GNGTS 2017 - 36° Convegno Nazionale

GNGTS 2017 S essione 3.3 735 11 shots were located outside the receivers line (2 of them at -2 m and 2 m from its extremities and the other two at -4 m and 4 m, respectively); the other source-points were placed inside the receivers line, evenly spaced at a distance of about 2.7 m. The geophone-interval for the 2D acquisition was 0.3 m. In the present work we refer only to the seismograms belonging to the 2D acquisition. In Fig. 2a we show an example of a field seismogram referred to the 2 nd shot (placed at -2 m left side from the first receiver - Fig. 1 - left side lower corner). The wave propagation along the line clearly evidences the presence of the sand body. Methodology. For the numerical simulations, we used the spectral elements code developed in the frame of the SEISCOPE Consortium (http://seiscope2.osug.fr ). The code is written in Fortran 95. It has two levels of MPI parallelization (the domain decomposition and the possibility to run multiple shots simultaneously). It is based on non-overlapping hexahedra spectral elements in a deformed Cartesian-based mesh automatically built-up. Moreover, viscoelastic time-domain modelling can be considered as well as the misfit gradient with respect to density, stiffness coefficients and attenuation factors, in the frame of the FWI whole machinery. More details about the code and methods behind for modeling and inversion can be found in Trinh et al. (2017a, 2017b, 2017c). The method used to obtain the initial model from the surface-waves data involves two steps: the extraction of the dispersion curves (DCs), together with their uncertainties, from the experimental seismograms and the laterally constrained inversion of the DCs. The extraction of DCs has been performed using a space-varying Gaussian windowing approach (Bergamo et al. , 2012). This technique allows to obtain a set of DCs, each one in correspondence of the moving Gaussian window maxima and each one referring to a different subsurface portion. The number of the DCs for a given seismic line depends on a parameter related to the width of the window. This parameter is inversely proportional to the Gaussian- window standard deviation; its value is chosen as a trade-off between the width of the window in the time domain and the spectral resolution in the frequency-wavenumber (f-k) domain. After appropriate selection of these parameters, for each window position several shots are considered and the picking of the DCs is performed over the stacked f-k spectrum of several source positions. Once all the DCs are extracted from the field data, they are inverted in a LCI approach (Socco et al. , 2009). This is a deterministic inversion in which all the DCs along the profile are linked together by mutual constraints, referring to the variance allowed for the same parameter between adjacent models. In particular, small values of variance are required for rigid constraints and bigger values for weak constraints. The final result of the inversion is a pseudo-2D model of the shear-waves velocities (Vs) distribution along the line. This pseudo-2D model is later interpolated to obtain a smooth 2D Vs model, more suitable for the forward modelling code. Starting from this model we associated an appropriate Vp model by assuming a constant Poisson value. The 2D models are then extended in 3D in order to respect the input format required by the SEM3D code and perform the 3D numerical simulations of wave propagation. In this particular case, after the 2D to 3D conversion, it was preserved for the y direction the same geometry as for the x direction. Elastic modelling tests and results. For the numerical simulations we used an element size (i.e. distance between two adjacent points of the 3D mesh) of 0.2 m to satisfy the volume condition for 4 th order SEM simulation (Trinh et al. , 2017a). The CFL stability condition leads us to use a 1e-5 s time-step value and 51200 time-samples to reach the same duration as the registration length used during the field acquisition (0.512 s). For the first series of simulations we used a Ricker source with a central frequency of 60 Hz and a maximum frequency of 150 Hz, in order to reproduce the frequency content of the field data. In Fig. 2b we show the results of the simulation performed, for the same shot position where we have shown experimental data, using this Ricker wavelet. In order to better reproduce