Near-zone Direct and Indirect Topographic Effects Based on the Rectangular Prism and Surface Element

作者：Jian MA,Ziqing WEI,Zhenghui YANG,Xiaogang LIU,Jianfeng JI

摘要：Helmert’s second method of condensation is an effective method for terrain reduction in the geoid and quasi-geoid determinations. Condensing the masses outside the geoid to a surface layer on the geoid produces several forms of topographic effects: direct effect on gravity, secondary indirect effect on gravity and indirect effects on the (quasi-) geoid, respectively. To strike a balance between computation accuracy and numerical efficiency, the global integration region of topographic effects is usually divided into near zone and far zone. We focus on the computation of near-zone topographic effects, which are functions of actual topographic masses and condensed masses. Since there have already been mature formulas for gravitational attraction and potential of actual topographic masses using rectangular prism model, we put forward surface element model for condensed masses. Afterwards, the formulas for near-zone direct and indirect effects are obtained easily by combining the rectangular prism model and surface element model. To overcome the planar approximation errors involved with the new formulas for near-zone topographic effects, the Earth’s curvature can be taken into account. It is recommended to apply the formulas based on the rectangular prism and surface element considering the Earth’s curvature to calculate near-zone topographic effects for high-accuracy demand to determine geoid and quasi-geoid.

發文機構：Xi’an Research Institute of Surveying and Mapping State Key Laboratory of Geo-information Engineering Institute of Geospatial Information of Information Engineering University Geological Engineering and Geomatics School of Chang’an University

關鍵詞：helmert'ssecondmethodofcondensationDIRECTEFFECTindirectEFFECTrectangularPRISMSURFACEELEMENT

分類號： P[天文地球]