A rigorous modification model and its application for computing the vertical gradient of gravity anomaly

Integral singularity and numerical discontinuity are two major problems in the modification model for computing the vertical gradient of gravity anomaly. We study the method of model modification and point out the theoretical flaws of the traditional modification method. Then a comprehensive remove-restore transformation to the integral model is suggested based on an equation of integral identity, and a set of step-by-step modification formulae of the global integration model for computing the vertical gradient of gravity anomaly are derived according to the measured data conditions. A corrected formula to compensate the omission of the traditional modification model is proposed. 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 calculation accuracy of step-by-step modified models and their application effect to downward continuation are analyzed and evaluated. It is shown from different aspect that adopting the rigorous modified model is necessary and effective.