A stable downward continuation by using the ISVD method

Abstract

Summary Downward continuation of potential fields represents a very interesting way to enhance the information content of a gravity or magnetic map. In fact, apart from the increase of resolution, shared with many recent methods involving the use of directional derivatives, the downward continued data have the advantage of maintaining the physical dimensions of the original ones. This means that the interpretative tools that may be used are the same as for the untransformed data, but the obtainable models can fully exploit the benefits of the increased resolution of the field. However, because of its inherent instability, this method has progressively lost popularity. In this paper a stable downward continuation algorithm is presented. It is based on the computation of stable vertical derivatives obtained by the ISVD method and Taylor series expansion of the field. The algorithm uses both frequency and space domain transformations. Tests on synthetic examples proved its utility especially in cases where the signal is corrupted by noise, when the continuation level is greater than the data sampling step or when the needed continuation level is close to the source top level. Its application to real gravity data of Southern Italy shows that a stable downward continuation of a potential field to a close‐to‐source level gives very valuable information. In this case, while our algorithm can give meaningful results even continuing the field to a level close to sources, the use of a standard method dramatically decreased the signal‐to‐noise ratio necessitating low‐pass filtering of the transformed map.

Gravity and Topography of the Terrestrial Planets

“…In contrast, if the coefficients were determined at the altitude of an orbiting satellite, and if this equation were used to determine the potential field on the surface of the planet, then the highfrequency terms would instead be relatively amplified. Since the spherical harmonic coefficients always possess some uncertainty, which generally increases with increasing l, the process of downward continuing a potential field is not stable and must generally be compensated by some form of filtering (e.g., Fedi and Florio, 2002;Phipps Morgan and Blackman, 1993;Wieczorek and Phillips, 1998).…”

Geological appraisal over the Singhbhum-Orissa Craton, India using GOCE, EIGEN6-C2 and in situ gravity data

“…the application of Laplace equation (Agarwal and Lal, 1969;Gupta and Ramani, 1982;Rapolla et al, 2002;Fedi and Florio, 2002;Vaish and Pal, 2014). The second vertical derivative enhances near surface effects at the expense of deeper anomalies.…”

“…Second derivatives are a measure of curvature and large curvatures are associated with shallow anomalies. The second vertical derivative can be obtained from the horizontal derivatives because the gravity field satisfies Laplace's equation (Agarwal and Lal, 1969;Gupta and Ramani, 1982;Telford et al, 1990;Rapolla et al, 2002;Fedi and Florio, 2002):…”

Comparative Study of the Spherical Downward Continuation

“…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. We use a regional and near-global coverage with data from the GOCE mission (ESA 1999), whereas the motivation originates from a number of recent activities in gravity and magnetic gradiometry on a satellite (ESA 1999) or on an airplane (Lee 2001;Schmidt et al 2004).…”