GNGTS 2018 - 37° Convegno Nazionale

GNGTS 2018 S essione 3.2 673 in which t and t 0 are the cross-gradients function and its a priori value respectively and λ CG is the regularization parameter that weights the cross-gradients function. In order to minimize the objective function, in a first attempt the Gauss-Newton method (Gunther, 2004) was used writing the model update as: (4) where S 1 and S 2 are the jacobian matrices for the two methods, and B 1 and B 2 are the jacobian matrices associated with the cross-gradient function. Because of the high number of model parameters, the system of equations (4) has been iteratively solved using the conjugate gradient method (Gunther, 2004). Field data. The field data have been acquired with the aim of characterizing the shallow subsurface around and below a historic building situated near Rieti (Central Italy). The construction, built in 1910 as a two-floor masonry building and now used as a National research centre for agricultural studies (Fig.1a), exhibits some fractures on the load-bearing walls and possible differential settlements phenomena in the soil foundations. The area is situated “within a travertine outcropping area, with variable soil thickness above the travertine bedrock” (Cercato and De Donno, 2018). Different types of geophysical measurements were conducted on the site (Fig. 1b), but we will focus on the L3 line, which allows the reconstruction of the shallow subsoil near the building. The ERT measurements were acquired with a 48-electrodes IRIS Instruments SyscalPro48 using a combination of dipole- dipole and Wenner-Schlumberger configurations with stainless steel electrodes 2m spaced apart, while the SRT data using a 48-channel system of 4.5 Hz vertical geophones 1m spaced (we examined the P-wave data) and a 7 kg hammer on a steel plate as source, with a Geometrics Geode seismograph at a sampling rate of 0.125ms. Results. In a first attempt, the ERT and SRT data were inverted separately. In order to choose the optimal value of λ for the inversion, the L- curve (Zhdanov, 2015) was constructed both for ERT and SRT (Fig. 2a,b). The ERT convergence was reached after 4 iterations, while the SRT after 5 iterations. The ERT section (Fig. 3a) showed three different layers: the conductive one with values of resistivity <20Ωm for the shallower and in the range of 30-60Ωm for the middle one, and a deeper resistive layer, in the left part of the section, with a resistivity >100Ω·m, that probably represents a travertinous formation. The SRT map (Fig. 3b) confirms the ERT map results, since a first layer with low P-wave, with velocities in the range of 300-600m/s is individuated. These values are typical of a weathered layer. Then, velocities increase with depth, reaching values >800m/s for the middle layer and >1000m/s in the left part of the section in a position that overlaps the one of the ERT map. These high velocities (>1000m/s) suggest the presence of a travertineous Fig. 1 - a) Photograph of the historical building; b) location of geophysical and geotechnical measurements (Cercato and De Donno, 2018).