2D Continuous Wavelet Transform of potential fields due to extended source distributions

Abstract

We analyse the real Continuous Wavelet Transform 2D (CWT2D) of potential fields for the investigation of potential field singularities. We focus our attention to extended geological sources, in order to verify the reliability of this method with realistic fields. 3D space-scale representation (3D Scalogram) related to synthetic models were generated, showing the Wavelet Transform Modulus Maxima (WTMM) at each scale. The WTMM are related to the shape of the source, so defining some sort of source boundary analysis through the CWT. Wavelets of different order may help to gain resolution and define source features. Selecting a range of scales where the sources behave as if they are approximately isolated, the depth to the source may be estimated basing on the property that the lines joining the modulus maxima of the wavelet coefficients at different scales (WTMML) intersect each other at the edges of the causative body. Therefore, it is possible to manage the information contained in the wavelet transform of fields related to extended sources. In the real case of the anomaly gravity map of the Vesuvius area (Italy), we estimated the depth of the Mesozoic carbonate basement in the Pompei Basin. We showed also how the WTMML information can be integrated to that of another multiscale method, the Depth from Extreme Points (DEXP) transformation, which is also related to the source density distribution of a given region.