Localized depth estimation of potential fields by CWT scalogram analysis

Spectral analysis of potential fields, based on the Fourier Transform, allows high-resolution analysis in the wavenumber domain but not in the space domain. Because of this lack of spatial resolution, well-known methods, such as the Spector and Grant's one, gives information on the source depth but not on the horizontal source position. In addition, the estimated depth is often an average of the depths of different sources. Conversely, one significant feature of the Continuous Wavelet Transform (CWT) analysis is that it has both space and wavenumber resolution. We propose to address these concerns by a CWT scalogram analysis obtained using a Morlet wavelet as analyzing wavelet. In particular, we used a multidirectional Morlet fan, with n-fold symmetry. We show that it is possible to associate specific subregions of the scalogram coefficients to different sources, so to lead to a local implementation of the Spector and Grant spectral method directly within the 3D CWT scalogram. This may be made by selecting specific sub-volumes, 2D sections, or 1D profiles along the scale axis. Morlet wavelets with different central wavenumbers can be used to adjust the space and wavenumber resolutions differently: larger values allow for better wavenumber resolution, while smaller values increase the space resolution. We will demonstrate that both of these features are useful for performing a valid local spectral estimation. The method is tested on synthetic data, and it is also applied to the real aeromagnetic datasets of Mt. Vulture and NW Sardinia, Italy. For the Mt. Vulture we were able to compute the depth of intrusive rocks, lying from about 4 to 20 km depth. For the NW Sardinia, we estimated the occurrence of intrusive volcanic rocks down to about 12 km depth.