Flexible Dataset Combination and Modelling by Domain Decomposition Approaches

Abstract

For geodetic and geophysical purposes, such as geoid determination or the study of the Earth’s structure, heterogeneous gravity datasets of various origins need to be combined over an area of interest, in order to derive a local gravity model at the highest possible resolution. The quality of the obtained gravity model strongly depends on the use of appropriate noise models for the different datasets in the combination process. In addition to random errors, those datasets are indeed often affected by systematic biases and correlated errors.

Here we show how wavelets can be used to realize such combination in a flexible and economic way, and how the use of domain decomposition approaches allows to recalibrate the noise models in different wavebands and for different areas. We represent the gravity potential as a linear combination of Poisson multipole wavelets (Holschneider et al. 2003). We compute the wavelet model of the gravity field by regularized least-squares adjustment of the datasets. To solve the normal system, we apply the Schwarz iterative algorithms, based on a domain decomposition of the models space. Hierarchical scale subdomains are defined as subsets of wavelets at different scales, and for each scale, block subdomains are defined based on spatial splittings of the area. In the computation process, the data weights can be refined for each subdomain, allowing to take into account the effect of correlated noises in a simple way. Similarly, the weight of the regularization can be recalibrated for each subdomain, introducing non-stationarity in the a priori assumption of smoothness of the gravity field.

We show and discuss examples of application of this method for regional gravity field modelling over a test area in Japan.