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.

在这篇文章中，我们对 Bölling 和 Grafarend (2005) 发表在 J.Geod 上的题为“地球引力势的椭球体光谱特性及其一阶和二阶导数”的研究文章中出现的错误进行了评论和彻底识别。79（6-7）：300-330。影响 Bölling 和 Grafarend (J Geod 79(6-7):300-330, 2005) 主要理论结果的主要问题如下： (1) 切向-切向张量球谐函数对于不同的调和次数不是正交的，并且相同的谐波次数。因此，球梯度边值问题的相应解和增量重力梯度张量切向-切向分量的球积分公式是无效的。(2) 切向-切向、切向-剪切、切向-膨胀、切向-法向和法向-法向张量椭球谐波对于不同调和次数和相同调和阶次不正交。因此，椭球梯度边值问题和增量重力梯度张量分量之间变换的椭球积分公式的解是不正确的。