scholarly journals On the convergence of spherical harmonic expansion of topographic and atmospheric biases in gradiometry

2009 ◽  
Vol 39 (4) ◽  
pp. 273-299 ◽  
Author(s):  
Mehdi Eshagh
Keyword(s):  
Spherical Harmonic ◽  
Order Term ◽  
Spherical Harmonic Expansion ◽  
Downward Continuation ◽  
Gravity Gradient ◽  
Gravity Gradients ◽  
Satellite Gravity ◽  
Gravity Gradient Tensor ◽  
The Third ◽  
Binomial Expansion

On the convergence of spherical harmonic expansion of topographic and atmospheric biases in gradiometryThe gravity gradiometric data are affected by the topographic and atmospheric masses. In order to fulfill Laplace-Poisson's equation and to simplify the downward continuation process, these effects should be removed from the data. However, if the analytical downward continuation is considered, the gravity gradients can be continued downward disregarding such effects but the result will be biased. The topographic and atmospheric biases can be expressed in terms of spherical harmonics and studying these biases gives some ideas about analytical downward continuation of these quantities to sea level. In formulation of harmonic coefficients of the topographic and atmospheric biases, a truncated binomial expansion of topographic height is used. In this paper, we show that the harmonics are convergent to the third term of this binomial expansion. The harmonics of the biases onVzzare convergent to the first term and they are convergent inVxyfor all the terms. The harmonics of the other components of the gravity gradient tensor are convergent to the second terms, while the third terms are only asymptotically convergent. This means that in terrestrial and airborne gradiometry the biases should be computed just to the second order term, while in satellite gravity gradiometry, e.g. GOCE, the third term can also be considered.

scholarly journals The earth’s gravity field recovery using the third invariant of the gravity gradient tensor from GOCE

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Lin Cai ◽  
Xiaoyun Wan ◽  
Houtse Hsu ◽  
Jiangjun Ran ◽  
Xiangchao Meng ◽  
...  
Keyword(s):  
Gravity Field ◽  
Field Model ◽  
Gravity Gradient ◽  
Gravity Gradients ◽  
Gravity Field Model ◽  
Gravity Gradient Tensor ◽  
The Third ◽  
Third Invariant ◽  
Gravity Field Determination ◽  
2D Fft

AbstractDue to the independence of the gradiometer instrument’s orientation in space, the second invariant $$I_2$$ I 2 of gravity gradients in combination with individual gravity gradients are demonstrated to be valid for gravity field determination. In this contribution, we develop a novel gravity field model named I3GG, which is built mainly based on three novel elements: (1) proposing to utilize the third invariant $$I_3$$ I 3 of the gravity field and steady-state ocean circulation explorer (GOCE) gravity gradient tensor, instead of using the $$I_2$$ I 2 , similar to the previous studies; (2) applying an alternative two-dimensional fast fourier transform (2D FFT) method; (3) showing the advantages of $$I_3$$ I 3 over $$I_2$$ I 2 in the effect of measurement noise from the theoretical and practical computations. For the purpose of implementing the linearization of the third invariant, this study employs the theory of boundary value problems with sphere approximation at an accuracy level of $$O(J_2^2\cdot T_{ij})$$ O ( J 2 2 · T ij ) . In order to efficiently solve the boundary value problems, we proposed an alternative method of 2D FFT, which uses the coherent sampling theory to obtain the relationship between the 2D FFT and the third invariant measurements and uses the pseudo-inverse via QR factorization to transform the 2D Fourier coefficients to spherical harmonic ones. Based on the GOCE gravity gradient data of the nominal mission phase, a novel global gravity field model (I3GG) is derived up to maximum degree/order 240, corresponding to a spatial resolution of 83 km at the equator. Moreover, in order to investigate the differences of gravity field determination between $$I_3$$ I 3 with $$I_2$$ I 2 , we applied the same processing strategy on the second invariant measurements of the GOCE mission and we obtained another gravity field model (I2GG) with a maximum degree of 220, which is 20 degrees lower than that of I3GG. The root-mean-square (RMS) values of geoid differences indicates that the effects of measurement noise of I3GG is about 20% lower than that on I2GG when compared to the gravity field model EGM2008 (Earth Gravitational Model 2008) or EIGEN-5C (EIGEN: European Improved Gravity model of the Earth by New techniques). Then the accuracy of I3GG is evaluated independently by comparison the RMS differences between Global Navigation Satellite System (GNSS)/leveling data and the model-derived geoid heights. Meanwhile, the re-calibrated GOCE data released in 2018 is also dealt with and the corresponding result also shows the similar characteristics.

