Comments and corrections to: “Ellipsoidal spectral properties of the Earth’s gravitational potential and its first and second derivatives” by Bölling and Grafarend (2005) in J. Geod. 79(6-7):300-330

Abstract

In this contribution, we comment on and thoroughly identify errors which occur in the research article titled “Ellipsoidal spectral properties of the Earth’s gravitational potential and its first and second derivatives” by Bölling and Grafarend (2005) published in J.Geod. 79(6-7):300-330. The major issues affecting the main theoretical results by Bölling and Grafarend (J Geod 79(6-7):300-330, 2005) are as follows: (1) The tangential-tangential tensor spherical harmonics are not orthogonal for different harmonic degrees and the same harmonic orders. Consequently, the corresponding solution of the spherical gradiometric boundary value problem and the spherical integral formulas relating the tangential-tangential components of the incremental gravity gradient tensor are invalid. (2) The tangential-tangential, tangential-shear, tangential-dilation, tangential-normal, and normal-normal tensor ellipsoidal harmonics are not orthogonal for different harmonic degrees and the same harmonic orders. As a result, the solutions of the ellipsoidal gradiometric boundary value problems and the ellipsoidal integral formulas transforming the components of the incremental gravity gradient tensor among themselves are incorrect.