Abstract: The purpose of gravity topographic correction   is to eliminate the influence of terrain quality  on  observed gravity, including traditional topographic correction and intermediate layer correction,which  is the most important part of  external correction of gravity exploration, and  also the key factor affecting the accuracy of gravity exploration. For a long time, researchers have carried out a lot of research on  calculation models of topographic correction, calculation methods, and  influencing factors of calculation accuracy, but neglected the unification of topographic correction methods in the process of different measurement methods such as land gravity, ship-borne gravity, air-born gravity and well gravity, as well as  the discussion on the variation law and selection principles of different influencing factors. This paper introduces in detail the research progress and prospect of the fundamental theory, the calculation methods, and the influencing factors of topographic correction. Simultaneously, there are some problems in  topographic correction methods, such as the topographic correction methods of different gravity measurement techniques are not uniform, the significance of gravity anomaly is not uniform, and the research degree of influencing factors of topographic correction accuracy is different. According to the basic principle of topographic correction methods with different gravity measurement methods, it is necessary to formulate a unified topographic correction standard for the overall use of gravity data. Through discussing and analyzing the influence of topographic grid spacing, topographic correction radius and stratum density on topographic correction accuracy, it is proposed that   the regular relationship between topographic grid sapcing,topographic correction radius and stratum density  should be studied  to realize the flexible selection of grid spacing and correction radius in practical work and improve the applicability of  topographic correction methods.

Key words: gravity topographic correction, terrain quality, calculation models, calculation methods, influencing factors, research progress and prospect