GNGTS 2019 - Atti del 38° Convegno Nazionale

188 GNGTS 2019 S essione 1.3 the corresponding data misfit value between observed and predicted seismograms. However, GA as well as many other stochastic algorithms are computationally very expensive and the computing time required for reaching convergence increases exponentially with the number of unknowns. In our case, the unknowns are the P-wave velocities at the nodes of the grid which parametrizes the model.To limit this problem, our GA FWI employs two grids: a coarse grid with large spacings and few unknowns for the GA optimization, and a fine grid with short spacings between the nodes for the forward modeling. A bilinear interpolation brings each coarse grid model to the corresponding fine grid one. Due to the large spacings of the inversion grid, the model estimated by GA FWI contains the long wavelengths only of the velocity field, and thus it is a suitable starting model for a subsequent local GB FWI. Our GB FWI code makes use of the steepest descent as optimization method and computes the gradient of the data misfit function by means of the adjoint method. The input data are the same transmitted waves used in the previous GA FWI, but with an extended frequency band. Due to the much greater efficiency of the local optimization, the number of unknowns, that is of the grid nodes, are much higher than for GA FWI. The increased frequency band of the input data and the fine inversion grid allows for a significant increase of the resolution of the estimated model. In the case of the GB FWI of the CROP/18A the number of unknowns amounts to 131292, that are the 84 x 1563 nodes of the grid with an equal spacing of 30 m in the horizontal and in the vertical directions. For computing the synthetic seismograms, we developed a time-domain finite difference code that solves the acoustic wave equation with an accuracy of second order in time and fourth order in space (Galuzzi et al. 2017). It properly considers the varying elevations, which for the CROP/18 line vary between 100 m and 500 m a.s.l. The full methodological description and applications of our FWI can be found in Sajeva et al., 2016; Mazzotti et al. 2017; Aleardi et al. 2016, for body waves and in Xing and Mazzotti (2019a,b) for Rayleigh wave inversion. Sajeva et al., 2017, and Pierini et al., 2019 discuss and compare the effectiveness of several stochastic optimization algorithms, including genetic algorithms, on similar problems or on analytical tests. Results of the GA+GB FWI on the CROP/18Adata. Fig. 2 shows the final velocity model estimated down to 2.5 km depth by the sequence of GA + GB FWI. The overall shape of the velocity field shows undulating structures and also many fine details are evident, especially down to depths of about 1 km where the illumination of the transmitted waves is greater. Note the rapidly varying velocities near the surface that properly match the sequence of outcropping soft and hard formations. In general, the upper structure (above 0.5 km depth) is characterized by velocities between 2.5 and 4 km/s, and probably pertains to Neogene formations and to the Ligurian units. At greater depths, the green-orange colors, approximately corresponding to velocities of 5–6 km/s, may be associated to metamorphic formations, while the red globular structures with velocities close to 7 km/s may delineate the presence of intrusive bodies (granites) whose location and structure could be of interest for geological studies and for geothermal exploration. Fig. 2 - Best velocity model estimated by the sequence GA + GB FWI along the CROP/18A profile. The colors indicate the P-wave velocity.