Combining Different Types of Gravity Observations in Regional Gravity Modeling in Spherical Radial Basis Functions

2015 ◽  
pp. 115-120 ◽  
Author(s):  
Katrin Bentel ◽  
Michael Schmidt
Keyword(s):  
Radial Basis Functions ◽  
Basis Functions ◽  
Gravity Modeling ◽  
Different Types ◽  
Radial Basis ◽  
Spherical Radial Basis Functions ◽  
Regional Gravity

scholarly journals Regularization methods for the combination of heterogeneous observations using spherical radial basis functions

2019 ◽  
Author(s):  
Qing Liu ◽  
Michael Schmidt ◽  
Roland Pail ◽  
Martin Willberg
Keyword(s):  
Radial Basis Functions ◽  
Regularization Parameter ◽  
Basis Functions ◽  
Parameter Determination ◽  
Data Sets ◽  
Radial Basis ◽  
Spherical Radial Basis Functions ◽  
Ill Posed ◽  
Curve Method ◽  
Regional Gravity

Abstract. Various types of heterogeneous observations can be combined within a parameter estimation process using spherical radial basis functions (SRBF) for regional gravity field refinement. However, this process is in most cases ill-posed, and thus, regularization is indispensable. We discuss two frequently used methods for choosing the regularization parameter which are the L-curve method and variance component estimation (VCE). Based on these two methods, we propose two new approaches for the regularization parameter determination, which combine the L-curve method and VCE. The first approach, denoted as ‘VCE + L-curve method’, starts with the calculation of the relative weights between the observation techniques by means of VCE. Based on these weights the L-curve method is applied to determine the regularization parameter. In the second approach, called ‘L-curve method + VCE’, the L-curve method determines first the regularization parameter and it is set to be fixed during the calculation of the relative weights between the observation techniques from VCE. These methods are investigated based on two different estimation concepts for combining various observation techniques. All the methods are applied and compared in six study cases using four types of observations in Europe. The results show that the ‘VCE + L-curve method’ delivers the best results in all the six cases, no matter using SRBFs with smoothing or non-smoothing features. The ‘L-curve method + VCE’ also gives rather good results, generally outperforming the cases just using the L-curve method or VCE. Therefore, we conclude that the newly proposed methods are decent and stable for regularization parameter determination when different data sets are combined and can be recommended regardless of the type of SRBFs used.

PDF-to-ODF Inversion by Approximation with Spherical Radial Basis Functions

2005 ◽  
pp. 313-318 ◽  
Author(s):  
Ralf Hielscher ◽  
Swanhild Bernstein ◽  
Helmut Schaeben ◽  
K.Gerald van den Boogaart ◽  
Judith Beckmann ◽  
...  
Keyword(s):  
Radial Basis Functions ◽  
Basis Functions ◽  
Radial Basis ◽  
Spherical Radial Basis Functions

The combination and contribution of different gravity measurements in regional quasi-geoid determination based on spherical radial basis functions

2021 ◽  
Author(s):  
Qing Liu ◽  
Michael Schmidt ◽  
Laura Sánchez
Keyword(s):  
Radial Basis Functions ◽  
Gravity Data ◽  
Basis Functions ◽  
Airborne Gravity ◽  
Frequency Noise ◽  
Geoid Model ◽  
Topographic Model ◽  
Radial Basis ◽  
Spherical Radial Basis Functions ◽  
Terrestrial Data

<p>In this study, we investigate the optimal combination of local gravity observations and their contributions to the regional quasi-geoid model. The study area is located in Colorado, USA, with two types of regional data sets, namely terrestrial gravity data and airborne gravity data, available within the “1 cm geoid experiment”. The approach based on series expansions in terms of spherical radial basis functions (SRBF) is applied, which has been developed at DGFI-TUM in the last two decades. We use two different types of basis functions covering the same spectral domain separately for the terrestrial and the airborne measurements. The Shannon function is applied to the terrestrial data, and the Cubic Polynomial (CuP) function which has smoothing features is applied to the airborne data for filtering their high-frequency noise.</p><p>To assess the contributions of the regional terrestrial and airborne gravity data to the final quasi-geoid model, four solutions are compared, namely the combined solution, the terrestrial only, the airborne only, and finally the model only solution, i.e., only the global gravity model and the topographic model are used without any gravity data from regional measurements. By adding the terrestrial data to the GGM and the topographic model, the RMS error of the quasi-geoid model w.r.t the validation data (the mean solution of independent computations delivered by fourteen institutions from all over the world) drops from 4 to 1.8 cm, and it is further reduced to 1 cm by including the airborne data.</p>

All-Frequency Lighting with Multiscale Spherical Radial Basis Functions

2010 ◽  
Vol 16 (1) ◽  
pp. 43-56 ◽  
Author(s):  
Ping-Man Lam ◽  
Tze-Yiu Ho ◽  
Chi-Sing Leung ◽  
Tien-Tsin Wong
Keyword(s):  
Radial Basis Functions ◽  
Basis Functions ◽  
Radial Basis ◽  
Spherical Radial Basis Functions
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