[S-GD01] Geodesy and Global Geodetic Observing System

[SGD01-13] Second-order smoothness prior over the Delaunay Tessellation and its application to gravity Bayesian inversion.

*Yuanyuan Niu¹, Jiancang Zhuang^2,1 (1.The Graduate University for Advanced Studies, 2.The Institute of Statistical Mathematics)

Prior information is always used to form up additional restrictions in geophysical inversions to solve the non-uniqueness problem of the solution. The smoothness (second-order derivative) of the model is one of such important restrictions. Smoothness is usually calculated through interpolation over the regular grids for the reason of easy implementation in numerical calculation. When observed data are irregularly distributed such as in geodetic inversions, Delaunay Tessellation (DT) based interpolation is popularly used to avoid additional interpolations. However, the numerical calculation of the second-order derivatives (smoothness) of a function based on the DT interpolation is more difficult than that of the first-order derivative (flatness). We propose a new method for calculating the smoothness with DT-based interpolation: the quadratic interpolators. The new method is tested through numerical experiments in the framework of full Bayesian inversion and applied to a gravity Bayesian inversion problem.