共查询到20条相似文献，搜索用时 15 毫秒
1.
本文利用澳大利亚北领地West Arnhem Land 地区实测重力异常数据并联合DEM(9")和SRTM3(3")地形高程数据,使用移去-恢复技术和Stokes积分方法计算了该地区两条剖面的重力梯度及其功率谱密度,使用FFT方法解算了整个地区的重力梯度值,结果证明了联合重力异常数据和高分辨率地形高程数据能有效地提高重力梯度的解算精度;功率谱密度的计算结果与国外成熟的重力梯度功率谱密度模型相吻合,表明高于0.3 Hz频率范围的功率谱密度可看做噪声,为重力梯度数据处理中噪声的辨别和剔除提供了借鉴,另外对重力梯度辅助导航基准图的构建以及重力梯度测量系统的标定提供了有益的探索. 相似文献
2.
Mehdi Eshagh 《Acta Geophysica》2010,58(2):215-243
The traditional expressions for gravity gradients in local north-oriented frame and tensor spherical harmonics have complicated
forms involved with first- and second-order derivatives of spherical harmonics and also singular terms. In this paper we present
alternative expressions for these quantities, which are simpler and contain no singular terms. The presented formulas are
useful for those disciplines of geosciences which are involved with potential theory, tensor spherical harmonics and second-order
derivatives of spherical harmonic series in the local north-oriented frame. A simple numerical test on the solution of the
gradiometric boundary value problems presents the correctness of these new expressions and ability of the solutions to continue
the gravity gradients from satellite level down to sea level using spherical harmonics. 相似文献
3.
Mehdi Eshagh 《Geophysical Prospecting》2014,62(1):158-171
The idea of this paper is to present estimators for combining terrestrial gravity data with Earth gravity models and produce a high‐quality source of the Earth's gravity field data through all wavelengths. To do so, integral and point‐wise estimators are mathematically developed, based on the spectral combination theory, in such a way that they combine terrestrial data with one and/or two Earth gravity models. The integral estimators are developed so that they become biased or unbiased to a priori information. For testing the quality of the estimators, their global mean square errors are generated using an Earth gravity model08 model and one of the recent products of the gravity field and steady‐state ocean circulation explorer mission. Numerical results show that the integral estimators have smaller global root mean square errors than the point‐wise ones but they are not efficient practically. The integral estimator of the biased type is the most suited due to its smallest global root mean square error comparing to the rest of the estimators. Due largely to the omission errors of Earth gravity models the point‐wise estimators are not sensitive to the Earth gravity model commission error; therefore, the use of high‐degree Earth gravity models is very influential for reduction of their root mean square errors. Also it is shown that the use of the ocean circulation explorer Earth gravity model does not significantly reduce the root mean square errors of the presented estimators in the presence of Earth gravity model08. All estimators are applied in the region of Fennoscandia and a cap size of 2° for numerical integration and a maximum degree of 2500 for generation of band‐limited kernels are found suitable for the integral estimators. 相似文献
4.
Mehdi Eshagh 《Pure and Applied Geophysics》2014,171(9):2391-2406
Subcrustal stress induced by mantle convection can be determined by the Earth’s gravitational potential. In this study, the spherical harmonic expansion of the simplified Navier–Stokes equation is developed further so satellite gradiometry data (SGD) can be used to determine the subcrustal stress. To do so, we present two methods for producing the stress components or an equivalent function thereof, the so-called S function, from which the stress components can be computed numerically. First, some integral estimators are presented to integrate the SGD and deliver the stress components and/or the S function. Second, integral equations are constructed for inversion of the SGD to the aforementioned quantities. The kernel functions of the integrals of both approaches are plotted and interpreted. The behaviour of the integral kernels is dependent on the signal and noise spectra in the first approach whilst it does not depend on extra information in the second method. It is shown that recovering the stress from the vertical–vertical gradients, using the integral estimators presented, is suitable, but when using the integral equations the vertical–vertical gradients are recommended for recovering the S function and the vertical–horizontal gradients for the stress components. This study is theoretical and numerical results using synthetic or real data are not given. 相似文献
5.
