A New Combination Approach for Gibbs Phenomenon Suppression in Regional Validation of Global Gravity Field Model: A Case Study in North China

Abstract

A global gravity field model (GGM) is essential to be validated with ground-based or airborne observational data for the accurate application of the GGM at a regional scale. Furthermore, accurately understanding the commission errors between the GGM and observational data are crucial for improving regional gravity fields. Taking the North China region as an example, to circumvent the omission errors, it is necessary to unify the spatial resolutions of the EIGEN-6C4 model and terrestrial gravity observational data to 110 km (determined by the distribution of gravity stations) by employing the spherical harmonic function for the EIGEN-6C4 model and the Slepian basis function for the gravity data, respectively. However, the application of spherical harmonic function expansions in the gravity model results in the Gibbs phenomenon, which may be a primary factor contributing to commission errors and impedes the accurate validation of the EIGEN-6C4 model with terrestrial gravity data. To effectively mitigate this issue, this study proposes a combination approach of window function filtering and regional eigenvalue constraint (based on the Slepian basis). Utilizing the EIGEN-6C4 gravity model to derive the gravity disturbance field at a resolution of 110 km (with spherical harmonic expansion up to the 180th degree and order), the combination approach effectively suppresses over 90% of high-degree (above the 120th degree) Gibbs phenomena. This approach also reduces signal leakage outside the region, thus enhancing the spatial accuracy of the regional gravity disturbance field. A subsequent comparison of the regional gravity disturbance field derived from the true model and terrestrial gravity data in North China indicates excellent consistency, with a root mean squared error (RMSE) of 0.80 mGal. This validation confirms that the combined approach of window function filtering and regional eigenvalue constraints effectively mitigates the Gibbs phenomenon and yields precise regional gravity fields. This approach is anticipated to significantly benefit scientific applications such as improving the accuracy of regional elevation benchmarks and accurately inverting the Earth’s internal structure.

Keywords

• EIGEN-6C4
• Gibbs phenomenon suppression
• Slepian basis function
• regional eigenvalue constraint
• regional gravity disturbance field
• North China