Geopotential Reconstruction,Decomposition, Fast Computation,and Noise Cancellation by Harmonic Wavelets

Harmonic wavelets are introduced within the framework of the Sobolev-like Hilbert space H of potentials with square-integrable restrictions to the Earth's (mean) sphere _R . Basic tool is the construction of H-product kernels in terms of an (outer harmonics) orthonormal basis in H. Scaling function and wavelet are defined by means of so-called H-product kernels. Harmonic wavelets are shown to be building blocks that decorrelate geopotential data. A pyramid scheme enables fast computations. Multiscale signal-to-noise thresholding provides suitable denoising. Multiscale modelling of the Earth's anomalous potential from EGM96-model data is illustrated by use of bandlimited harmonic wavelets, i.e. Shannon and CP-wavelets.