GNGTS 2017 - 36° Convegno Nazionale

GNGTS 2017 S essione 3.1 547 be on the same valley of the misfit function as the global minimum. This means that the initial model must be accurate enough to give a good match between the observed and predicted data. To attain this, in our work, we use the velocity model obtained from a previous inversion (Fig. 2a), that makes use of the application of genetic algorithms on a coarse grid (Sajeva et al.�, 2016). The details and the results can be found in Tognarelli et. al. (2015) and Mazzotti et al. ( 2017). The model accuracy is checked by the degree of flattening of the events on the CIGs, obtained after the pre-stack Kirchhoff depth migration (PSDM). Fig. 3a shows 11 CIGs evenly spaced along the profile up to 1.2 km of depth (the maximum depth of the modelling grid), computed with the starting model of Fig. 2a. In Fig. 3a a trace-by-trace normalization and a gain is applied for display purposes. A preliminary alignment of some events can be observed, but the gathers still present complex move-outs that can be improved using a local FWI based on a gradient line-search method. Inversion procedure and results. As a local optimization method, we use the steepest descend algorithm (Nocedal et al��., 2006), where the descend direction corresponds to the negative direction of the gradient of the misfit function and the step length is obtained by a line search that satisfies the Wolfe conditions (Wolfe, 1969). The gradient is computed using the adjoint method (Tromp et al. , 2005; Plessix, 2006). The unknowns are the model velocity values situated under the sea layer, for a total of 242x30 unknowns. The velocities range between 1480 m/s and 3500 m/s. We perform 500 iterations for the minimization procedure. Fig. 2b shows a comparison of four vertical velocity profiles obtained at the end of the inversion process, related to four CDP positions along the seismic profile (the green points in Fig. 2a). The long- wavelength structure of the starting model is not significantly changed, except for the upper part just below the sea bed where a consistent change of the velocity values can be noted. Fig. 2c shows the difference between the observed and predicted data for two shot gathers before and after the optimization procedure, where the decrease of the differences of the inverted data can be observed. Finally, Fig. 3b shows the CIGs obtained by pre-stack depth migrating the data, using the final velocity model. Comparing Fig. 3a and Fig. 3b, a significant improvement of the horizontal alignment of the events can be noted, especially for the events just below the seabed reflection and located in the central part of the model. Fig. 3 - CIGs derived from PSDM (Kirchoff) using (a) the starting velocity model for the local optimization and (b) the final velocity model obtained at the end of the optimization procedure. Conclusion. In this work, we have described an acoustic FWI experience made on a 2D seismic marine data set extracted from a 3D volume. We designed a specific processing sequence to be applied on the observed and the predicted data to reduce the non-linearity of the misfit function. This allows to make the whole procedure more robust against the cycle skipping