The estimation of the wavelet that is used for the forward modelling of synthetic shots is one of the main challenges that we must face when applying FWI on real data. We show in this report the negative effects of an incorrect wavelet and propose a methodology to mitigate this problem. We apply phase-shift plus interpolation (PSPI) migration with well calibration instead of reverse time migration (RTM) and line search to produce the velocity perturbation. The use of PSPI reduces the computational time, and we take advantage of this fact to implement our methodology. The process starts with an estimated wavelet that has similar frequency content than the seismic data. This wavelet does not have the optimal amplitude and phase for reproducing the observed shots. In order to address this problem, we migrate and stack the observed and modelled shots separately. Then we convert both datasets from depth to time by using the current velocity model. The comparison of these reflectivity datasets in time domain provides the elements for the estimation of an amplitude and phase that make the modelled data more similar to the observed data. Next, we take the difference between the observed and the amplitude-and-phase corrected modelled data to create the gradient. After that, we calibrate the gradient with well information to produce the velocity perturbation. The amplitude-and-phase correction estimated in this way is applied to update the wavelet that will be used in the next iteration. We applied this methodology on synthetic and Hussar datasets obtaining encouraging results.
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