GNGTS 2017 - 36° Convegno Nazionale

598 GNGTS 2017 S essione 3.1 we also employ a frequency marching strategy (Bunks et al. , 1995). Via considering the long- wavelength components of the observed data at initial generations, the genetic algorithm efficiently rejects the parent models whose main features do not coincide with those of the true one. As a result, the convergence is accelerated. In Fig. 1 we show three reference Vs models, which are generally considered as complex near-surface models, and their inversion results by using our two-grid GA-FWI inversion code. Details on the inversions and on the analyses of the results can be found in Xing and Mazzotti (2017a) and Xing and Mazzotti (2017b). Actually, the model prediction in Fig. 1e is not the optimal one because it has been obtained by an early version of our GA-FWI code and the updated code provides an improved reconstruction. However, we would like to use it as the starting model for a local optimization FWI to show that, notwithstanding its imperfections, it still allows the local FWI to derive a refined model. As an example, the comparison between one common shot of the observed data, which is contaminated by random noise, and the predicted data pertaining to the model in Fig. 1a, is presented in Fig. 3c. The data prediction is already very satisfactory, meaning that the GA-FWI has reached convergence. In Fig. 3a and in Fig. 3b we respectively show the evolutions of the data misfits and the model misfits related to the model in Fig. 1a. In Fig. 3a it can be seen that, in each frequency band parted by cyan lines, the evolution of data misfits is nearly always interrupted from fitting observed data further, and that the final data misfit, although greatly reduced, is not yet close to zero (which could be expected for a synthetic data example, albeit noise contaminated). This leaves space for a subsequent data fitting by using FWI with a local optimization method. From Fig. 3b we see that the final Vs model predicted according to the smallest data misfit fits the true model slightly better than the mean model of the last generation. Nevertheless, they are very near. Model refinement by FWI with a local optimization method. To further refine the predicted models shown in Fig. 1d to Fig. 1f, FWI with the preconditioned conjugate gradient method (PCG-FWI) (Kohn et al. , 2012) is used. Guided by gradients, local optimization methods could be much faster than global ones. However, especially for nonlinear optimization problems, the local algorithm has to start from a “good enough” initial model to be able to reach the global minimum and not to be trapped in local minima. Generally, “good enough” means that the long wavelength features of the velocity model must be well presented in the starting model. The starting models are shown in Figs. 2a to 2c. As the models shown in Figs. 1d and 1f predicted by the global optimization method are reasonable enough, they are used as the starting models for PCG-FWI without any modification. The model shown in Fig. 1e instead is smoothed by a Gaussian function to become the starting model displayed in Fig. 2b. The same observed data used in two-grid genetic algorithm FWI is used in PCG-FWI. The model prediction results are shown in Figs. 2d to 2f. With the GA-FWI models displayed in Figs. 1d to 1f as references, we see that models refined by PCG-FWI (Figs. 2d to 2f) have improved the details of the structures if compared with the initial models. Moreover, PCG-FWI tends to render models with velocities nearer to the true values. This could be seen more obviously with the profiles given in Figs. 2g to 2i. However, erroneous velocities existent at several parts of the starting models are amplified in the final predicted models. For instance, PCG-FWI renders an erroneous very low velocity zone at the bottom center in the model shown in Fig. 2d. The small erroneous high velocity zone at the 2 nd layer under the convex surface in Fig. 1f becomes much more evident in Fig. 2f. Furthermore, through the comparison between the starting models and the refined models, we could infer that the starting models have an extremely strong impact on final prediction results in PCG-FWI, no matter whether the predictions are towards a correct or wrong direction. This impact is even independent of data misfits. In Fig. 3d we show the data prediction produced by PCG-FWI, related to the model in Fig. 1a. Apparently, there is a slight improvement of the data misfit compared with that shown in Fig. 3c, but it is difficult to tell how much practical significance there is as random noise exists in the observed data.