Multiscale Feature Extraction of Potential Fields Using Poisson Wavelets

Wavelets are a common tool for multiscale feature extraction. We present wavelets that are well-suited for analysing potential fields, evaluated on the sphere, in arbitrary scaling levels. Well-suited in the sense that they provide a convincing physical interpretation and offer possibilities to analyse on orientational features in different angular resolutions. The wavelets are constructed based on the concept of differentiating the function after convolution with a smoothing filter of the corresponding scale. The order of differentiation is associated with the order of the wavelet and determines the angular resolution. The smoothing filter is the poisson kernel extending the function harmonically on spheres of radii determined by the scales. In this sense, we can interpret the wavelettransforms as regarding the potential field from different heighs and analysing them on their spatial evolution by taking deviations. In the presentation, we will give first results on the application of the wavelets on the geoid. The geoid is analyzed on oriented structures like oscillations in different scales. -------------------------------------------------- Geophysique Spatiale et Planetaire --------------------------------------------------