Spherical approximating and interpolating moving least squares in geodesy and geophysics: a case study for deriving gravity acceleration at sea surface in the Persian Gulf

Abstract

This paper is aimed at introducing the concept of Spherical Interpolating Moving Least Squares to the problems in geodesy and geophysics. Based on two previously known methods, namely Spherical Moving Least Squares and Interpolating Moving Least Squares, a simple theory is formulated for using Spherical Moving Least Squares as an interpolant. As an application, a case study is presented in which gravity accelerations at sea surface in the Persian Gulf are derived, using both the approximation and interpolation mode of the Spherical Moving Least Squares. The roles of the various elements in the methods-weight function, scaling parameter, and the degree of spherical harmonics as the basis functions-are investigated. Then, the results of approximation and interpolation are compared with the field data at sea surface, collected by shipborne gravimetry approach. Finally, the results are compared with another independent interpolation method-spline interpolation. It is shown that in this particular problem, SMLS approximation and SIMLS interpolation present a better accuracy than spherical splines.

A precise machine learning aided algorithm for land subsidence or upheave prediction from GNSS time series

“…Besides using the (conventional) machine learning methods, the precise setting of the problem, including transformations for converting the coordinates to the local coordinate system are used. It is important to notice that, as also [7] asserts, the machine learning algorithms we use are based on the supervised learning for prediction, which gives the idea of extrapolation, like the numerical methods in [7], in contrast to the most methods of approximation in geosciences [8]- [12] and [13]- [15]. The rest of this paper is organized as follows.…”