A new potential field shape descriptor using continuous wavelet transforms
Potential field characterization aims at determining source depths, inclination, and type, preferably without a priori information. For ideal sources, the type is often defined from the field's degree of homogeneity, derived from its expression in the space domain. We have developed a new shape descriptor for potential field source functions, stemming from spectral-domain parameters, which manifest clearly when using continuous wavelet transforms (CWTs). We generalize the use of the maximum wavelet coefficient points in the CWT diagram for the analysis of all types of potential fields (gravity, magnetic, and self-potential). We interpret the CWT diagram as a similarity diagram between the wavelet and the analyzed signal, which has fewer limitations than its interpretation as a weighted and upward-continued field projection. We develop new formulas for magnetic source depth prediction, as well as for effective inclination estimation, using various kinds of wavelets. We found that the potential field source functions exhibit precise behaviors in the CWT analysis that can be predicted using a single parameter d, which is related to their Fourier transforms. This parameter being scale and rotation-invariant can be used as a source-body shape descriptor similar to the commonly used structural index (SI). An advantage of the new descriptor is an increased level of discrimination between sources because it takes different values to describe the horizontal or the vertical cylinder structures. Our approach is illustrated on synthetic examples and real data. The method can be applied directly with the native form of the CWT without scaling factor modification, negative plane diagram extension, or downward plotting. This framework offers an alternative to existing wavelet-like projection methods or other classic deconvolution techniques relying on SI for determining the source depth, dip, and type without a priori information, with an increased level of differentiation between source structures thanks to the new shape descriptor.