On the Choice of Basis Functions for Modeling Earth's Elastic Deformation Due To Surface Loading

Abstract

Accurately modeling Earth's elastic deformation due to surface loads is essential for geodetic and geophysical studies, including investigations of climate change, hydrology, and tectonics. Various basis functions, such as spherical harmonics, Green's functions, disk functions, and Slepian functions, are commonly used to describe the relationship between surface loads and deformation. However, the strengths and limitations of these basis functions have not been systematically compared, leading to potential uncertainties in the modeling results. This study evaluates six basis functions, including the above four and two newly developed approaches of infinite Green's functions and clustered disk-load Green's functions. We analyze their performance in forward modeling of Earth's vertical displacement and assess two primary sources of uncertainty: (a) native errors inherent to each basis function and (b) artificial errors introduced by improper configuration, for example, over-smoothing and aliasing. Our results demonstrate that these errors can be as significant as the uncertainties associated with Earth structure assumptions. Furthermore, we emphasize the importance of how surface load data is treated, whether as discrete point values, as uniform block values, or as block mean values, and how this choice impacts the selection of the basis function and the accuracy of the model. Based on our findings, we provide practical recommendations for selecting the most suitable basis function for different applications. Although our study focuses on vertical displacement, the insights gained are also relevant to modeling geoid changes, gravity variations, and strain fields. These findings contribute to improving the reliability of geodetic methods for studying Earth's dynamic processes.