Mehdi Eshagh 《Acta Geophysica》2011,59(1):29-54
Solution of the gradiometric boundary value problems leads to three integral formulas. If we are satisfied with obtaining
a smooth solution for the Earth’s gravity field, we can use the formulas in regional gravity field modelling. In such a case,
satellite gradiometric data are integrated on a sphere at satellite level and continued downward to the disturbing potential
(geoid) at sea level simultaneously. This paper investigates the gravity field modelling from a full tensor of gravity at
satellite level. It studies the truncation bias of the integrals as well as the filtering of noise of data. Numerical studies
show that by integrating T
zz
with 1 mE noise and in a cap size of 7°, the geoid can be recovered with an error of 12 cm after the filtering process. Similarly,
the errors of the recovered geoids from T
xz,yz
and T
xx-yy, 2xy
are 13 and 21 cm, respectively. 相似文献
6.
Determination of gravity anomaly at sea level from inversion of satellite gravity gradiometric data 总被引：1，自引：0，他引：1
Gravity gradients can be used to determine the local gravity field of the Earth. This paper investigates downward continuation of all elements of the disturbing gravitational tensor at satellite level using the second-order partial derivatives of the extended Stokes formula in the local-north oriented frame to determine the gravity anomaly at sea level. It considers the inversion of each gradient separately as well as their joint inversion. Numerical studies show that the gradients Tzz, Txx, Tyy and Txz have similar capability of being continued downward to sea level in the presence of white noise, while the gradient Tyz is considerably worse than the others. The bias-corrected joint inversion process shows the possibility of recovering the gravity anomaly with 1 mGal accuracy. Variance component estimation is also tested to update the observation weights in the joint inversion. 相似文献
7.
This study investigates the utility of the potential fields (gravity and magnetics) in volcanic settings as observed on the Møre margin. Synthetic models are used to investigate the effect of volcanics on the gravity and magnetic fields. The focus is on detecting sub-basaltic basement structures. The methods applied to the models are Euler deconvolution on magnetic data, gravity gradients and integrated 3D gravity and magnetic forward modelling. The same methods are used on the Møre margin and the results compared to the synthetic models. The Euler deconvolution on the magnetic signal does provide limited depth solutions in the volcanic environment and the use of different observation levels does not enhance the results. Forward gravity and magnetic models provide a valuable tool to estimate both the basalt and sub-basaltic sedimentary thickness but are limited by the ambiguity inherent in potential field methods. The use of gravity gradients significantly decreases the available model solutions and provides boundary detection even in sub-basaltic settings. 相似文献
8.
9.
考虑到不同坐标系下各个方向观测值对反演地球重力场的频谱贡献不同,建立了顾及多方向观测值权比的动力积分法,并利用该方法反演了高精度的GOCE HL-SST卫星重力场模型.首先,分析了不同坐标系下各个方向观测值与地球重力场信息的响应关系,其中惯性系(IRF)下X、Z方向的观测值分别对扇谐系数、带谐系数最为敏感,Z方向的解算精度在全频段均略高于X、Y方向;地固系(EFRF)下各个方向的独立解算精度均与能量守恒法的解算精度相当;局部指北坐标系(LNOF)下X、Z和Y三个方向的解算精度依次递减,且Y方向在47阶附近有明显"驼峰"现象.其次,比较了不同坐标系下顾及三个方向观测值权比的加权解算模型,其中加权联合解算模型精度在20至70阶次均明显优于等权解算模型,在带谐项和共振阶次精度提升明显,且LNOF下的加权联合解算精度要优于IRF和EFRF.最后,比较了GOCE和CHAMP卫星的模型解算精度,采用本文计算方法,仅利用2个月GOCE轨道观测值解算的模型精度优于包含更长观测时段信息的AIUB-CHAMP01S和EIGEN-CHAMP03S模型,且略优于ASU-GOCE-2months模型. 相似文献
10.
