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<p>In this study, a novel three-scale spherical radial basis function (SRBF) modeling method is proposed for regional geoid determination in Colorado. By sequentially constructing the SRBF model across three distinct frequency bands—medium, high, and ultrahigh—this approach effectively captures detailed signals that traditional single- and two-scale SRBF approaches may fail to resolve. In addition, unlike conventional methods that remove residual terrain model (RTM) contributions prior to modeling, the proposed approach retains RTM effects within the SRBF modeling frequency bands, potentially minimizing errors associated with their removal and subsequent restoration. Validation against the geoid slope validation survey 2017 (GSVS17) data indicates that the geoid model derived from the three-scale SRBF approach achieves a standard deviation (STD) of 2.0&#xa0;cm, outperforming models derived from single- and two-scale SRBF methods. Furthermore, retaining RTM effects during SRBF modeling yields a slight improvement over models where these effects are removed beforehand. These results highlight the effectiveness of the three-scale SRBF method in constructing high-accuracy regional geoid models, particularly in mountainous areas.</p>

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Geoid determination in Colorado based on the three-scale SRBF modeling method

  • 期刊论文

  • 发表日期：

    2025年7月9日

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  • Zhiwei Ma

摘要

In this study, a novel three-scale spherical radial basis function (SRBF) modeling method is proposed for regional geoid determination in Colorado. By sequentially constructing the SRBF model across three distinct frequency bands—medium, high, and ultrahigh—this approach effectively captures detailed signals that traditional single- and two-scale SRBF approaches may fail to resolve. In addition, unlike conventional methods that remove residual terrain model (RTM) contributions prior to modeling, the proposed approach retains RTM effects within the SRBF modeling frequency bands, potentially minimizing errors associated with their removal and subsequent restoration. Validation against the geoid slope validation survey 2017 (GSVS17) data indicates that the geoid model derived from the three-scale SRBF approach achieves a standard deviation (STD) of 2.0 cm, outperforming models derived from single- and two-scale SRBF methods. Furthermore, retaining RTM effects during SRBF modeling yields a slight improvement over models where these effects are removed beforehand. These results highlight the effectiveness of the three-scale SRBF method in constructing high-accuracy regional geoid models, particularly in mountainous areas.