Comparison between compactly-supported spherical radial basis functions and interpolating moving least squares meshless interpolants for gravity data interpolation in geodesy and geophysics

TL;DR

This study compares the efficiency of compactly-supported spherical radial basis functions and interpolating moving least squares for gravity data interpolation, finding that the former is faster and more accurate in a geophysical context.

Contribution

It provides a detailed comparison of two meshless interpolation methods for gravity data, highlighting the superior performance of spherical radial basis functions in this application.

Findings

Radial basis functions are faster and more accurate.

Compactly-supported basis functions outperform moving least squares.

The study covers various basis function classes and types.

Abstract

The present paper is focused on the comparison of the efficiency of two important meshless interpolants for gravity acceleration interpolation. Compactly-supported spherical radial basis functions and interpolating moving least squares are used to interpolate actual gravity accelerations in southern Africa. Interpolated values are compared with actual values, gathered by observation. A thorough analysis is presented for the standard deviation of the differences between interpolated and actual values. Three different class of spherical radial basis functions-Poisson, singularity, and logarithmic-and four different type of basis functions for interpolating moving least squares approach-planar, quadratic, cubic, and spherical harmonics-are used. It is shown that in this particular problem compactly-supported spherical radial basis functions are faster and capable of achieving higher accuracies, compared to interpolating moving least squares scheme.