# SRBF_package: spherical radial basis functions

# 1. Introduction

SRBF_package is a collection of a few routines for gravity field modelling with band-limited spherical radial basis functions (SRBFs), allowing both analysis and synthesis of the gravitational field. Harmonically analyzed can be the gravitational potential (or any other continous scalar function on a 2D sphere), while synthesis is possible for the gravitational potential, the gravitational vector in LNOF and the gravitational tensor in LNOF. To our knowledge, the equations to synthesize the gravitational tensor are novel and are more efficient than other formulae (e.g., that from Appendix of Bucha et al., 2016). This is because only three radial basis functions are needed to compute six unique elements of the gravitational tensor. This may improve the computational speed, as the evaluation of band-limited spherical radial basis functions (the sum over harmonic degrees) is the most time-consuming part of the synthesis.

The package is an enhanced version of the MATLAB-based routines used by Bucha et al. (2016). It is available as MATLAB-based functions and Fortran 95 routines accompanied by a Python wrapper. The MATLAB synthesis is parallelized using "parfor" and the Fortran synthesis and analysis are parallelized using OpenMP (the "!$OMP PARALLEL DO" directive). When using the same number of CPUs, the Fortran routines can be up to about 10 times faster than their MATLAB-counterparts. The Python wrapper allows an easy access to the Fortran routines for Python users.

Attached to the package are also also test data, manuals with a detailed description of the package and scripts with two test computations to verify the correctness of the implementation in MATLAB, Fortran and Python. While the test examples are based on global gravity field modelling for clarity, SRBF_package was developed primarily for regional applications with a residual gravity field. This is because SRBF_package is significantly slower when compared to FFT-based SHS and SHA, both of which are designed for global applications. Although the package was designed mainly for gravity field modelling, other applications are possible. Further details can be found in the attached PDF.

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# 2. Reference

Bucha, B., Janák, J., Papčo, J., Bezděk, A., 2016. High-resolution regional gravity field modelling in a mountainous area from terrestrial gravity data. Geophysical Journal International. 207, 949-966. http://doi.org/10.1093/gji/ggw311

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