Dr. Ivan I. Mueller 《Pure and Applied Geophysics》1961,48(1):1-6
Summary The significance of the vertical gradients of gravity is great in geophysics and also in geodesy. In geophysics the observed vertical gradients can give valuable information about mass distributions close to the surface of the earth and in geodesy they may be used in determining the shape of the equipotential surfaces. The observed vertical gradients are very sensitive to masses close to the surface of the earth and they change very rapidly. Therefore, they should not be used for purposes such as the reduction of the observed gravity to the sea level. The normal vertical gradients are not the best either for this purpose because they are much too uniform on the surface of the earth. The best values for practical purposes are probably the regional vertical gradients.This paper presents a method to determine the regional vertical gradient anomalies in large areas from geodetic observations which, added to the normal part, will give the regional vertical gradients. 相似文献
11.
Satellite gradiometry is an observation technique providing data that allow for evaluation of Stokes’ (geopotential) coefficients.
This technique is capable of determining higher degrees/orders of the geopotential coefficients than can be achieved by traditional
dynamic satellite geodesy. The satellite gradiometry data include topographic and atmospheric effects. By removing those effects,
the satellite data becomes smoother and harmonic outside sea level and therefore more suitable for downward continuation to
the Earth’s surface. For example, in this way one may determine a set of spherical harmonics of the gravity field that is
harmonic in the exterior to sea level.
This article deals with the above effects on the satellite gravity gradients in the local north-oriented frame. The conventional
expressions of the gradients in this frame have a rather complicated form, depending on the first-and second-order derivatives
of the associated Legendre functions, which contain singular factors when approaching the poles. On the contrary, we express
the harmonic series of atmospheric and topographic effects as non-singular expressions. The theory is applied to the regions
of Fennoscandia and Iran, where maps of such effects and their statistics are presented and discussed. 相似文献
12.
Heikki Virtanen 《Journal of Geodynamics》2004,38(3-5):407
Loading by atmosphere and by the Baltic Sea cause gravity change at Metsähovi, located 15 km from the open sea. Gravity is changed by both the Newtonian attraction of the loading mass and by the crustal deformation. We have performed loading calculations using appropriate Green's function for both gravity and deformation, for both atmospheric and Baltic loading. The loading by atmosphere has been computed using a detailed surface pressure field from high resolution limited area model (HIRLAM) for north Europe up to 10° distances. Baltic Sea level is modelled using tide gauge records. Calculations show that 1 m of uniform layer of water corresponds to 31 nm s−2 in gravity and −11 mm in height. Modelled loading is compared with observations of the superconducting gravimeter T020 for years 1994–2002. The combination of HIRLAM and a tide gauge record decreases RMS of gravity residuals by 14% compared to single admittance in air pressure corrections without sea level data. Regression of gravity residuals on the tide gauge record at Helsinki (at 30 km distance) gives a gravity effect of 26 nm s−2 m−1 for Baltic loading.The gravity station is co-located with a permanent GPS station. We have also associated the loading effects of the atmosphere and of the Baltic Sea with temporal height variations. The range of modelled vertical motion due to air pressure was 46 mm and that due to sea level 18 mm. The total range was 38 mm. The effects of the Baltic Sea and of the atmosphere partly cancel each other, since at longer periods the inverse barometer assumption is valid. Regression of the modelled height on local air pressure gives −0.37 mm hPa−1, corresponding approximately to width 6° for pressure system.We have tested the models using one year of daily GPS data. Multilinear regression on local air pressure and sea level in Helsinki gives the coefficient −0.34 mm hPa−1 for pressure, and −11 mm m−1 for sea level. These match model values. Loading by air pressure and Baltic Sea explains nearly 40% of the variance of daily GPS height solutions. 相似文献
13.
The enhancement of potential field data using filters based on horizontal and vertical derivatives is common. As well as the direct use of the gradients themselves they are used in filters such as sunshading, total horizontal derivative, analytic signal, horizontal and vertical tilt angles, the Theta map and other filters. These techniques are high‐pass filters of different types and so enhance noise as well as detail in the data. A new derivative operator is introduced in this paper, which generalizes the effects of some of the previously mentioned filters. This filter is a linear combination of the horizontal and vertical field derivatives, normalized by the analytic signal amplitude. The filter is demonstrated on aeromagnetic and gravity data from South Africa. 相似文献
14.