Combining GGM and RTM to model the gravity gradient tensor

2020 ◽  
Author(s):  
Jinzhao Liu
Keyword(s):  
Spherical Harmonic ◽  
Shuttle Radar Topography Mission ◽  
Gravity Gradient ◽  
Geopotential Model ◽  
Gradient Tensor ◽  
Gravity Gradient Tensor ◽  
Terrain Model ◽  
Truncation Errors ◽  
Elevation Model ◽  
High Degree

<p>In this paper, by combining the Global Geopotential Model (GGM, specifically, EGM2008 is used) and the Residual Terrain Model (RTM) data, we have modeled the Gravity Gradient Tensor (GGT) in eastern Tian shan mountains areas, China. The RTM data are obtained from the Shuttle Radar Topography Mission (SRTM) elevation model and the DTM2006.0 high degree spherical harmonic reference surface. The integration of RTM data reduces the truncation errors (or called omission errors) due to the finite expansion terms of the spherical harmonic coefficients of the GGM, and compensates for the high frequency information and spatial resolution of the GGT within the study area.</p>

The role of a laterally varying density contrast for gravity inversion of the Moho depth

2020 ◽  
Author(s):  
Peter Haas ◽  
Joerg Ebbing ◽  
Wolfgang Szwillus ◽  
Philipp Tabelow
Keyword(s):  
Global Scale ◽  
Density Contrast ◽  
Gradient Field ◽  
Moho Depth ◽  
Gravity Gradient ◽  
Gravity Inversion ◽  
Gravity Gradients ◽  
Regional Study ◽  
Satellite Gravity ◽  
Amazonian Craton

<p>We present a new inverse approach to invert satellite gravity gradients for the Moho depth under consideration of a laterally varying density contrast between crust and mantle. The inverse problem is linearized and solved with the classical Gauss-Newton algorithm in a spherical geometry. To ensure stable solutions, the Jacobian is smoothed with second-order Tikhonov regularization. During the inversion, the Moho depth is discretized into tesseroids by reference Moho depth and density contrast, from which the gravitational effect can be calculated. As a computational benefit, the Jacobian is calculated only once and afterwards weighted with the laterally varying density contrast. We look for a Moho depth model that simultaneously explains the gravity gradient field and a least misfit to existing seismic Moho depth determinations. We perform the inversion both on regional and global scale.</p><p>The laterally varying density contrast is based on different tectonic units, which are defined by independent global geological and geophysical data, such as regionalization of dispersion curves. This is beneficial in remote areas, where seismic investigations are very sparse and the crustal structure is to a large extent unknown. Applying the inversion to the Amazonian Craton and its surroundings shows a lower density contrast at the Moho depth for the continental interior compared to oceanic domains. This is in accordance with the tectono-thermal architecture of the lithosphere. The inverted values of the density vary between 300-450 kg/m<sup>3</sup>. The inverted Moho depth shows a clear separation between the Sao Francisco Craton and shallower Amazonian Craton.</p><p>Gravity inversion with a laterally varying density contrast requires a uniform reference Moho depth. On a global scale, we utilize our inversion to estimate a reference Moho depth that is in accordance with crustal buoyancy. The inverted density contrasts show a similar trend like the regional study area. The inverted Moho depth shows expected tectonic features. Our method of computing the Jacobian once and weighting with lateral variable density contrasts is a valuable optimization of standard gravity inversion.</p>

scholarly journals Error assessment of GOCE SGG data using along track interpolation

2003 ◽  
Vol 1 ◽  
pp. 27-32 ◽  
Author(s):  
J. Bouman ◽  
R. Koop
Keyword(s):  
Measurement Errors ◽  
A Priori ◽  
Error Model ◽  
Interpolation Error ◽  
Gravity Gradient ◽  
Gravity Gradients ◽  
Satellite Gravity ◽  
Gravity Field Recovery ◽  
End To End ◽  
Along Track

