Composite continuous wavelet transform of potential fields with different choices of analyzing wavelets

In potential field problems, the continuous wavelet transform (CWT) has allowed the estimation of the source properties, such as the depth to the source and the structural index (N). The natural choice for the analyzing wavelets has been the set belonging to the Poisson kernel. However, a much larger set of analyzing wavelets has been used for analyzing signals other than potential fields. Here we extend the CWT of potential fields to other wavelet families. Since the field is intrinsically dilated with Poissonian wavelets from the source depth to the measurement level, distortions are unavoidably introduced when CWT uses a different wavelet from the measurement level to other scales. To fix the problem, we define a new form for the continuous wavelet transform convolution product, called "composite continuous wavelet transform" (CCWT). CCWT removes the field dilations with Poisson wavelets, intrinsically contained at the measurement level and replaces them with dilations performed with any other kind of wavelet. The method is applied to synthetic and real cases, involving sources as poles, dipoles, intrusions in complex magnetized basement topography and buried steel drums, from measurements taken at the Stanford University test site. CCWT takes advantage from the special features of the several considered wavelets, e.g., the Gaussian wavelet is useful for its low pass filtering characteristic and Morlet wavelet for its localization property. Hence, depending on the case, an important parameter for the choice of the analyzing wavelet is its central frequency.