• Biased and unbiased combination;
  • Global root mean square error;
  • Gravity anomaly estimator;
  • Point-wise estimator;
  • Spectral combination


The idea of this paper is to present estimators for combining terrestrial gravity data with Earth gravity models and produce a high-quality source of the Earth's gravity field data through all wavelengths. To do so, integral and point-wise estimators are mathematically developed, based on the spectral combination theory, in such a way that they combine terrestrial data with one and/or two Earth gravity models. The integral estimators are developed so that they become biased or unbiased to a priori information. For testing the quality of the estimators, their global mean square errors are generated using an Earth gravity model08 model and one of the recent products of the gravity field and steady-state ocean circulation explorer mission. Numerical results show that the integral estimators have smaller global root mean square errors than the point-wise ones but they are not efficient practically. The integral estimator of the biased type is the most suited due to its smallest global root mean square error comparing to the rest of the estimators. Due largely to the omission errors of Earth gravity models the point-wise estimators are not sensitive to the Earth gravity model commission error; therefore, the use of high-degree Earth gravity models is very influential for reduction of their root mean square errors. Also it is shown that the use of the ocean circulation explorer Earth gravity model does not significantly reduce the root mean square errors of the presented estimators in the presence of Earth gravity model08. All estimators are applied in the region of Fennoscandia and a cap size of 2° for numerical integration and a maximum degree of 2500 for generation of band-limited kernels are found suitable for the integral estimators.