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1.
Short-wavelength Spectral Properties of the Gravity Field from a Range of Regional Data Sets 总被引：1，自引：0，他引：1
Jakob Flury 《Journal of Geodesy》2006,79(10-11):624-640
The GRACE (gravity recovery and climate experiment) and GOCE (gravity field and steady-state ocean circulation explorer) dedicated gravity satellite missions are expected to deliver the long-wavelength scales of the Earth’s gravity field with extreme precision. For many applications in Earth sciences, future research activities will have to focus on a similar precision on shorter scales not recovered by satellite missions. Here, we investigate the signal power of gravity anomalies at such short scales. We derive an average degree variance and power spectral density model for topography-reduced gravity anomalies (residual terrain model anomalies and de-trended refined Bouguer anomalies), which is valid for wavelengths between 0.7 and 100 km. The model is based on the analysis of gravity anomalies from 13 test regions in various geographical areas and geophysical settings, using various power spectrum computation approaches. The power of the derived average topography-reduced model is considerably lower than the Tscherning–Rapp free air anomaly model. The signal power of the individual test regions deviates from the obtained average model by less than a factor of 4 in terms of square-root power spectral amplitudes. Despite the topographic reduction, the highest signal power is found in mountainous areas and the lowest signal power in flat terrain. For the derived average power spectral model, a validation procedure is developed based on least-squares prediction tests. The validation shows that the model leads to a good prediction quality and realistic error measures. Therefore, for least-squares prediction, the model could replace the use of autocovariance functions derived from local or regional data. 相似文献
2.
Model computations were performed for the study of numerical errors which are interjected into local geoid computations byFFT. The gravity field model was generated through the attractions of granitic prisms derived from actual geology. Changes in
sampling interval introduced only0.3 cm variation in geoid heights. Although zero padding alone provided an improvement of more than5 cm in theFFT generated geoid, the combination of spectral windowing (tapering) and padding further reduced numerical errors. For theGPS survey of Franklin County, Ohio, the parameters selected as a result of model computations, allow large reduction in local
data requirements while still retaining the centimeter accuracy when tapering and padding is applied. 相似文献
3.
William E. Strange 《Journal of Geodesy》1982,56(4):300-311
Errors are introduced in orthometric height computations by the use of standard formulas to estimate mean gravity along the
plumb line. Direct measurements of gravity between the Earth’s surface and sea level from bore hole gravimetry were used to
determine the magnitude of these errors. For the seven cases studied, errors in orthometric height, due to the use of the
Helmert method for computing mean gravity along the plumb line, were generally small (<2 cm). However, in one instance the error was substantial, being9.6 cm. The results verified the general validity of the Poincaré-Prey approach to estimation of gravity along the plumb line and
demonstrated that the suggestion byVanicek (1980) that the air gradient is more appropriate is incorrect. With sufficient topographic information to compute terrain
corrections, and density estimates from surface gravity, errors in mean gravity along the plumb line should contribute no
more than 3cm to orthometric height computation. 相似文献
4.
5.
The temporal changes of the Earth’s gravity field can be observed on a global scale with low–low satellite-to-satellite tracking (SST) missions. One of the largest restrictions of the quality of low–low SST gravity fields is temporal aliasing. This study investigates the design of optimal satellite orbits for temporal gravity retrieval regarding temporal aliasing. We present a method with which optimal altitudes for the orbit of a gravity satellite mission with the goal of temporal gravity retrieval can be identified. The two basic orbit frequencies, the rates of the argument of the latitude and the ascending node, determine the mapping of the signal measured along the orbit onto the spherical harmonic (SH) spectrum. The main spectral characteristics of temporal aliasing are maxima at specific SH orders. The magnitude of the effects depends on the basic frequencies. This is analyzed with numerical low–low SST closed-loop simulations including both tidal and non-tidal background models and GRACE-like observation noise. Analyses of actual monthly GRACE solutions show that these characteristics do not depend on the low–low SST processing method. Optimal orbits are found in specific altitude bands. The best altitude bands regarding temporal aliasing for polar low Earth orbiters (LEOs) are around 301, 365, 421 and 487 km. In these bands, major aliasing effects do not occur for SH degrees and orders below 70. This study gives unique and in-depth insights into the mechanism of temporal aliasing. As it provides an important orbit design approach, it is independent of any (post-) processing method to reduce temporal aliasing. 相似文献
6.
