The Use of the 2D and 3D Complex Wavelet and Ridgelet Transforms in Geophysical Prospecting: Case of Potential Fields Data

Abstract

The complex wavelet and ridgelet transforms are used in the potential field data interpretation for identifying the buried structures responsible for potential field anomalies. Its basis is the use of particular analyzing wavelets belonging to the Poisson semigroup that possess amazing properties regarding potential fields. In fact, the analyzed anomaly displays a conical signature in the wavelet domain and whose apex is pointing out at the causative homogeneous structure. Fundamentally, the interpretation is performed in the upward-continued domain where, the dilation of the wavelet transform is the upward-continuation altitude. This confers on the wavelet transform a considerable advantage: its robustness with respect to noise. The method is also developed to identify the depth, horizontal positions, size, strike direction, dips and shape of elongated 3D structures such as finite-dimensional dykes and faults. For this type of anomaly, the 2D wavelet transform corresponds to the ridgelet transform performed in the Radon domain, where elongated anomalies are recognized by high amplitude signatures. A reminder of the developed theory and applications in the 2D and 3D cases on real case studies are shown.