GNGTS 2015 - Atti del 34° Convegno Nazionale

So, inequalities 8 and 9 allow to manage the overall tolerance of this particular technique. The problem thus posed is the resolution of a single sounding. In the cases shown below, each sounding is resolved independently of each other. The role of matrices F and the vector h is important because they allow to solve the problem by mitigating the effect of a trend or data errors. Synthetic example. We tested the IML method on synthetic magnetic data obtained from the calculation of the magnetic effect of a single body in the investigated volume. The data at different heights were generated thanks to an algorithm that calculates the magnetic response, at a fixed altitude, of a prismatic sources for which are defined physical (magnetization or susceptibility) and geometrical properties. The vertical profiles are selected by field measurements at N altitudes. For real cases it is quite unlikely to collect data at different heights; in this case the vertical sounding is built by using a property of the potential field that allows the computation of the data at different altitude starting from those at a fixed level, namely upward continuation (Fedi and Rapolla, 1993). The use of an upward continuation algorithm introduces an error, that may be managed by using a third-order polynomial, as shown in Castaldo et al. (2014) during the inversion process. From the anomaly maps, calculated and continued at fixed altitudes, we have extracted the values of the field along the points of a profile, which passes centrally on the analyzed anomaly. The set of points of the profile at different levels defines the vertical soundings (Fig. 2a). For the calculation of the kernel a theoretical volume has been defined with horizontal dimensions that are in agreement with those of the body that generates the anomaly. These dimensions may be estimated using a technique of boundary analysis (Fedi and Florio, 2001): by calculating the module of horizontal derivative field along the two horizontal directions and selecting the distance between the identified maxima. The vertical dimension of the theoretical volume is defined so as to completely contain the source of anomaly and it is discretized, with a high number of layers (up to 99) of the same thickness. For this test we used a single body with horizontal dimension equal to 110 m × 130 m at depths from 50 m to 250 m. The magnetization contrast with the surrounding volume is 5 A/m. The vertical soundings consist of magnetic data calculated and continued at 20 different altitudes from the first level at 5 m up to the last level at 100 m with a 5 m constant step. For this test, we used the real magnetization contrasts, setting the lower bound equal to 0 and the upper bound equal to 5 A/m. For the experimental error data, we noticed that the continued data need an higher tolerance value to get results. In this experiment we have set, for the calculated data, an experimental error data equal to 10 -6 nT while for the continued data we used a value equal to 10 -2 nT. Fig. 2 shows the inversion results obtained from the calculated data (Fig. 2b) and the continued data (Fig. 2c). The black rectangle identifies the exact location of the buried body. For both cases the algorithm provides excellent results in estimating the position and the magnetization contrast of the body. As regards the results obtained from the inversion of continued data, the depth of the bottom is not so well defined in comparison with that for calculated data. From the estimated parameters, we calculated also the estimated data along the considered profile, at a fixed altitude, and we compared them with the initial data related to the same profile. As we can see in Figs. 2d and 2e, the fitting is really good for both kinds of data. These results are not trivial if we consider that the inversion method is applied on vertical soundings of field data, each one inverted independently. Case history. We applied this particular inversion method to a dataset over the sedimentary basin of the Frenchman Flat Basin, Nevada Test Site, USA (Phelps and Graham, 2002). According to Phelps and Graham (2002), the basin’s bottom is located at 2.4 km depth in the northeast sector of the basin, and the maximum density contrast, between less dense sediments and the basement, is about 0.4 g/cm 3 . 170 GNGTS 2015 S essione 3.3