Simulation study of a follow-on gravity mission to GRACE 总被引：9，自引：3，他引：6
The gravity recovery and climate experiment (GRACE) has been providing monthly estimates of the Earth’s time-variable gravity
field since its launch in March 2002. The GRACE gravity estimates are used to study temporal mass variations on global and
regional scales, which are largely caused by a redistribution of water mass in the Earth system. The accuracy of the GRACE
gravity fields are primarily limited by the satellite-to-satellite range-rate measurement noise, accelerometer errors, attitude
errors, orbit errors, and temporal aliasing caused by un-modeled high-frequency variations in the gravity signal. Recent work
by Ball Aerospace & Technologies Corp., Boulder, CO has resulted in the successful development of an interferometric laser
ranging system to specifically address the limitations of the K-band microwave ranging system that provides the satellite-to-satellite
measurements for the GRACE mission. Full numerical simulations are performed for several possible configurations of a GRACE
Follow-On (GFO) mission to determine if a future satellite gravity recovery mission equipped with a laser ranging system will
provide better estimates of time-variable gravity, thus benefiting many areas of Earth systems research. The laser ranging
system improves the range-rate measurement precision to ~0.6 nm/s as compared to ~0.2 μm/s for the GRACE K-band microwave
ranging instrument. Four different mission scenarios are simulated to investigate the effect of the better instrument at two
different altitudes. The first pair of simulated missions is flown at GRACE altitude (~480 km) assuming on-board accelerometers
with the same noise characteristics as those currently used for GRACE. The second pair of missions is flown at an altitude
of ~250 km which requires a drag-free system to prevent satellite re-entry. In addition to allowing a lower satellite altitude,
the drag-free system also reduces the errors associated with the accelerometer. All simulated mission scenarios assume a two
satellite co-orbiting pair similar to GRACE in a near-polar, near-circular orbit. A method for local time variable gravity
recovery through mass concentration blocks (mascons) is used to form simulated gravity estimates for Greenland and the Amazon
region for three GFO configurations and GRACE. Simulation results show that the increased precision of the laser does not
improve gravity estimation when flown with on-board accelerometers at the same altitude and spacecraft separation as GRACE,
even when time-varying background models are not included. This study also shows that only modest improvement is realized
for the best-case scenario (laser, low-altitude, drag-free) as compared to GRACE due to temporal aliasing errors. These errors
are caused by high-frequency variations in the hydrology signal and imperfections in the atmospheric, oceanographic, and tidal
models which are used to remove unwanted signal. This work concludes that applying the updated technologies alone will not
immediately advance the accuracy of the gravity estimates. If the scientific objectives of a GFO mission require more accurate
gravity estimates, then future work should focus on improvements in the geophysical models, and ways in which the mission
design or data processing could reduce the effects of temporal aliasing. 相似文献
7.
The second-order derivatives of the Earth’s potential in the local north-oriented reference frame are expanded in series of
modified spherical harmonics. Linear relations are derived between the spectral coefficients of these series and the spectrum
of the geopotential. On the basis of these relations, recurrence procedures are developed for evaluating the geopotential
coefficients from the spectrum of each derivative and, inversely, for simulating the latter from a known geopotential model.
Very simple structure of the derived expressions for the derivatives is convenient for estimating the geopotential coefficients
by the least-squares procedure, at a certain step of processing satellite gradiometry data. Due to the orthogonality of the
new series, the quadrature formula approach can be also applied, which allows avoidance of aliasing errors caused by the series
truncation. The spectral coefficients of the derivatives are evaluated on the basis of the derived relations from the geopotential
models EGM96 and EIGEN-CG01C at a mean orbital sphere of the GOCE satellite. Various characteristics of the spectra are studied
corresponding to the EGM96 model.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. 相似文献
8.
Errors in high-frequency ocean tide models alias to low frequencies in time-variable gravity solutions from the Gravity Recovery
and Climate Experiment (GRACE). We conduct an observational study of apparent gravity changes at a period of 161 days, the
alias period of errors in the S2 semidiurnal solar tide. We examine this S2 alias in the release 4 (RL04) reprocessed GRACE monthly gravity solutions for the period April 2002 to February 2008, and
compare with that in release 1 (RL01) GRACE solutions. One of the major differences between RL04 and RL01 is the ocean tide
model. In RL01, the alias is evident at high latitudes, near the Filchner-Ronne and Ross ice shelves in Antarctica, and regions
surrounding Greenland and Hudson Bay. RL04 shows significantly lower alias amplitudes in many of these locations, reflecting
improvements in the ocean tide model. However, RL04 shows continued alias contamination between the Ronne and Larson ice shelves,
somewhat larger than in RL01, indicating a need for further tide model improvement in that region. For unknown reasons, the
degree-2 zonal spherical harmonics (C20) of the RL04 solutions show significantly larger S2 aliasing errors than those from RL01. 相似文献
9.
