The Application of the Wavelet Transform to the Processing of Aeromagnetic Data

Frequency is a key physical parameter in potential field theory. Accordingly, Fourier transforms play an important role in aeromagnetic processing and many common enhancements are efficiently implemented in the Fourier domain. However, the trade-off for accurately measuring the frequency content of a signal is a complete absence of spatial localisation in the Fourier domain. Fourier-based enhancements cannot adapt to local properties of the signal. The frequency content of aeromagnetic data varies depending on the local characteristics of the magnetic stratigraphy and the noise. The wavelet transform measures this local frequency content allowing wavelet-based enhancements to adapt to local features in the signal. Two major aspects of wavelet-based aeromagnetic data processing are discussed in this thesis. The first is the design of spatially-varying filters. These filters are defined in terms of frequency response, but unlike Fourier convolution filters, can vary this frequency response with position. A construction based on the discrete wavelet transform (DWT) allows for the separation of signal and noise at similar frequencies during the calculation of profile derivatives. This leads to better preservation of anomaly gradients in the calculated derivatives than is possible using conventional Fourier or space domain smoothing techniques. A broader range of spatially-varying filters can be implemented in the wavelet domain using the continuous wavelet transform (CWT) including grid-based variable upward and downward continuation with locally-adaptive noise reduction. The wavelet implementation produces a superior result compared with conventional techniques such as Taylor-series and chessboard algorithms. The second major aspect of wavelet processing is signal compression. Aeromagnetic data often possess localisation in both the space and frequency domains and can therefore be efficiently represented in the wavelet domain using a low number of significant coefficients. This compression property is used to reduce the number of elements in a dipole equivalent layer, thereby reducing the computation required to forward model the layer. The result is a computationally efficient and accurate method for upward continuing irregularly spaced aeromagnetic data onto an arbitrary surface. The wavelet transform provides a useful alternative to Fourier methods in the enhancement of aeromagnetic data. The advantages result from the trade-off in the wavelet domain between localisation in space and frequency, allowing for the design of methods exploiting the best features of both space and frequency domain processing techniques.