Characterization of geological boundaries using 1-D wavelet transform on gravity data: Theory and application to the Himalayas

We investigate the use of the continuous wavelet transform for gravity inversion. The wavelet transform operator has recently been introduced in the domain of potential fields both as a filtering and a source-analysis tool. Here we develop an inverse scheme in the wavelet domain, designed to recover the geometric characteristics of density heterogeneities described by simple-shaped sources. The I-D analyzing wavelet we use associates the upward continuation operator and linear combinations of derivatives of any order. In the gravity case, we first demonstrate how to localize causative sources using simple geometric constructions. Both the upper part of the source and the whole source can be studied when considering low or high altitudes, respectively. The homogeneity degree of the source is deduced without prior information and allows us to infer its shape. Introducing complex wavelets, we derive analytically the scaling behavior of the wavelet coefficients for the dyke and the step sources. The modulus term is used in an inversion procedure to recover the thickness of the source. The phase term provides its dip. This analysis is performed on gravity data we measured along a profile across the Himalayas in Nepal. Good agreement of our results with well-documented thrusting structures demonstrates the applicability of the method to real data. Also, deeper, less constrained structures are characterized.