Normalized downward continuation of potential fields within the quasi‐harmonic region

Abstract

Downward continuation is a useful transformation, mainly used to enhance measured gravity or magnetic field anomalies. It is known to be an unstable transformation that should be strictly used only in the harmonic region, apparently preventing any meaningful application to continuations inside the source volume. Despite these well-known theoretical and practical limitations it has been used to recover source parameters by different methods, here referred to as normalized full gradient methods. Such methods show that downward continuation may be extended to the source volume, which is assumed to contain one-point, isolated singularities, which is a quasi-harmonic region. We modify the normalized full gradient method focusing our attention to the way the downward continuation is normalized. Differently from normalized full gradient methods, we study the effect of the normalization not only on the analytical signal modulus of the downward continued field but also on the downward continuation of the gravity or magnetic fields themselves. With our method, called normalized downward continuation, several statistically meaningful normalizations are considered, some of them yielding improved, more resolved depth estimations for synthetic as well as measured total-field anomalies. From a statistical point of view, the downward continued field tends to have right-skewed histograms at shallow depths, while becoming symmetrically distributed at greater depths. This occurs because, as the depth of continuation increases, the intrinsic error propagation of the downward continuation allows the error to dominate with respect to the source-related signal. For non-isolated anomalies, consistent results are also obtained but the normalizing factors must be computed within windows centred to the studied anomaly

Pseudo resistivity cross section imaging using VLF-EM data

“…It is important to determine the maximam limit of harmonic in downward continuation process (Sindirgi et al, 2008;Fedi et al, 2011). We examine the downward continuation field with the NFG operator, which give us better images of resistivity anomaly.…”

Improved normalized full-gradient method and its application to the location of source body

“…This method has also been applied to self-potential data (Sindirgi et al, 2008), electromagnetic data (Dondurur, 2005), and seismic signal data (Karsli and Bayrak, 2010). Significant improvement were made by Fedi and Florio (2011), who introduced several different normalizing functions to implement the singular point method and suggested a separate analysis of nearby anomalies to obtain good results.…”

“…Currently, the most frequently used technique is the Euler deconvolution method (Thompson, 1982;Reid, 2007, 2010;Fedi and Florio, 2014). Other commonly used techniques include the general linear inversion method (Cribb, 1976), the correlation and/or probability imaging methods (Patella, 1997;Guo et al, 2012), the migration method (Zhdanov, 2002, Zhdanov et al 2010, continuous wavelet transform (Sailhac and Gibert, 2003;Cooper, 2006), the DEXP method (Fedi, 2007;, the all-direction imagery method (An, 2001), and the normalized full-gradient (NFG) method (Berezkin, 1967;Zeng et al 2002;Fedi and Florio, 2011). In the present study, a modified NFG method was used to detect the position of the source body.…”

Comparative Study of the Spherical Downward Continuation

“…Most recently, the problem was treated with help from Tikhonov's regularization (Pašteka et al 2012;Zeng et al 2013), with the help from Landweber's iteration on the plane (Xu et al 2007;Zhang et al 2013) and on the sphere . Besides the approaches applicable in source-free regions (satisfying the Laplace equation), there are also numerous approaches for working with potential data inside a source region (see, e.g., Elysseieva and Pašteka 2009;Fedi and Florio 2011). While the regional studies usually work within a planar approximation, where the Fourier image of kernel functions is known (Parker 1973;Huestis and Parker 1979;Fedi and Florio 2002;Li et al 2009;Pašteka et al 2012), an appropriate comparative study of different approaches for the spherical domain is still missing.…”