Identification of sources of potential fields with the continuous wavelet transform: Two‐dimensional wavelets and multipolar approximations

Abstract

We show new continuous wavelet‐based transformation techniques of potential field maps and propose interpretation schemes for characterizing three‐dimensional (3‐D) sources having some finite extent. As in previous studies, we use wavelets derived from the Poisson kernel which generate a position‐altitude representation of potential field data initially measured at one level above the ground. We use first‐order or second‐order wavelets to obtain wavelet transform parameters related to the 3‐D analytic signals or 3 × 3 tensors of the data. We show how such parameters can be used to characterize the sources, first, by using the assumption of their local homogeneity and, second, by using multipolar expansions to estimate the sizes of the horizontal or vertical extent of the 3‐D source. Thus we generalize to 3‐D the Taylor expansion of upward continued 2‐D analytic signals previously shown for the interpretation of profiles transformed using complex wavelets. Such a 3‐D interpretation scheme based upon position‐altitude representations has been developed to interpret the maps of scalar potential field anomalies (e.g., magnetic total field anomalies or vertical gravity anomalies) but can be also used for upward continued maps of vector or tensor of potential field anomalies as obtained by new surveys of the full tensor of gravity; this also concerns the interpretation of derived potentials considered in poroelasticity and electrokinetic in porous materials of the Earth. We illustrate the technique on synthetic data; in addition, a first application on aeromagnetic data from French Guyana shows the potential of the technique.