Patching local empirical covariance functions - a problem in altimeter data processing

Abstract

When gravity field modelling is carried out in larger regions a subdivision of the region into smaller areas may be carried out in order to handle the data volume. This may create problems during the estimation since the use of the optimal local empirical covariance function tends to give different results at the borders when the statistical characteristics change from one area to the next. In this paper an approximation to the covariance function that allows spatial variations in both magnitude and in spectral characteristics is presented. The different magnitudes are taken into account by a scaling function. Differences in the spectral characteristics are taken into account by changing the depth to the Bjerhammar sphere, so that it is located at a shallow depth in areas with a rough gravity field. In areas with a smooth gravity field the Bjerhammar sphere is located more deeply.