Adaptive filtering of GOCE-derived gravity gradients of the disturbing potential in the context of the space-wise approach 总被引：1，自引：0，他引：1
Filtering and signal processing techniques have been widely used in the processing of satellite gravity observations to reduce measurement noise and correlation errors. The parameters and types of filters used depend on the statistical and spectral properties of the signal under investigation. Filtering is usually applied in a non-real-time environment. The present work focuses on the implementation of an adaptive filtering technique to process satellite gravity gradiometry data for gravity field modeling. Adaptive filtering algorithms are commonly used in communication systems, noise and echo cancellation, and biomedical applications. Two independent studies have been performed to introduce adaptive signal processing techniques and test the performance of the least mean-squared (LMS) adaptive algorithm for filtering satellite measurements obtained by the gravity field and steady-state ocean circulation explorer (GOCE) mission. In the first study, a Monte Carlo simulation is performed in order to gain insights about the implementation of the LMS algorithm on data with spectral behavior close to that of real GOCE data. In the second study, the LMS algorithm is implemented on real GOCE data. Experiments are also performed to determine suitable filtering parameters. Only the four accurate components of the full GOCE gravity gradient tensor of the disturbing potential are used. The characteristics of the filtered gravity gradients are examined in the time and spectral domain. The obtained filtered GOCE gravity gradients show an agreement of 63–84 mEötvös (depending on the gravity gradient component), in terms of RMS error, when compared to the gravity gradients derived from the EGM2008 geopotential model. Spectral-domain analysis of the filtered gradients shows that the adaptive filters slightly suppress frequencies in the bandwidth of approximately 10–30 mHz. The limitations of the adaptive LMS algorithm are also discussed. The tested filtering algorithm can be connected to and employed in the first computational steps of the space-wise approach, where a time-wise Wiener filter is applied at the first stage of GOCE gravity gradient filtering. The results of this work can be extended to using other adaptive filtering algorithms, such as the recursive least-squares and recursive least-squares lattice filters. 相似文献
10.
L. E. Sjöberg 《Journal of Geodesy》2000,74(2):255-268
The topographic potential and the direct topographic effect on the geoid are presented as surface integrals, and the direct
gravity effect is derived as a rigorous surface integral on the unit sphere. By Taylor-expanding the integrals at sea level
with respect to topographic elevation (H) the power series of the effects is derived to arbitrary orders. This study is primarily limited to terms of order H
2. The limitations of the various effects in the frequently used planar approximations are demonstrated. In contrast, it is
shown that the spherical approximation to power H
2 leads to a combined topographic effect on the geoid (direct plus indirect effect) proportional to H˜2 (where terms of degrees 0 and 1 are missing) of the order of several metres, while the combined topographic effect on the
height anomaly vanishes, implying that current frequent efforts to determine the direct effect to this order are not needed.
The last result is in total agreement with Bjerhammar's method in physical geodesy. It is shown that the most frequently applied
remove–restore technique of topographic masses in the application of Stokes' formula suffers from significant errors both
in the terrain correction C (representing the sum of the direct topographic effect on gravity anomaly and the effect of continuing the anomaly to sea
level) and in the term t (mainly representing the indirect effect on the geoidal or quasi-geoidal height).
Received: 18 August 1998 / Accepted: 4 October 1999 相似文献
11.
Performance of three types of Stokes's kernel in the combined solution for the geoid 总被引：8，自引：6，他引：2
When regional gravity data are used to compute a gravimetric geoid in conjunction with a geopotential model, it is sometimes
implied that the terrestrial gravity data correct any erroneous wavelengths present in the geopotential model. This assertion
is investigated. The propagation of errors from the low-frequency terrestrial gravity field into the geoid is derived for
the spherical Stokes integral, the spheroidal Stokes integral and the Molodensky-modified spheroidal Stokes integral. It is
shown that error-free terrestrial gravity data, if used in a spherical cap of limited extent, cannot completely correct the
geopotential model. Using a standard norm, it is shown that the spheroidal and Molodensky-modified integration kernels offer
a preferable approach. This is because they can filter out a large amount of the low-frequency errors expected to exist in
terrestrial gravity anomalies and thus rely more on the low-frequency geopotential model, which currently offers the best
source of this information.
