Applications of wavelet transforms in aeromagnetic data processing

Wavelet transforms are a powerful new tool in aeromagnetic data processing. The wavelet transform preserves both spatial and frequency information about a signal allowing us to design a range of spatially-varying filters that act on the wavelet coefficients. Two methods are outlined in this paper. The first, using the continuous wavelet transform, is used to construct 1D and radially-symmetric 2D linear filters with spatially-dependent frequency responses. An application of this is the level to variable-surface upward continuation operator. The second method uses the considerably more efficient discrete wavelet transform to generate a range of 1D derivatives with locally adaptive noise reduction. Both methods provide robust and efficient new frameworks for designing filters that are impractical to implement using conventional space or frequency domain techniques.