Identification of sources of potential fields with the continuous wavelet transform: Application to VLF data

Abstract

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.

The theory of the continuous wavelet transform in the interpretation of potential fields: a review

“…This geometric property can be used in inversion (Moreau 1995; Martelet et al 2001). It is easier and automatic to do linear regressions of log‐log plots of normalized modulus | W / a γ | versus apparent depths a + z s (Moreau et al 1999; Sailhac et al 2000; Boukerbout, Gibert and Sailhac 2003, etc.). By using complex wavelets, one actually deals with upward continued analytic signals and the phase can be used to estimate dip angles of faults or dikes and is simply related to the inclination in magnetics (Sailhac et al 2000; Martelet et al 2001).…”

“…The first approach used to perform this geometrically‐based downward continuation was a manual process with pencil and ruler (see Moreau 1995; Martelet et al 2001). We then introduced a statistical process to characterize every point in the lower half‐space by testing if it could be the apex of conic‐structures with consistent scaling parameters (Sailhac 1999; Boukerbout et al 2003; Boukerbout 2004).…”

Comment on “Self‐potential signals associated with preferential groundwater flow pathways in sinkholes” by A. Jardani, J. P. Dupont, and A. Revil

“…The case of real extended source (i.e., other than point sources) is much more complicated because only the equivalent point source of an extended source is actually localized with the wavelet transform. In the general case, for complex (e.g., other than spherical) geometry of the source, the complex patterns of the η function have to be interpreted through a Taylor or multipolar expansion of the wavelet transform [e.g., Sailhac et al , 2000; Sailhac and Gibert , 2003; Boukerbout et al , 2003]. Recovering the shape of an extended source from its localized equivalent multipolar sources is a nonunique inverse problem.…”

Identification of deep magnetized structures in the tectonically active Chlef area (Algeria) from aeromagnetic data using wavelet and ridgelet transforms

“…The wavelet theory can be found in the book of Holshneider (1995) and the theory of its application to potential fields data can be found in Moreau et al, (1997Moreau et al, ( , 1999, Hornby et al, (1999), Sailhac et al, (2000), Sailhac and Gibert (2003), Boukerbout and Gibert (2006), Sailhac et al, (2009), Fedi et al, (2010), Fedi and Cascone (2011) and so on. Many studies illustrate application of this method, for instance we can refer to applications to aeromagnetic and magnetic data (Sailhac et al, 2000;Pouliquen and Sailhac, 2003;Boschetti et al, 2004;Vallée et al, 2004;Yang et al, 2010), electromagnetic data (Boukerbout et al, 2003), spontaneous electrical potential (Gibert and Pessel, 2001;Sailhac and Marquis, 2001, Saracco et al, 2004, Gibert and Sailhac, 2008Mauri et al, 2010) and gravity data (Martelet et al, 2001;Fedi et al, 2004;Cooper, 2006;Chamoli et al, 2011;Abtout et al, 2014).…”