time-series of tidal gravity observations recorded with superconducting gravimeters at 20 stations
belonging to the Global Geodynamic Project (GGP). We investigate the diurnal waves around the liquid core resonance, i.e.,
K
1, ψ1 and φ1, to determine the free core nutation (FCN) period, and compare these experimental results with models of the Earth response
to the tidal forces. For this purpose, it is necessary to compute corrected amplitude factors and phase differences by subtracting
the ocean tide loading (OTL) effect. To determine this loading effect for each wave, it was thus necessary to interpolate
the contribution of the smaller oceanic constituents from the four well determined diurnal waves, i.e., Q
1, O
1, P
1, K
1. It was done for 11 different ocean tide models: SCW80, CSR3.0, CSR4.0, FES95.2, FES99, FES02, TPXO2, ORI96, AG95, NAO99
and GOT00. The numerical results show that no model is decisively better than the others and that a mean tidal loading vector
gives the most stable solution for a study of the liquid core resonance. We compared solutions based on the mean of the 11
ocean models to subsets of six models used in a previous study and five more recent ones. The calibration errors put a limit
on the accuracy of our global results at the level of ± 0.1%, although the tidal factors of O
1 and K
1 are determined with an internal precision of close to 0.05%. The results for O
1 more closely fit the DDW99 non-hydrostatic anelastic model than the elastic one. However, the observed tidal factors of K
1 and ψ1 correspond to a shift of the observed resonance with respect to this model. The MAT01 model better fits this resonance shape.
From our tidal gravity data set, we computed the FCN eigenperiod. Our best estimation is 429.7 sidereal days (SD), with a
95% confidence interval of (427.3, 432.1). 相似文献
17.
C. C. Tscherning 《Journal of Geodesy》1999,73(6):332-336
A reproducing-kernel Hilbert space (RKHS) of functions harmonic in the set outside a sphere with radius R
0, having a reproducing kernel K
0(P,Q) is considered (P, Q, and later P
n
being points in the set of harmonicity). The degree variances of this kernel will be denoted σ0
n
.
The set of Riesz representers associated with the evaluation functionals (or gravity functionals) related to distinct points
P
n
,n = 1,…,N, on a two-dimensional surface surrounding the bounding sphere, will be linearly independent. These functions are used to
define a new N-dimensional RKHS with kernel (a
n
>0)
If the points all are located on a concentric sphere with radius R
1>R
0, and form an ε-net covering the sphere, and a
n
are suitable area elements (depending on N), then this kernel will converge towards an isotropic kernel with degree variances
Consequently, if K
N
(P,Q) is required to represent an isotropic covariance function of the Earth's gravity potential, COV(P,Q), σ0
n
can be selected so that σ
n
becomes equal to the empirical degree variances.
If the points are chosen at varying radial distances R
n
>R
0, then an anisotropic kernel, or equivalent covariance function representation, can be constructed. If the points are located
in a bounded region, the kernel may be used to modify the original kernel
Values of anisotropic covariance functions constructed based on these ideas are calculated, and some initial ideas are presented
on how to select the points P
n
.
Received: 24 September 1998 / Accepted: 10 March 1999 相似文献
18.
A methodology for precise determination of the fundamental geodetic parameter w
0, the potential value of the Gauss–Listing geoid, as well as its time derivative 0, is presented. The method is based on: (1) ellipsoidal harmonic expansion of the external gravitational field of the Earth
to degree/order 360/360 (130 321 coefficients; http://www.uni-stuttgard.de/gi/research/ index.html projects) with respect
to the International Reference Ellipsoid WGD2000, at the GPS positioned stations; and (2) ellipsoidal free-air gravity reduction
of degree/order 360/360, based on orthometric heights of the GPS-positioned stations. The method has been numerically tested
for the data of three GPS campaigns of the Baltic Sea Level project (epochs 1990.8,1993.4 and 1997.4). New w
0 and 0 values (w
0=62 636 855.75 ± 0.21 m2/s2, 0=−0.0099±0.00079 m2/s2 per year, w
0/&γmacr;=6 379 781.502 m,0/&γmacr;=1.0 mm/year, and &γmacr;= −9.81802523 m2/s2) for the test region (Baltic Sea) were obtained. As by-products of the main study, the following were also determined: (1)
the high-resolution sea surface topography map for the Baltic Sea; (2) the most accurate regional geoid amongst four different
regional Gauss–Listing geoids currently proposed for the Baltic Sea; and (3) the difference between the national height datums
of countries around the Baltic Sea.
Received: 14 August 2000 / Accepted: 19 June 2001 相似文献
19.
A. J. E. Smith B. A. C. Ambrosius K. F. Wakker P. L. Woodworth J. M. Vassie 《Journal of Geodesy》1997,71(11):695-703
Three years of TOPEX/POSEIDON altimeter data have been processed at Delft Institute for Earth-Oriented Space Research (DEOS)
to solve the major diurnal and semi-diurnal constituents of the global ocean tide using the two classical methods of tidal
analysis, i.e. the harmonic and response analyses. Some experiments with the parameters in the response formalism show that the tidal admittance
in both the diurnal and semi-diurnal band can be adequately described with a lag interval of 2 days and a number of lags of
three. Results of both methods are evaluated from the differences with the most recent Grenoble hydrodynamic model (FES95.2)
and from the fit with the harmonic constants of a globally distributed set of tide gauges. It was found that the solutions
of the two methods differ at the millimeter level and are thus fully equivalent, which is confirmed by the tide gauges and
the differences with FES95.2. From the comparisons with the Grenoble model it was found that the M
2 and S
2 solutions of that model likely contain bathymetric errors which are of the order of 1–2 cm for M
2 and 0.5 cm for S
2.
Received: 18 December 1996 / Accepted: 12 May 1997 相似文献
20.
G. Blaha 《Journal of Geodesy》1978,52(1):19-23
A simple formula is presented giving the value of γ−γ
r
to better than 0.001 mgal associated with an arbitrary reference ellipsoid, where γ is the normal gravity and γ
r
is its radial component. Further simplifications of this formula are possible, depending on the desired accuracy. Since in
the actual field g−gr equals γ−γ
r
to a good approximation, this formula makes it possible to work in terms of gr rather than in terms of the measured quantity g. Such a choice is attractive mainly because the spherical harmonic expansion
of gr is very simple. 相似文献