The static Earth’s gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth’s surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet’s boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green’s kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth. 相似文献
15.
We have used satellite solutions to the low degree zonal harmonics of the Earth's gravitational potential, and rates of surface accumulation to partially constrain, by means of repeated forward solution, the time rates of thickness change over the Antarctic and Greenland Ice Sheets (dTA and dTG respectively). In addition to the observed zonal coefficients j2 through j5 we impose only one other constraint: That dTA and dTG are proportional to surface accumulation. The lagged response of the Earth to secular changes in ice thickness spanning recent time periods (up to 2000 years before present) and the late Pleistocene is accounted for by means of two viscoelastic rebound models. The sea level contributions from the ice sheets, calculated from dTA and dTG, lower mantle viscosity, and the start time of present-day thickness change are all variables subject to the constraints. For a given set of post glacial rebound inputs, a family of solutions that have similar characteristics and that agree well with observation are obtained from the large number of forward solutions. The off axis position of the Greenland ice sheet makes its contribution to the low degree zonal coefficients less sensitive to the spatial details of the mass balance than to the overall sea level contribution. dTG is therefore modeled as surface mass balance offset by a uniform and constant mass loss. Though dTA varies widely with choices of input parameters, the combined sea level contribution from both ice sheets is reasonably well constrained by the gravity coefficients, and is predicted to range from -0.9 to +1.6 mm yr-1. The sign of the slope of the low degree zonal coefficients versus sea level contribution for Greenland is positive, but for Antarctica, the sign of the slope is positive for even degree and negative for odd degree harmonics. By using this property of the zonal coefficients, it is possible to determine the individual sea level contributions for Greenland and Antarctica. They vary from -0.6 to +0.3 mm yr-1 for the Greenland Ice Sheet, and from -0.3 to +1.3 mm yr-1 for the Antarctic Ice Sheet. 相似文献
16.
The eigenvalue decomposition technique is used for analysis of conditionality of two alternative solutions for a determination
of the geoid from local gravity data. The first solution is based on the standard two-step approach utilising the inverse
of the Abel-Poisson integral equation (downward continuation) and consequently the Stokes/Hotine integration (gravity inversion).
The second solution is based on a single integral that combines the downward continuation and the gravity inversion in one
integral equation. Extreme eigenvalues and corresponding condition numbers of matrix operators are investigated to compare
the stability of inverse problems of the above-mentioned computational models. To preserve a dominantly diagonal structure
of the matrices for inverse solutions, the horizontal positions of the parameterised solution on the geoid and of data points
are identical. The numerical experiments using real data reveal that the direct gravity inversion is numerically more stable
than the downward continuation procedure in the two-step approach. 相似文献
17.
Andrzej Bobojć 《Acta Geophysica》2016,64(2):521-540
The possibility of improving the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission satellite orbit using gravity gradient observations was investigated. The orbit improvement is performed by a dedicated software package, called the Orbital Computation System (OCS), which is based on the classical least squares method. The corrections to the initial satellite state vector components are estimated in an iterative process, using dynamic models describing gravitational perturbations. An important component implemented in the OCS package is the 8th order Cowell numerical integration procedure, which directly generates the satellite orbit. Taking into account the real and simulated GOCE gravity gradients, different variants of the solution of the orbit improvement process were obtained. The improved orbits were compared to the GOCE reference orbits (Precise Science Orbits for the GOCE satellite provided by the European Space Agency) using the root mean squares (RMS) of the differences between the satellite positions in these orbits. The comparison between the improved orbits and the reference orbits was performed with respect to the inertial reference frame (IRF) at J2000.0 epoch. The RMS values for the solutions based on the real gravity gradient measurements are at a level of hundreds of kilometers and more. This means that orbit improvement using the real gravity gradients is ineffective. However, all solutions using simulated gravity gradients have RMS values below the threshold determined by the RMS values for the computed orbits (without the improvement). The most promising results were achieved when short orbital arcs with lengths up to tens of minutes were improved. For these short arcs, the RMS values reach the level of centimeters, which is close to the accuracy of the Precise Science Orbit for the GOCE satellite. Additional research has provided requirements for efficient orbit improvement in terms of the accuracy and spectral content of the measured gravity gradients. 相似文献
18.