Received: 11 August 1997 / Accepted: 18 August 1998 相似文献
12.
本文所采用的基于输入－输出系统论的谱方法在计算结果的精度上与最小二乘配置方法相当,却很容易用于异性场的计算。用该谱方法对卫星测高及海洋重力资料进行组合求解重力场量（大地水准面差距和重力异常）,其误差估计结果表明各向异性场的计算精度优于各向同性场的精度。 相似文献
13.
应用求解沿轨迹重力异常的垂线偏差法以及求解空间分辨率的交叉谱分析法,建立了高度计测距精度与沿轨迹重力异常反演精度以及空间分辨率的关联性模型。首先依据卫星测高原理,给出了沿轨迹重力异常的误差传播公式,然后以此为基础通过推导交叉谱分析中一致性系数与信噪比的数学表达式,建立了高度计测距精度与空间分辨率的解析关系。数值仿真结果表明:雷达高度计测距精度与沿轨迹重力异常反演精度成正比关系,与空间分辨率成幂函数关系,即高度计测距精度提高m倍,沿轨迹重力异常反演精度提高m倍,全球海域平均空间分辨率提高m0.464 4倍。将数值仿真结果与相关文献中对实际测高数据的处理结果进行比较,验证了理论分析及模型的正确性。 相似文献
14.
从经典边值问题理论及球谐函数理论出发,在空域推导获得了由大地水准面高以及垂线偏差计算扰动重力的解析计算公式,为利用卫星测高数据反演海洋扰动重力提供了理论基础。针对全球海洋区域和局部海洋区域的扰动重力反演,在前人已有工作基础上,提出了改进的基于一维FFT的精确快速算法,保证了计算结果与原解析方法完全一致,且计算速度提高约20倍。该算法在提高计算效率的同时避免了由于引入FFT而产生的混叠、边缘效应问题,而且对观测数据的序列长度没有硬性要求,使得应用更加灵活。利用EGM2008地球重力场模型分别生成了2.5'分辨率大地水准面高数据和垂线偏差数据,按照本文提出的改进方法(采用全球积分计算)分别反演获得了全球及局部海洋区域的扰动重力。经比较分析,由大地水准面和垂线偏差分别反演获得的扰动重力其差异在0.8×10-5 m/s2以内,这说明两种反演方法是基本一致的,但在数据包含系统误差的情况下,由垂线偏差反演扰动重力具有一定优势。 相似文献
15.
The aim of this investigation is to study some FFT problems related to the application of FFT to gravity field convolution integrals. And the others, such as the effect of spectral leakage, edge effects, cyclic convolution and effect of padding, are also discussed. A numerical test for these problems is made. A large area of Western China selected for the test is located between 30°N～36°N and 96°E～102°E and includes 1 858 gravity observations on land. The results show that the removal of the bias in the residual gravity anomalies is important to avoid spectral leakage. One hundred percent zero padding is highly recommended for further research of the geoid to remove cyclic convolution errors and edge effects. 1-D FFT is recommended for precise local geoid determination because it does not use kernel approximation. 相似文献
16.
星载加速度计的动力法校准 总被引：1，自引：0，他引：1
通过模拟轨道，利用动力法对星载加速度计校准进行了研究。用不同参考重力场模型获得的校准参数分别重新积分卫星轨道，与模拟轨道的差异最大可达m级。结果表明，参考重力场模型误差对加速度计校准的影响不可忽略，在校准加速度计的同时应解算重力场模型，以削弱模型误差的影响。 相似文献
17.
