Objectives Taylor series expansion is often used in the downward continuation of potential field, and its performance depends on the accuracy and reliability of vertical partial derivatives or radial partial derivatives (RPDs) of potential field parameters.

Methods In order to avoid the singularity on spherical boundary and the uncertainty to the computational results by using the closed analytic kernel function to solve the partial derivative, first, this paper considers the fact that all kinds of gravity observations behave as a type of limited spectrum bandwidth signal after being filtered, and proposes to express the kernel function of the Poisson integral for the external gravity anomaly by a spherical harmonic series expansion, which is truncated into a band-limited summation with the same spectrum range as the gravity observation. Then, we derive a set of band-limited formulas to calculate the high-order RPDs, which are modified and applied to the downward continuation of the gravity anomaly by Taylor series expansion.

Results and Conclusions The formulas are validated using the ultra-high-degree geopotential model EGM2008 by a two-stage procedure. The numerical tests of the band-limited formulas and the Taylor series expansion downward continuation model show that the proposed band-limited formulas have good reliability and validity, and are superior to other models in terms of stability and accuracy.