SRBF_Soft: a Python-based open-source software for regional gravity field modeling using spherical radial basis functions based on the data-adaptive network design methodology


EARTH SCIENCE INFORMATICS, vol.15, no.2, pp.1341-1353, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.1007/s12145-022-00790-y
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, CAB Abstracts, Geobase, INSPEC
  • Page Numbers: pp.1341-1353
  • Keywords: Regional gravity field modeling, Spherical radial basis functions, Remove-compute-restore, Quasi-geoid, K-SRBF, Python, REPRESENTATION, VALIDATION
  • Middle East Technical University Affiliated: Yes


This study introduces a novel open-source Python software package called SRBF_Soft for the high-resolution regional gravity field determination using various spherical radial basis functions (SBRFs) in terms of point mass, Poisson, and Poisson wavelet kernel. The modeling approach considers residual gravity field functionals generated by the well-known remove-compute-restore (RCR) technique where the long and short wavelength parts of the gravity signal are provided by a global geopotential model (GGM) and digital terrain model (DTM), respectively. A new data-adaptive network design methodology called k-SRBF is used to construct a network of SRBFs. The appropriate bandwidths (depths) are chosen using the generalized cross-validation (GCV) technique. The unknown SRBFs coefficients are estimated by applying the least-squares method where the extended Gauss Markov Model (GMM) with additional prior information is applied if the normal equation matrix is ill-conditioned. In such a case, the optimal regularization parameter is determined by variance component estimation (VCE). By utilizing parallel processing in every stage of the RCR technique, including creating the design matrix, the computational time is remarkably decreased relative to the number of processors used in the modeling. The performance of the software has been tested and validated in the Auvergne test area (France) on the basis of real terrestrial gravity data. The differences between estimated and observed height anomaly points (GNSS/leveling) amount to about 3 cm in terms of standard deviation (STD) for all kernels indicating that the SRBF_Soft possesses the capability to be applied in regional gravity field modeling as an efficient and reliable software.