Joint application of continuous and discrete wavelet transform on gravity data to identify shallow and deep sources

The discrete wavelet transform (dwt), using the good property of localization of wavelet bases has been used as a powerful tool in filtering and denoising problems. The continuous wavelet transform (cwt) exploits the upward continuation properties of the field horizontal derivative and allows the location of potential field singularities in a simple geometrical manner. Within the cwt space- scale framework, the lines formed by joining, at different scales, the modulus maxima of the wavelet coefficients (multiscale edge detection method) intersect each other at the position of the point source or along the edges of the causative body. As long as the multiscale edge detection method is applied to experimental data the procedure may, however, fail, since the observed anomalies are the superposition of effects of sources having different density contrast, geometrical size and depths. We show that wavelet transform modulus maxima lines attributed to deep sources do not converge toward the true depths, but yield completely erroneous solutions. On the other hand, use of nth- order derivatives of the potential field allows the enhancement of the shallowest source effects, preventing us from obtaining information on the deeper ones. In this paper we therefore try to overcome this problem by a joint application of cwt and dwt. A localized dwt filter coupled to compactness criterion allows the separation of the effects due to the deeper sources from those of the shallower ones. Hence, the multiscale edge detection method, applied separately to the original and the filtered signals enabled the estimation of the depth of shallower and deeper sources, respectively. This analysis, performed on the gravity anomalies of Sardinia (Italy), has given estimations of the depths to both the Campidano graben and the Moho discontinuity, in good agreement with previous interpretations of gravity and seismic data.