Degree‐Depth Relation for Planetary Gravity Field Model Based on Wavelength

Abstract

AbstractIn this paper we investigate the relation between the spherical harmonic (SH) degree of gravity field model and the corresponding depth of the source body. By investigating the gravity of a buried point mass, we find that a relationship can be found between the horizontal extent of the signal (which we assume to be indicative of the wavelength) and the depth of the source. We introduce a threshold to define the gravity anomaly wavelength of an isolated mass body. The region where the gravity anomaly of an isolated mass body is larger than the threshold defines its gravity anomaly wavelength. For an isolated point mass with fixed total mass, the wavelength is a function of the depth. The ratio between the maximum wavelength and the depth at which the maximum wavelength occurs (effective resolvable depth) is invariant provided that the mass and threshold are determined. When this maximum wavelength is larger than the minimum resolvable wavelength of n‐degree gravity field, this isolated mass body is considered as a reliable density feature. Combining the relation between maximum wavelength and effective resolvable depth of the isolated mass body and the relation between minimum resolvable wavelength and SH degree of gravity field, we derived the degree‐depth relation under the limiting resolvable condition: . This relation was validated with Gravity Recovery and Interior Laboratory gravity field data at lunar Orientale basin region, and provided insights for the planetary gravity field analysis.