Gravity Degree-Depth Relations for High-Order Disturbing Potential Gradients

Abstract

Abstract The degree-depth relation links the spherical harmonic degree to an operational depth scale for gravity signals. Previous studies have primarily examined the degree-depth relation for the gravity anomaly, the vertical component of the gravitational vector, and the gravity disturbance. However, degree-depth relations for other high-order radial disturbing potential gradients, such as the second- and third-order radial derivatives of the disturbing potential, remain unestablished. This study reviews existing degree-depth relations and their applications in modeling and spectral-scale interpretation of observed gravity signals. degree-depth relations are derived for the components of the second- and third-order radial derivatives of the disturbing potential. Furthermore, the general degree-depth relation for the s th-order ( $$s \ge 1$$ s ≥ 1 ) radial disturbing potential gradients is established. Numerical results show that, for all degree-depth relations, operational depths decrease as spherical harmonic degrees increase, and vice versa. Results further indicate that distinct degree-depth relations should be applied to the corresponding orders of radial disturbing potential gradients. The derived degree-depth relations offer a self-consistent set of bounds for spectral-filtering choices when working with high-order radial gradients in geodesy, geophysics, and planetary sciences.