Separation and reconstruction of residual and regional gravity sources in wavelet transform domain

The wavelet transform is used to estimate geometrical parameters of two-dimensional cross sections of gravity sources in which the continuous wavelet transform shows the location of the potential field singularities in a geometrical pattern as a simple cone the apex of which tend to the corners of the source cross section. Within the space-scale framework، the continuous wavelet transform، in special scales domain related to the wavelength of causative body anomaly، the lines formed by joining the modulus maximum of the wavelet coefficients، intersect each other at the position of the point source or along the edges of the anomaly source (multi-scale edge detection method). However، the procedure may fail، since the observed anomalies are superpositions of effects of different sources. Therefore، the total anomaly signal is separated based on dividing its high to low frequencies into several levels. This method was applied to synthetic data of a complex model in which the shallow source، a structure with a triangular cross section is located above the intersection of two trapezoids with infinite lengths which are cross sections of a deep structure. Therefore، shallow and deep effects are often located in low and high levels، respectively. To attenuate the effect of shallow sources، a majority of the wavelet reconstruction coefficients of the signal were muted in low levels. Eventually، the whole of wavelet coefficients reconstructed and filtered anomaly signal due to the deeper sources resulted. Then، the signal was analyzed and the corners of the cross section of the deep source were estimated by the multi-scale edge detection method. Therefore، the effects due to the deeper sources from those of the shallower ones were reconstructed by a joint application of discrete wavelet transform as a powerful tool and continuous wavelet transform. The method was also applied to noisy data (4%). The available real data was that of Sardinia (Italy). From a geological point of view، it has a Paleozoic basement، consisting mainly of granitic metamorphic rocks; its western sector is intersected by an N-S trending Oligo-Miocene Rift (the Sardinia Rift) containing the Campidano graben the limits of which are the Gulfs of Oristano and Cagliari extended in the southern part of the island. The upper part of the depression is filled by a Pliocene Quarternary sequence. In this research، the boundaries and the length position of the graben were estimated by applying the method to a profile consisting of 334 data points with a 0. 6 km step، extended to 512 data points in order to avoid end effect of the edges، which was in good agreement with other geological and geophysical interpretations.