Exploring error estimation methods for natural neighbour interpolation: preliminary research and analysis

Interpolation of scalar data, in the 2D space, is an important topic in many fields of environmental and geoscience studies, and uncertainty assessment is as important as interpolation itself. An example of this is the Kriging method, which is well-established in geostatistics and enables the automatic evaluation of uncertainties by solving a linear equation, taking into account the bivariate spatial continuity of the data. The Sibson interpolation method (natural neighbour) has the important property of providing unambiguous and reproducible results. However, since it is fundamentally a deterministic method, it does not have qualitative and/or quantitative control of the uncertainty based on the sampling spatial distribution geometry. In this paper, we show the different steps leading to an analytical approach to evaluate the uncertainties of the Sibson method. After a series of tests with a synthetic data set and a surface with a known differentiable function, we show an example using the data set of accelerometric data from the M 6.5 Norcia earthquake of 30 October, 2016.