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Proper understanding of how the Earth’s mass distributions and redistributions influence the Earth’s gravity field-related functionals is crucial for numerous applications in geodesy, geophysics and related geosciences. Calculations of the gravitational curvatures (GC) have been proposed in geodesy in recent years. In view of future satellite missions, the sixth-order developments of the gradients are becoming requisite. In this paper, a set of 3D integral GC formulas of a tesseroid mass body have been provided by spherical integral kernels in the spatial domain. Based on the Taylor series expansion approach, the numerical expressions of the 3D GC formulas are provided up to sixth order. Moreover, numerical experiments demonstrate the correctness of the 3D Taylor series approach for the GC formulas with order as high as sixth order. Analogous to other gravitational effects (e.g., gravitational potential, gravity vector, gravity gradient tensor), numerically it is found that there exist the very-near-area problem and polar singularity problem in the GC east–east–radial, north–north–radial and radial–radial–radial components in spatial domain, and compared to the other gravitational effects, the relative approximation errors of the GC components are larger due to not only the influence of the geocentric distance but also the influence of the latitude. This study shows that the magnitude of each term for the nonzero GC functionals by a grid resolution 15\(^{{\prime } }\,\times \) 15\(^{{\prime }}\) at GOCE satellite height can reach of about 10\(^{-16}\) m\(^{-1}\) s\(^{2}\) for zero order, 10\(^{-24 }\) or 10\(^{-23}\) m\(^{-1}\) s\(^{2}\) for second order, 10\(^{-29}\) m\(^{-1}\) s\(^{2}\) for fourth order and 10\(^{-35}\) or 10\(^{-34}\) m\(^{-1}\) s\(^{2}\) for sixth order, respectively. 相似文献
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Studia Geophysica et Geodaetica - Topographic effects on gravity field modeling are important for geodesy, geophysics and related geosciences. In this study we evaluate the gravitational effects of... 相似文献
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Deng Xiao-Le Shen Wen-Bin Yang Meng Kuhn Michael Ran Jiangjun 《Surveys in Geophysics》2022,43(4):1233-1262
Surveys in Geophysics - Similar to the gravitational curvatures in the gravity field, the magnetic curvatures (i.e., third-order derivatives of the magnetic potential) have been recently proposed... 相似文献
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岩心CT三维成像与多相驱替分析系统 总被引：2，自引：1，他引：1
介绍了研制"岩心CT三维成像、多相驱替分析系统"软件的主要研究对象,一是平面图像处理部分,二是DR试验中饱和度计算问题,三是岩心三维实体重建. 相似文献
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Xiao-Le Deng Thomas Grombein Wen-Bin Shen Bernhard Heck Kurt Seitz 《Journal of Geodesy》2016,90(6):585-587
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Liu Kai-Wei Jiang Ning-Jun Qin Jun-De Wang Yi-Jie Tang Chao-Sheng Han Xiao-Le 《Acta Geotechnica》2021,16(2):467-480
Acta Geotechnica - Due to more extreme weather events and accelerating sea-level rise, coastal sand dunes are subjected to more frequent storm wave inundation and surge impacts, which contribute to... 相似文献
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The forward modeling of the topographic effects of the gravitational parameters in the gravity field is a fundamental topic in geodesy and geophysics. Since the gravitational effects, including for instance the gravitational potential (GP), the gravity vector (GV) and the gravity gradient tensor (GGT), of the topographic (or isostatic) mass reduction have been expanded by adding the gravitational curvatures (GC) in geoscience, it is crucial to find efficient numerical approaches to evaluate these effects. In this paper, the GC formulas of a tesseroid in Cartesian integral kernels are derived in 3D/2D forms. Three generally used numerical approaches for computing the topographic effects (e.g., GP, GV, GGT, GC) of a tesseroid are studied, including the Taylor Series Expansion (TSE), Gauss–Legendre Quadrature (GLQ) and Newton–Cotes Quadrature (NCQ) approaches. Numerical investigations show that the GC formulas in Cartesian integral kernels are more efficient if compared to the previously given GC formulas in spherical integral kernels: by exploiting the 3D TSE second-order formulas, the computational burden associated with the former is 46%, as an average, of that associated with the latter. The GLQ behaves better than the 3D/2D TSE and NCQ in terms of accuracy and computational time. In addition, the effects of a spherical shell’s thickness and large-scale geocentric distance on the GP, GV, GGT and GC functionals have been studied with the 3D TSE second-order formulas as well. The relative approximation errors of the GC functionals are larger with the thicker spherical shell, which are the same as those of the GP, GV and GGT. Finally, the very-near-area problem and polar singularity problem have been considered by the numerical methods of the 3D TSE, GLQ and NCQ. The relative approximation errors of the GC components are larger than those of the GP, GV and GGT, especially at the very near area. Compared to the GC formulas in spherical integral kernels, these new GC formulas can avoid the polar singularity problem. 相似文献
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Microbial induced calcite precipitation (MICP), a bio-cementation process, can be adopted to improve the engineering properties of granular soils. Bio-stimulation, via directly enriching indigenous ureolytic bacteria, is a sustainable and economical approach to achieve MICP. In this study, batch solution experiment was firstly conducted to investigate the biochemical aspects of the bio-stimulated MICP process in coral sands. Three different enrichment media were compared. The statistical analysis was performed to reveal statistically significant factors that influence ureolytic activity, pH value, and viable cell number. Then, the unconfined compression and rainfall-induced erosion tests were conducted to investigate the strength and erosion-resistance of bio-stimulated MICP treated coral sands. The experimental results demonstrate that the enrichment duration, initial urea concentration, and enrichment type are major influencing factors of the ureolytic activity. It is found in this study that yeast-extract-based enrichment media with 170 mM initial urea concentration and enriched for 72 h could achieve the best bio-stimulated MICP treatment efficiency. In addition, higher initial urea concentration in the enrichment medium could yield higher ureolytic activity, which could consequently result in higher cementation content and thus larger UCS and better resistance to rainfall-induced erosion.
相似文献9.
Calculating topographic gravitational potential (GP) is a time-consuming process in terms of efficiency. Prism, mass-point, mass-line, and tesseroid formulas are generally used to calculate the topographic GP effect. In this study, we reformulate the higher-order formula of the tesseroid by Taylor series expansion and then evaluate the fourth-order formula by numerical tests. Different simulation computations show that the fourth-order formula is reliable. Using the conventional approach in numerical calculations, the approximation errors in the areas of the north and south poles are extremely large. Thus, in this study we propose an approach combining the precise numerical formula and tesseroid formulas, which can satisfactorily solve the calculation problem when the computation point is located in the polar areas or areas very near the surface. Furthermore, we suggest a “best matching choice” of new combination approach to calculate the GP precisely by conducting various experiments. Given the computation point at different positions, we may use different strategies. In the low latitude, we use a precise numerical formula, the fourth-order tesseroid formula, the second-order tesseroid formula, and the zero-order formula, in the 1° range (from the computation point), 1° to 15° range, 15° to 40° range, and the range outside 40°, respectively. The accuracy can reach 2 × 10?5 m2 s?2. For the high latitude, we use the precise numerical formula, fourth-order tesseroid, second-order tesseroid, and zero-order tesseroid formulas in the ranges of 0° to 1°, 1° to 10°, 10° to 30°, and the zones outside 30°, respectively. However, if an accuracy level of 2 × 10?5 m2 s?2 is required, the zero-order tesseroid formulas should not be used and the second-order tesseroid formula should be used in the region outside 15° for the low latitude and in the region outside 10° for the high latitude. 相似文献
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