GNGTS 2013 - Atti del 32° Convegno Nazionale

recognized from the original signal and can be really helpful to constrain geological models and guide the geological interpretation. However, as suggested by Grauch and Cordell (1987) and Rapolla et al. (2002), the maxima of the horizontal gradient magnitude can be offset from a position directly above the geologic contacts, especially when contacts are not steep or when several contacts are close together; so this link between maximum points and edges position is consistent only in the case of vertical or sub-vertical discontinuities. For example Khattach et al. (2004) associated the horizontal gradient magnitude of the Bouguer gravity anomaly to the upward continuation of the field to characterize the faults of the Triffa basin in North Morocco. However, in the presence of oblique surfaces, the maxima of the horizontal derivative are located in correspondence with the discontinuity at an intermediate depth (Grauch and Cordell, 1987), without any information about the dipping direction. Therefore, the efficacy of this simple method is good in the case of structural features typical of an extensional regime (normal faults, transform faults) or in the presence of dykes, volcanic conduits, plutonites, etc. On the contrary, the method is hardly usable when the structural setting is characterised by a compressive tectonic style (presence of inverse faults, transpressive faults, multiple thrust systems, etc.). To overcome this issue many authors (i.e. Cella et al. , 2000; Martelet et al ; 2001; Rapolla et al. , 2002; Tatchum et al. , 2011; Fedi and Pilkington, 2012) propose to couple upward continuation with gradient: first upward continuing the data and then computing its horizontal derivative to see how its maxima shift with respect to the subsurface structure. In fact, the position of the maxima of the horizontal derivative of the continued field will be laterally shifted toward the dipping direction of the discontinuity, proportionally to the continuation level. The DEXP method adds a third step to this procedure consisting in multiply the derived field with a scaling function (Fedi, 2007; Fedi and Pilkington, 2012). The maxima of the horizontal derivative of the field continued at different levels can also be localized automatically (see for example Blakely and Simpson, 1986) to speed up the data analysis. In this work we propose to follow this procedure, but taking in account the VUC method for upward continuation. One of the first advantages of using VUC instead of standard upward continuation algorithms is that edge effects are automatically encountered as long as the final result is built. Another important advantage occurs especially in the gravity case, where the VUC has an intrinsic connection also with the vertical derivative of the field. These two topics will be better clarified in the paragraph on VUC method. Volume Upward Continuation. We propose a new approach to upward continue potential field data, based on the minimum-length solution of the inverse potential field problem. The method yields a volume upward continuation, and reveals to be advantageous over the classical techniques based on the Fast Fourier transform (Cordell, 1985; Pilkington and Roest, 1992; Blakely, 1996; Fedi et al. , 1999; and Ridsdill-Smith, 2000) especially when dealing with truncated anomalies and when draped-to-level upward continuation is needed. This approach has the advantage of generating the field in the upward continuation domain (i.e., at many altitudes) as a unique solution in a 3D volume. Within this volume, all the three types of continuation (level-to-level, level-to-draped and draped-to-level) are naturally defined. In fact, the upward continued data volume can be immediately visualized and used to obtain the field on several surfaces of whatever kind (draped or level). Due to this feature we will call this method Volume Upward Continuation (VUC). In the VUC the border effects, typical of upward continuation, are controlled in an optimal way: the upward continued data are in fact proportional to a least-square solution of the inverse problem. Starting from the continuous inverse geomagnetic problem (e.g., Fedi et al. , 2005) discretized over a volume Ω of N cells, each of them with constant magnetization m j , we can write a linear system of equations: 145 GNGTS 2013 S essione 3.2