Abstract. GOCE will be the first satellite gravity mission measuring gravity gradients in space using a dedicated instrument called a gradiometer. High resolution gravity field recovery will be possible from these gradients. Such a recovery requires a proper description of the gravity gradient errors, where the a priori error model is for example based on end-to-end instrument simulations. One way to test the error model against real data, i.e. to see if the a priori model really describes the actual error, is to compare along track interpolated gradients with the measured gradients. The difference between the interpolated and measured gravity gradients is caused by, among others, the interpolation error and the measurement errors. The idea is that if the interpolation error is small enough, then the differences should be predicted reasonably well by the error model. This paper discusses a simulation study where the gravity gradient errors are generated with an end-to-end instrument simulator. The measurement error will be compared with the interpolation error and we will assess the latter as a function of the sampling interval.

Decoupling the crustal and mantle gravity signature at subduction zones with satellite gravity gradients: case study Sumatra

2020 ◽  
Author(s):  
Bart Root ◽  
Wouter van der Wal ◽  
Javier Fullea
Keyword(s):  
Subduction Zones ◽  
European Space Agency ◽  
High Sensitivity ◽  
Gravity Gradient ◽  
Gravity Gradients ◽  
Satellite Mission ◽  
Satellite Gravity ◽  
Data Set ◽  
Space Agency ◽  
3D Geometry

<p>The GOCE satellite mission of the European Space Agency has delivered an unprecedented view of the gravity field of the Earth. In this data set, the strongest gravity gradient signals are observed at subduction zones in the form of a dipole. Despite numerous studies on subduction zones, it is still unclear what is causing this strong signal. Is the source of the observed dipole situated in the crust, mantle, or a combination of these?</p><p>We have constructed a 3D geometry of the Sumatra slab using the global SLAB1.0 model. This geometry is substituted in a global upper mantle model WINTERC5.4, a product of the ESA Support to Science Element: 3DEarth. The density in the subducting crust, mantle, or a combination of both is fitted to the gravity gradients at satellite height. Lateral varying Green’s functions are used to compute the gravity gradients from the densities. In the case of a combined crust/mantle model, spectral information of the sensitivity of satellite gradients is used to construct a weighted inversion.</p><p>Preliminary results show that crustal mass transport (mostly from the overriding plate) in the direction of the subducting plate is mostly responsible for the negative anomaly observed in between the trench and the volcanic arc. This signal is, however, not visible along the complete subduction zone. Most crustal transport is seen where normal subduction takes place. Oblique subduction shows less crustal transport and more intra-crustal faulting. The satellite gravity gradients show high sensitivity to this particular crustal signature and therefore can be used to analyze subduction zones globally.</p>

Borehole gravity gradiometry

Geophysics ◽  
1989 ◽  
Vol 54 (2) ◽  
pp. 225-234 ◽  
Author(s):  
A. G. Nekut
Keyword(s):  
Linear Combination ◽  
Simple Relation ◽  
Gravity Gradient ◽  
Gravity Gradients ◽  
Gravity Gradiometer ◽  
Gravity Gradiometry ◽  
Gradient Tensor ◽  
Gravity Gradient Tensor ◽  
Joint Interpretation

Gravity gradients measured in a borehole are of interest due to their direct, simple relation to the density of the formations surrounding the hole. Borehole gravity meters (BHGMs) are used to measure gravity differences along the borehole and from these differences, we compute averaged values for a linear combination of the gravity gradient tensor elements. One way to implement a borehole gravity gradiometer (BHGGM) is to measure the torque exerted on a pair of masses separated by a beam. A BHGGM directly measures all the elements of the gravity gradient tensor. Knowledge of these elements provides information about the direction to density anomalies in the vicinity of the borehole and enhances the analysis of dipping beds. The BHGGM may be superior to the BHGM for resolving the density of thin beds. Density variations remote from the borehole are best detected and characterized by joint interpretation of BHGM and BHGGM data.

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