我国在海域开展了大规模的航空重力勘探,这些资料对构建高精度大地水准面具有重要价值.基于此,本文提出一种利用海域航空重力测量数据快速构建大地水准面的方法.该方法基于移去-恢复法思想,利用位场最小曲率方法对航空重力数据进行高精度向下延拓并获取相应的扰动位,实现航空重力测量快速构建海域大地水准面.与斯托克斯积分计算相比,采用了处理效率更高的频率域位场转换,解决了向下延拓及垂向积分时航空重力异常数据空白及扩边问题,具有较高的位场转换精度.本文应用EGM2008模拟航空重力数据进行模型验证,计算结果与其给出的水准面的精度相当;同时,也选取GRAV-D计划的航空重力数据进行实际验证,计算结果与xGEOID18B水准面模型精度基本一致.模型验证和实际应用验证了本方法的实用性. 相似文献
19.
Optimal Model for Geoid Determination from Airborne Gravity 总被引：2，自引：0，他引：2
Two different approaches for transformation of airborne gravity disturbances, derived from gravity observations at low-elevation flying platforms, into geoidal undulations are formulated, tested and discussed in this contribution. Their mathematical models are based on Green's integral equations. They are in these two approaches defined at two different levels and also applied in a mutually reversed order. While one of these approaches corresponds to the classical method commonly applied in processing of ground gravity data, the other approach represents a new method for processing of gravity data in geoid determination that is unique to airborne gravimetry. Although theoretically equivalent in the continuous sense, both approaches are tested numerically for possible numerical advantages, especially due to the inverse of discretized Fredholm's integral equation of the first kind applied on different data. High-frequency synthetic gravity data burdened by the 2-mGal random noise, that are expected from current airborne gravity systems, are used for numerical testing. The results show that both approaches can deliver for the given data a comparable cm-level accuracy of the geoidal undulations. The new approach has, however, significantly higher computational efficiency. It would be thus recommended for real life geoid computations. Additional errors related to regularization of gravity data and the geoid, and to accuracy of the reference field, that would further deteriorate the quality of estimated geoidal undulations, are not considered in this study. 相似文献
20.
In this paper, we present a case study on the use of the normalized source strength (NSS) for interpretation of magnetic and gravity gradient tensors data. This application arises in exploration of nickel, copper and platinum group element (Ni‐Cu‐PGE) deposits in the McFaulds Lake area, Northern Ontario, Canada. In this study, we have used the normalized source strength function derived from recent high resolution aeromagnetic and gravity gradiometry data for locating geological bodies. In our algorithm, we use maxima of the normalized source strength for estimating the horizontal location of the causative body. Then we estimate depth to the source and structural index at that point using the ratio between the normalized source strength and its vertical derivative calculated at two levels; the measurement level and a height h above the measurement level. To discriminate more reliable solutions from spurious ones, we reject solutions with unreasonable estimated structural indices. This method uses an upward continuation filter which reduces the effect of high frequency noise. In the magnetic case, the advantage is that, in general, the normalized magnetic source strength is relatively insensitive to magnetization direction, thus it provides more reliable information than standard techniques when geologic bodies carry remanent magnetization. For dipping gravity sources, the calculated normalized source strength yields a reliable estimate of the source location by peaking right above the top surface. Application of the method on aeromagnetic and gravity gradient tensor data sets from McFaulds Lake area indicates that most of the gravity and magnetic sources are located just beneath a 20 m thick (on average) overburden and delineated magnetic and gravity sources which can be probably approximated by geological contacts and thin dikes, come up to the overburden. 相似文献