TY - JOUR

T1 - A comparison of fixed- and free-positioned point mass methods for regional gravity field modeling

AU - Lin, Miao

AU - Denker, Heiner

AU - Müller, Jürgen

N1 - Funding information: We thank two anonymous reviewers for their constructive comments that helped to improve the manuscript significantly. This work was financially supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) ? SFB 1128, project C04. All figures were plotted by the Generic Mapping Tools (GMT; Wessel and Smith, 1998 ).

PY - 2019/4

Y1 - 2019/4

N2 - Radial basis functions (RBFs) have been used widely for regional gravity field modeling. By using the RBFs with the point mass kernel, the RBF-based technique becomes the point mass method. The model setup of the point mass RBFs, consisting of the selection of the spectral bandwidths, depths and network, is crucial for the quality of recovered regional gravity field models. If the spectral bandwidths are defined, the point mass method can be classified into the fixed- and free-positioned methods. This study compares the two methods for modeling of regional gravity fields in a unified framework. The fixed-positioned method uses a Reuter grid to determine the RBF number and centers. The grid depth is chosen by experimenting several candidates to achieve the smallest root-mean-square (RMS) of the differences between predicted and observed values at a set of control points. The magnitudes of the RBFs are estimated by solving a linear equation system, where Tikhonov regularization is applied if the normal matrix is ill-conditioned. The free-positioned method starts with initially unknown positions of the RBFs, and also the number of RBFs is determined in the computation process. Here, we use a search process to select the RBFs automatically by means of solving a series of nonlinear problems with depth constraints on the RBFs to minimize the RMS difference between the predictions and observations. The magnitudes of all selected RBFs are later re-estimated in the least-squares sense while keeping their positions unchanged. EGM2008 coefficients are firstly used to simulate two harmonic fields to test the performance of the two methods on various Reuter grids, depth limits, and spectral bandwidths, in order to gain certain guidelines for a proper selection of the model parameters. The two methods are then applied to real gravity data sets in the Auvergne and White Sands test areas, respectively. The results reveal that the free-positioned method outperforms the fixed-positioned method in regions with rough gravity field features while using less RBFs. In regions with smooth gravity field features, both methods give similar results, where the fixed-positioned method needs more RBFs than the free-positioned method.

AB - Radial basis functions (RBFs) have been used widely for regional gravity field modeling. By using the RBFs with the point mass kernel, the RBF-based technique becomes the point mass method. The model setup of the point mass RBFs, consisting of the selection of the spectral bandwidths, depths and network, is crucial for the quality of recovered regional gravity field models. If the spectral bandwidths are defined, the point mass method can be classified into the fixed- and free-positioned methods. This study compares the two methods for modeling of regional gravity fields in a unified framework. The fixed-positioned method uses a Reuter grid to determine the RBF number and centers. The grid depth is chosen by experimenting several candidates to achieve the smallest root-mean-square (RMS) of the differences between predicted and observed values at a set of control points. The magnitudes of the RBFs are estimated by solving a linear equation system, where Tikhonov regularization is applied if the normal matrix is ill-conditioned. The free-positioned method starts with initially unknown positions of the RBFs, and also the number of RBFs is determined in the computation process. Here, we use a search process to select the RBFs automatically by means of solving a series of nonlinear problems with depth constraints on the RBFs to minimize the RMS difference between the predictions and observations. The magnitudes of all selected RBFs are later re-estimated in the least-squares sense while keeping their positions unchanged. EGM2008 coefficients are firstly used to simulate two harmonic fields to test the performance of the two methods on various Reuter grids, depth limits, and spectral bandwidths, in order to gain certain guidelines for a proper selection of the model parameters. The two methods are then applied to real gravity data sets in the Auvergne and White Sands test areas, respectively. The results reveal that the free-positioned method outperforms the fixed-positioned method in regions with rough gravity field features while using less RBFs. In regions with smooth gravity field features, both methods give similar results, where the fixed-positioned method needs more RBFs than the free-positioned method.

KW - Depth limits

KW - Point mass position

KW - Radial basis functions

KW - Spectral bandwidth

UR - http://www.scopus.com/inward/record.url?scp=85062463004&partnerID=8YFLogxK

U2 - 10.1016/j.jog.2019.01.001

DO - 10.1016/j.jog.2019.01.001

M3 - Article

AN - SCOPUS:85062463004

VL - 125

SP - 32

EP - 47

JO - Journal of geodynamics

JF - Journal of geodynamics

SN - 0264-3707

ER -