GNGTS 2017 - 36° Convegno Nazionale

GNGTS 2017 S essione 3.1 553 faults are present. Differently from the Marmousi-1, some reservoir levels with different fluid saturation conditions have also been included into the Marmousi-2 model. We employ a 2D time-domain elastic FWI code with the steepest-descent as the optimization tool and a finite difference method as forward modelling. The forward modelling code adopts absorbing boundaries to avoid artificial signal reflections at the edges of the model. In order to attenuate the risk to converge toward a local minimum of the objective function, we used the multi-scale approach. The inversion employs the standard adjoint state method to compute the gradient of the objective function that is the L2 norm misfit between observed and modelled seismic data. The modelling and the inversion grids contain 3601 grid points along the horizontal direction and 701 grid points along the vertical direction. For the computation of the synthetic observed data, we use the elastic wave equation and therefore the P-wave and S-wave velocity models, and the constant density model, were the input to the forward modelling. As the source wavelet, we employ a Ricker wavelet with 60 Hz maximum frequency and a 0.5 ms sampling interval. The acquisition geometry was defined by a towed-streamer system, composed by 181 sources (with a source interval of 50 m) and 357 receivers (with a receiver interval of 25 m) all placed in the water at a depth of 12.5 m. To make the EFWI inversion feasible, a long-offset (9 km) acquisition geometry was designed. The 5 m grid-spaced model is numerically stable and non-dispersive for the P- and S-waves velocities, and thus it ensures realistic results. We perform several experiments varying the acquisition geometry, the number of source gathers considered in the inversion, varying the starting model and its resolution. However, for the lack of space, in the following we only show the results obtained for a single test in which we consider 90 out of 181 shot gathers. We perform 70 iterations, 5 for each of the following frequencies: 2 Hz, 3 Hz, 5 Hz, 7 Hz, 9 Hz, 11 Hz, 13 Hz, 15 Hz, 17 Hz, 20 Hz, 22 Hz, 25 Hz, 27 Hz and 30 Hz. The proper choice of the initial model is crucial for the convergence of the gradient-based FWI to the global minimum. For this reason, in the following the starting models for both Vp and Vs are directly derived from the true model by applying a moving- average filter. Results. We now show the results obtained for a single inversion test. Figs. 1a to 1c show the true Vp , Vs and Vp / Vs models, respectively; Figs. 1d to 1f illustrate the elastic properties of the starting models, whereas Figs. 1g to 1i represent the final predicted Vp , Vs and the corresponding Vp / Vs fields, respectively. We observe that the EFWI has been able to progressively add high- frequency details to the starting Vp and Vs models. In particular, the inversion allows for a Fig. 1 - Vp , Vs and Vp/Vs of the true (a, b, c), starting (d, e, f) and final predicted (g, h, i) models.