Rigorous modification model of upward continuation and its applications on the downward continuation of gravity anomaly

The global integral model of upward continuation for gravity anomaly is often used in the data quality assessment for airborne gravity measurement and the iterative solution of downward continuation. In order to eliminate the singularity of the integral kernel function, we have to make a remove-restore transformation to the integral model based on an equation of integral identity. And at the same time, the global integral domain has to be divided into two parts of near and far zones. During this processing, the deviation of identical formula caused by the transformation of integral domain from global to local integration is often ignored in the traditional modified method, which leads to unnecessary model errors and ultimately affects the reliability of upward continuation solution, and even affects the stability of iterative solution of downward continuation. In response to this problem, some analysis and research have been made on the integral model modification of upward continuation and its application of downward continuation for gravity anomaly in this paper. Based on the measured data situation and the applied condition of the integral identity, a set of step-by-step modified formulas of the upward continuation integral model are derived, and a correction formula is proposed to compensate the omission of the traditional modified model. Finally, the rigorous modified model is applied to the iterative solution of downward continuation for gravity anomaly. The ultra-high-degree geopotential model EGM2008 is used as a standard potential field to carry out a set of numerical calculation test, and the calculated accuracy of step-by-step modified models of the upward continuation and the applied effect in the iterative solution of downward continuation for gravity anomaly are estimated and evaluated separately. It proves the necessity and effectiveness of adopting the rigorous modified model.