GNGTS 2017 - 36° Convegno Nazionale

GNGTS 2017 S essione 3.1 545 to compute the misfit function. As the starting model, we use a model obtained in a previous work (Tognarelli et al. , 2015; Mazzotti et al., 2017) by a global optimization method based on genetic algorithms. To validate the final model, we pre-stack depth migrate the data using the final estimated velocity field, and we check the improvements of the flattening of the events in the common-image-gathers (CIGs). The seismic data. The data used pertains to an inline extracted from a 3D marine survey. From the entire data set, we select 56 shot gathers evenly distributed along the line with a source-receiver offset varying from 180 m to 2000 m; in this way, a total of 3910 traces are considered. The receiver interval is 25 m, the time sampling is 4 ms and the record length is 1.6 s. The sea bed is flat with a depth of about 300 m. The sources and the receivers are located 12.5 m under the sea surface. A specific time window is defined to focus the inversion on the diving waves and on the shallow reflections of the data. The window length varies from a minimum of 0.1 s to a maximum of 0.5 s. Fig. 1a displays an example of a raw shot gather, whereas Fig. 1b shows its amplitude spectrum. In Fig. 1a the red contour represents the time window used to select the data for the inversion. Fig. 1 - a) A shot gather of the inline data and b) its amplitude spectrum. The red polygon delimits the portion of the seismogram considered in the inversion. Modelling. The synthetic data are obtained by means of an explicit, 2nd order in time, finite difference algorithm which is used to solve the 2D acoustic wave equation. The model dimensions are approximately 7 km in length and 1.2 km in depth. The modelling grid is made by 242x40 nodes, with a uniform grid size of dx=30 m. The sea bed is situated at the 10 th row of the grid. The order of approximation of the spatial derivatives is optimized to reduce the numerical dispersion. We put absorbing boundary conditions on the lateral and bottom sides of the model and reflecting boundary conditions at the top side to simulate the sea-air interface. More details of the numerical scheme can be found in (Galuzzi et al�. , 2015). The source wavelet is estimated from the sea-bed reflection. Misfit function. The data misfit is the L 1 norm between the predicted and the observed data. However, for both data a processing sequence that includes low pass filtering up to 10 Hz, trace-envelope computation and trace-by-trace normalization is applied. The filtering and the envelope operations are used to reduce the cycle skipping effect and, in general, the non- linearity of the misfit function. This gives a more robust inversion procedure than using the signal waveform, which can also be applied to data where the S/N ratio at low frequencies is low. Initial model. The initial model plays an important role in a high non-linear inverse problem such as FWI. To assure the convergence of a local optimization method, the starting point must