Aerogravity terrain correction method based on spherical coordinate system

      In recent years, due to the enhanced interference-resistance of airborne gravimeters and the advanced gravity anomaly calculation techniques, the China Geological Survey has carried out numerous airborne gravity survey missions in mid-high mountainous and deeply incised regions, including Tibet, Xinjiang, and Gansu. In practical applications, the measured free-air gravity anomalies need to have local topographic corrections and intermediate layer corrections to obtain Bouguer gravity anomalies for geological interpretation. Currently, commercial airborne gravity terrain correction software adopts the Nagy flat-topped prism method for near-field areas and the rod formula for far-field areas. This approach results in poor continuity between different terrain correction zones and fails to effectively eliminate terrain effects in deeply incised areas. This paper presents a novel method. By utilizing the coordinate surfaces in the spherical coordinate system, namely conical surfaces and semi-planes, the area is divided into rings (m rings) and blocks (n blocks), forming m×n "sectorial spherical shell blocks". A terrain correction calculation formula for these "sectorial spherical shell blocks" in the circular domain is derived, unifying the terrain correction formulas for both near and far regions. This unification allows for seamless connection among various terrain correction areas and obviates the need for intermediate layer corrections. The method has been validated by theoretical models, showing reliable accuracy in terrain correction value calculations. It has also been successfully applied in the West Kunlun airborne gravity survey. When compared with commercial software, it effectively eliminates terrain effects and achieves better terrain correction results.