Sub-daily alias and draconitic errors in the IGS orbits 总被引：6，自引：2，他引：4
Harmonic signals with a fundamental period near the GPS draconitic year (351.2 days) and overtones up to at least the sixth multiple have been observed in the power spectra of nearly all products of the International GNSS Service (IGS), including station position time series, apparent geocenter motions, orbit jumps between successive days, and midnight discontinuities in earth orientation parameter (EOP) rates. Two main mechanisms have been suggested for the harmonics: mismodeling of orbit dynamics and aliasing of near-sidereal local station multipath effects. Others have studied the propagation of local multipath errors into draconitic position variations, but orbit-related processes have been less examined. We elaborate our earlier analysis of GPS day-boundary orbit discontinuities where we observed some draconitic features as well as prominent spectral bands near 29-, 14-, 9-, and 7-day periods. Finer structures within the sub-seasonal bands fall close to the expected alias frequencies for 24-h sampling of sub-daily EOP tide lines but do not coincide precisely. While once-per-revolution empirical orbit parameters should strongly absorb any sub-daily EOP tide errors due to near-resonance of their respective periods, the observed differences require explanation. This has been done by simulating EOP tidal errors and checking their impact on a long series of estimated daily GPS orbits and EOPs. Indeed, simulated tidal aliases are found to be very similar to the observed IGS orbital features in the sub-seasonal bands. Moreover and unexpectedly, some low draconitic harmonics were also produced, potentially a source for the widespread errors in most IGS products. The results from this study are further evidence for the need of an improved sub-daily EOP tide model. 相似文献
18.
Quasi-stationary sea surface topography estimation by the multiple input/output method 总被引：1，自引：0，他引：1
Multiple input/multiple output system theory (MIMOST) is briefly presented, and the application of the method to the quasi-stationary
sea surface topography (QSST) estimation and the filtering of the input observations are discussed. The repeat character of
satellite altimetry missions provides more than one sample of the measured sea surface height (SSH) field, and an approximation
of the input signal and error power spectral densities can be determined using this successive information. A case study in
the Labrador Sea is considered using SSHs from ERS1 phases C and G, ERS1-GM, ERS2 phase A and TOPEX/POSEIDON altimetric missions
in combination with shipborne gravity anomalies. The time period of the observations in this study is from 1993 to 1998. Some
comparisons between the techniques used for the power spectral density approximation are carried out and some remarks on the
properties of the estimated QSST are presented.
Received: 19 October 1999 / Accepted: 23 October 2000 相似文献
19.
为实现大范围、高精度基准重力梯度数据库的构建,考虑到重力梯度场对地形质量的敏感效应,一般利用恒密度数字高程模型来求取重力梯度值,从而忽略了地形密度变化以及水准面以下密度异常对重力梯度的影响。根据重力位理论中求解边值问题的数值应用方法,直接利用重力异常数据求取重力梯度场,弥补了密度变化和密度异常在重力梯度上的反映。根据模型算例和实测重力异常数据求取了剖面重力梯度值,结果表明,限于重力数据空间分辨率的影响,利用重力异常数据可恢复中长波段重力梯度场。该方法与地形数据求取重力梯度和卫星重力梯度测量等方法技术相结合,对重力梯度数据库的建设具有实际应用价值。 相似文献
20.
Four integral-based methods for the inversion of gravity disturbances, derived from airborne gravity measurements, into the disturbing potential on the Bjerhammar sphere and the Earths surface are investigated and compared with least-squares (LS) collocation. The performance of the methods is numerically investigated using noise-free and noisy observations, which have been generated using a synthetic gravity field model. It is found that advanced interpolation of gravity disturbances at the nodes of higher-order numerical integration formulas significantly improves the performance of the integral-based methods. This is preferable to the commonly used one-point composed Newton–Cotes integration formulas, which intrinsically imply a piecewise constant interpolation over a patch centered at the observation point. It is shown that the investigated methods behave similarly for noise-free observations, but differently for noisy observations. The best results in terms of root-mean-square (RMS) height-anomaly errors are obtained when the gravity disturbances are first downward continued (inverse Poisson integral) and then transformed into potential values (Hotine integral). The latter has a strong smoothing effect, which damps high-frequency errors inherent in the downward-continued gravity disturbances. An integral method based on the single-layer representation of the disturbing potential shows a similar performance. This representation has the advantage that it can be used directly on surfaces with non-spherical geometry, whereas classical integral-based methods require an additional step if gravity field functionals have to be computed on non-spherical geometries. It is shown that defining the single-layer density on the Bjerhammar sphere gives results with the same quality as obtained when using the Earths topography as support for the single-layer density. A comparison of the four integral-based methods with LS collocation shows that the latter method performs slightly better in terms of RMS height-anomaly errors. 相似文献