Non-Singular Transformation for Inverting Gravity Anomalies Using Satellite Altimetry Data

Traditional measurement methods, like shipborne and aerial gravity measurements, cannot cover the entire sea area. Satellite altimetry provides large-scale and high-precision observational data, which can be inverted to give high-precision and high-resolution data on marine gravity anomalies. In this paper, to improve the precision of computing the innermost zone effects in gravitational altimetry data, the deflections of the vertical are expressed in the form of double cubic polynomials by treating the innermost zone as a rectangle, based on the inverse Vening Meinesz formula. Furthermore, formulas for computing gravity anomalies in the innermost zone are derived using a non-singular transformation. The numerical experiments show that the relative error of the algorithm in this paper, which uses a non-singular transformation, is less than 1.5%. Moreover, the practical computational results based on deflections of the vertical for data with a resolution of 2' ×2' from the South China Sea and its vicinity also demonstrate that gravity anomalies in the innermost zone have a non-negligible contribution when using a non-singular transformation.