Frédérique Moreau

Wavelet analysis of potential fields

It is shown how a continuous wavelet technique may be used to locate and characterize homogeneous point sources from the field they generate measured in a distant hyperplane. For this a class of wavelets is introduced on which the Poisson semi-group essentially acts as a dilation.

Identification of sources of potential fields with the continuous wavelet transform: Complex wavelets and application to aeromagnetic profiles in French Guiana

A continuous wavelet technique has been recently introduced to analyze potential fields data. First, we summarize the theory, which primarily consists of interpreting potential fields via the properties of the upward continued derivative field. Using complex wavelets to analyze magnetic data gives an inverse scheme to find the depth and homogeneity degree of local homogeneous sources and the inclination of their magnetization vector. This is analytically applied on several local and extended synthetic magnetic sources. The application to other potential fields is also discussed. Then, profiles crossing dikes and faults are extracted from the recent high-resolution aeromagnetic survey of French Guiana and analyzed using complex one dimensional wavelets. Maps of estimated depth to sources and their magnetization inclination and homogeneity degree are proposed for a region between Cayenne and Kourou.

Filtering non‐stationary geophysical data with orthogonal wavelets

A filtering method based on both orthogonal wavelet decomposition and chi-squared statistics is proposed to clean non-stationary signals embedded in a gaussian white noise. An application to a time series of thermistance data recorded in an underground quarry illustrates the interest of the technique.