The conventional L2 misfit function for Full Waveform Inversion (FWI) is known to suffer from the cycle-skipping problem that makes it strongly dependent on the initial solution. Moreover, its application is often limited to the use of the refracted energy only. In the last years several alternative misfit functions have been proposed with the aim of making FWI more robust. In this work, we propose to exploit the Normalized Integration Method (NIM), which consists in applying an integral transform to the data before computing the residuals, in order to compare monotonic signals instead of oscillating signals. The NIM cost function has been shown to provide full convexity with respect to signal shifts. However, its effectiveness has been only shown on transmission experiments. Here we show a method that allows exploiting such cost function also for reflected events, without the need of a starting model containing sharp contrasts. We show the effectiveness of the proposed methodology on synthetic data and on an offshore field dataset.


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