We consider the use of the continuous wavelet transform in the interpretation of potential field data. We report its development since the publication of the first paper by Moreauet al. in 1997. Basically, it consists in the interpretation in the upward continued domain since dilation of the wavelet transform is the upward continuation altitude. Thus within a range of altitudes, the wavelet transform of the noise is decreased faster than the wavelet transform of the potential field caused by underground sources; this means that the signal‐to‐noise ratio is much better than those involved in other enhancing methods (e.g., Euler deconvolution, gradient analysis, or the analytic signals). Similarly to the Euler deconvolution, its first target parameters were the source positions and shape. The method has then been developed to estimate size and directions of extended sources (e.g., faults and dikes of finite dimensions) and also the magnetization direction in the case of magnetic data. Latest developments show that when combined with a Radon transform, the continuous wavelet transform can help in the automatic detection of elongated structures in 3D, simultaneously to the estimation of their strike direction, shape and depth. Several applications to real case studies have been shown before; however for clarity's sake in the present paper, only synthetic cases have been reproduced to clearly sum up the development of the methodology.

A method to localize and characterize the sources of VLF tilt anomalies is proposed. It relies on the continuous wavelet transform computed with particular analyzing wavelets possessing remarkable properties with respect to potential fields. An example with a synthetic dyke model shows how the method allows to locate the top of conductive structures both horizontally and vertically. An application to real data acquired over a conductive dyke illustrates the robustness of the method with respect to noise.

[1] A method based on the wavelet transform is used to localize the causative sources of potential field anomalies. In previous studies we introduced a particular class of analyzing wavelets belonging to the Poisson semigroup and such that the analyzed anomaly has a conical signature in the wavelet domain with its apex pointing at the location of the causative homogeneous source. In the present paper we apply this formalism to the special case of anomalies produced by elongated sources like faults and dikes. We show that, for this particular type of anomalies, the two-dimensional (2-D) wavelet transform corresponds to the ridgelet analysis and reduces to the 1-D wavelet transform applied in the Radon domain. A complete synthetic example is used to illustrate all steps of the analysis method: Radon transform of the anomaly map, selection of the Radon signature of elongated anomalies, complex wavelet transform, and source localization with the conical signature in the wavelet domain. The azimuthal filtering performed in the Radon domain leads to high signal-to-noise ratio and good localization of the sources both horizontally and vertically. The synthetic example is completed by an application of the method to a real aeromagnetic survey acquired in Britanny (France) and the results are compared with source depth determinations made with the Euler deconvolution method.

Identification of deep magnetized structures in the tectonically active Chlef area (Algeria) from aeromagnetic data analyzed with 2-D and 3-D imaging derived from the wavelet and ridgelet transforms. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Appgeo(2017),

International audienceThe Cheliff basin (ex El Asnam) is known as one of the most seismic active zone in Algeria and the West Mediterranean region. We can cite the El Asnam earthquake which occurred in 10.10.01980 with magnitude of 7.3. It was generated by a thrust fault with NE–SW sinistral component. Until now, there is a little information about existence of deep active faults, which generate this strong activity. The gravity field is an important resource of information on crustal structure. The aim of this work is giving a reliable geometry of the major faults relative to the kinematics of this region.The results obtained from various filtered maps (derivatives, upward continuation) of the gravity data, were used to generate a structural map of the studied area. Whilst the continuous wavelet transform method can help in automatic detection of elongated structures in 3-D, to estimate their strike direction, shape and depth. It gives a 3-D image or a model of the region and confirms the existence of several faults, localized or inferred, from former geological studies