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

Due 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.

Speed and accuracy improvements in standard algorithm for prismatic gravitational field

SUMMARY By utilizing the addition theorems of the arctangent function and the logarithm, we developed a new expression of Bessel’s exact formula to compute the prismatic gravitational field using the triple difference of certain analytic functions. The use of the new expression is fast since the number of transcendental functions required is significantly reduced. The numerical experiments show that, in computing the gravitational potential, the gravity vector, and the gravity gradient tensor of a uniform rectangular parallelepiped, the new method runs 2.3, 2.3 and 3.7 times faster than Bessel’s method, respectively. Also, the new method achieves a slight increase in the computing precision. Therefore, the new method can be used in place of Bessel’s method in any situation. The same approach is applicable to the geomagnetic field computation.

Combining GGM and RTM to model the gravity gradient tensor

<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>

Gravity gradient tensor of a vertical pyramid model of flat top and bottom with depth-wise parabolic density variation

As an alternative to the popular rectangular parallelepiped model, we have developed a novel 3D analytical forward-problem solution for the gravity gradient tensor of a vertical pyramid model with parabolic density contrast variation. Its flexibility and effectiveness are demonstrated with the help of synthetic simulations and a case study involving Chintalapudi subbasin, India. We have addressed the singularities and numerical stability in numerical implementation of our algorithm for modeling and practical implementation.

Gravity gradient tensor analysis to an active fault: a case study at the Togi-gawa Nangan fault, Noto Peninsula, central Japan

Gravity gradient tensor analysis has been a powerful tool for investigating subsurface structures and recently its application to a two-dimensional fault structure has been developed. To elucidate the faulting type and spatial extent, specifically the continuity and the size, of the subsurface fault structure of an active fault through gravity gradient tensor analysis, we analyzed Bouguer anomalies, which were composed of dense gravity measurement data over the land and seafloor, and indices calculated from a gravity gradient tensor around the Togi-gawa Nangan fault (TNF), Noto Peninsula, central Japan. The features of Bouguer anomalies and their first horizontal and vertical derivatives demonstrate clearly that the TNF is a reverse fault dipping to the southeast. Furthermore, the combination of those derivatives and the dimensionality index revealed that the spatial extent of the subsurface fault structure is coincident with that of the surface fault trace and that it shows no evidence of connecting the TNF with surrounding active faults. Furthermore, the dip angle of the subsurface fault structure was estimated as 45°–60° from the minimum eigenvectors of the gravity gradient tensor. We confirmed that this result is coincident with the dip angle estimated using the two-dimensional Talwani’s method. This high dip angle as a reverse fault suggests that the TNF has experienced inversion tectonics.

A detailed research on the structural characteristics of Hoang Sa and Truong Sa archipelagos - East Vietnam Sea based on gravity data analysis

The Hoang Sa and Truong Sa archipelagos are the two archipelagos located in the East Vietnam Sea. In the geographic coordinate frame, the Hoang Sa archipelago is located more northward than the Truong Sa. Up to now many publications have discussed in detail structures of these archipelagos in terms of international and domestic scientific journals, the scientific workshop reports, as well as the outcome reports obtained from the research projects of different levels, such as state and ministry level projects. However the block characteristics of the two archipelago regions are still in controversy. By application of the new technique (Curvature Gravity Gradient Tensor - CGGT) for analysis and collection of the related available data, some new information about structural characteristics of the two blocks, such as their spatial distribution, the penetration of their boundaries and fault systems was obtained. According to the results, block characteristic is clearly reflected as a unique structural unit for Hoang Sa archipelago, which occupies a large area restricted mostly by the geographic coordinate frame: 111.2oE–113.2oE and 15.75oN–17.25oN. Here a large negative Hoang Sa structural block with the density less than 2.67 g/cm3 develops directly on a more negative regional structure. Unlike Hoang Sa block, the Truong Sa archipelago is not presented as a unique block. Its structure is divided into 3 main smaller blocks distributed along different directions. The first north - south structural block consists of a number of islands and sandbars: Dinh Ba, Song Tu Dong island, Song Tu Tay island, Thi Tu island, Ba Binh island, Ca Nham sandbar, Loai Ta island and Son Ca island, Nam Yet island, Truong Sa Lon island, Sinh Ton island, Ba Bau and Binh Nguyen island. The second structural block along the northeast - southwest direction includes the following islands and sandbars: Da Lat, Truong Sa island, Da Tay, Da Dong, Chau Vinh. The remaining Phan Vinh island, Toc Tan sandbar, Nui Le, Ky Van, Tham Hiem sandbar and Kieu Ngua sandbar are distributed in the third structural block. In addition, all the 3 blocks are the negative structures. In terms of geological structural boundaries: The estimated depth of the boundaries (uplifts, subduction zones, or faults,...) on Hoang Sa archipelago only reaches a maximum of 20 km. Meanwhile, that on Truong Sa archipelago is possibly over 20 km.