An Analysis of Gravitational Gradients in Rotated Frames and Their Relation to Oriented Mass Sources

Abstract

Many mass sources within the Earth and its fluid envelopes show elongated geometries, aligning with the orientations of plate boundaries and plate motions, coastlines, rivers, and drainage basins for instance. To enhance their identification and separation in global or regional gravity observations and models, a dedicated method based on gravitational gradients analysis is presented here. This approach provides a detailed description of the geographic pattern of the gravity variations, which are accurately mapped thanks to the regular spatial coverage of high-accuracy satellite data and arise from lateral density changes within the planet. First, gravity gradients are defined at different spatial scales in spherical frames, which are rotated along the radial axis according to the orientation of the source. The sensitivity of these gradients to the mass distribution inside a spherical Earth is described and analytical expressions relating the source to the observable are introduced. Then, the gravity gradients responses at different spatial scales to flat, elementary mass sources located at the surface and at increasing depth are studied. Specifically, the paper investigates how a source width and orientation can be determined, for localized and oscillatory mass anomalies with different width-to-length aspect ratios. This theoretical case study aims at providing a basis for the analysis of more complex mass structures, when applying the presented method to static or time-varying satellite gravity field models. It may help deciphering the nature of the gravity sources by the detection of meaningful geometries and orientations in the gravity field.