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Global Positioning System (GPS) has been proven to be an effective tool to retrieve high-precision displacement for the natural hazard monitoring. The network positioning and Precise Point Positioning (PPP) are the two basic approaches for its data solution, but the former one can only get a relative displacement within the local reference frame and requires a complex and continuously linked infrastructure, and the latter one with a long convergence time to obtain the absolute displacements within the global reference frame. To overcome these drawbacks, this paper proposed a method of fast determining the displacement by PPP velocity estimation (PPPVE). The key of the approach is that the velocity vector parameters are not correlated with other unknown parameters, such as ambiguities and atmosphere, so they can be fast and accurately estimated and integrated into displacements. The validation shows that the displacement can be provided with a precision of 1-2 cm in 1 min by PPPVE. In additional, the Kalman smoothing estimation can be used to improve the PPP solution.
Wavelet modelling of the gravity field by domain decomposition methods: an example over Japan
(2011)
With the advent of satellite gravity, large gravity data sets of unprecedented quality at low and medium resolution become available. For local, high resolution field modelling, they need to be combined with the surface gravity data. Such models are then used for various applications, from the study of the Earth interior to the determination of oceanic currents. Here we show how to realize such a combination in a flexible way using spherical wavelets and applying a domain decomposition approach. This iterative method, based on the Schwarz algorithms, allows to split a large problem into smaller ones, and avoids the calculation of the entire normal system, which may be huge if high resolution is sought over wide areas. A subdomain is defined as the harmonic space spanned by a subset of the wavelet family. Based on the localization properties of the wavelets in space and frequency, we define hierarchical subdomains of wavelets at different scales. On each scale, blocks of subdomains are defined by using a tailored spatial splitting of the area. The data weighting and regularization are iteratively adjusted for the subdomains, which allows to handle heterogeneity in the data quality or the gravity variations. Different levels of approximations of the subdomains normals are also introduced, corresponding to building local averages of the data at different resolution levels.
We first provide the theoretical background on domain decomposition methods. Then, we validate the method with synthetic data, considering two kinds of noise: white noise and coloured noise. We then apply the method to data over Japan, where we combine a satellite-based geopotential model, EIGEN-GL04S, and a local gravity model from a combination of land and marine gravity data and an altimetry-derived marine gravity model. A hybrid spherical harmonics/wavelet model of the geoid is obtained at about 15 km resolution and a corrector grid for the surface model is derived.