Global prediction of abyssal hill root-mean-square heights from small-scale altimetric gravity variability

Abyssal hills, which are pervasive landforms on the seafloor of the Earth's oceans, represent a potential tectonic record of the history of mid-ocean ridge spreading. However, the most detailed global maps of the seafloor, derived from the satellite altimetry-based gravity field, cannot be used to deterministically characterize such small-scale (<10 km) morphology. Nevertheless, the small-scale variability of the gravity field can be related to the statistical properties of abyssal hill morphology using the upward continuation formulation. In this paper, I construct a global prediction of abyssal hill root-mean-square (rms) heights from the small-scale variability of the altimetric gravity field. The abyssal hill-related component of the gravity field is derived by first masking distinct features, such as seamounts, mid-ocean ridges, and continental margins, and then applying a newly designed adaptive directional filter algorithm to remove fracture zone/discontinuity fabric. A noise field is derived empirically by correlating the rms variability of the small-scale gravity field to the altimetric noise field in regions of very low relief, and the noise variance is subtracted from the small-scale gravity variance. Suites of synthetically derived, abyssal hill formed gravity fields are generated as a function of water depth, basement rms heights, and sediment thickness and used to predict abyssal hill seafloor rms heights from corrected small-scale gravity rms height. The resulting global prediction of abyssal hill rms heights is validated qualitatively by comparing against expected variations in abyssal hill morphology and quantitatively by comparing against actual measurements of rms heights. Although there is scatter, the prediction appears unbiased.