GNGTS 2018 - 37° Convegno Nazionale

GNGTS 2018 S essione 3.2 617 site. However, with surface waves and especially with real data, the presence of noise, lateral shear velocity variations, the interference of further (more than two) modes and the combination of geometrical and intrinsic attenuation could compromise the success of the method. Given these reasons above, we developed a robust and effective algorithm which can be applied to real data under a certain set of conditions. When those conditions are not met we can, in some cases, pre-process the data in order to make them still suitable for the Multi-mode MOPA. In the following sections we will discuss the application of the algorithm to both synthetic and real cases. Results with synthetic data. A synthetic seismogram was generated using PUNCH (Kausel, 1989), a program based on a finite element solution in the direction of layering. For this reason, PUNCH can handle only 1D vertical velocity models, which is sufficient for the required demonstration. Note that in this work we do not consider lateral velocity variations, that will be the focus of a future piece of work. In the simulation we applied a single shot using a point-load source at the surface. The receiver array is composed of 81 vertical geophones, spaced 1 m along a line with minimum and maximum offsets of 20 m and 100 m. We adopted a 1D shear wave velocity profile with a very fast velocity layer at shallow depth, between 3 and 5 m. Velocities above and below the concrete block are assumed to progressively increase with depth. The presence of a fast layer surrounded by low-velocity materials produces a strong velocity inversion, that in turn is known to generate higher modes with high energy (Boaga et al. , 2014). From the analysis of the frequency normalized f-k spectrum (Fig. 2) we observe that in the range 15-30 Hz, most of Rayleigh wave energy is distributed between the fundamental and the first higher mode. For this reason, the Multi-Mode MOPA has been has been tested within this range. The analysis was performed in a fully automatic fashion using the algorithm mentioned in the previous section. The whole procedure is performed for each frequency independently. First of all, the algorithm searches for a positive periodic function (the norm of a sinusoid) which approximates the observed data (Fig. 2). From this first step we obtain, for each frequency, the value of ΔX and the offset locations of amplitude maxima and minima. Secondly, the algorithm extracts the individual amplitudes of the two modes (call them A 0 and A 1 ). In order to do so, amplitudes are first corrected for geometrical spreading and intrinsic attenuation. Then, amplitude minima and maxima are computed as the weighted, with respect to offset, average of all minima and maxima found in the previous step. The weight is advisable Fig. 2: Example with synthetic data. Left-upper panel: unwrapped phase at 19 Hz (blue stars) with values selected for each independent k loci computation (red circles). Left-bottom panel: Normalized amplitude at 19 Hz (blue stars), normalized amplitude after correction for attenuation (green line), fitting sinusoid (red line). Right panel: f-k spectrum overlapped by computed fundamental (blue stars) and higher order (red stars) modes.