Full waveform inversion (FWI) delivers high-resolution quantitative images and is a promising technique to obtain macroscale physical property model of the subsurface. In most geophysical applications, prior information, such as that collected in wells, is available and should be used to increase the image reliability. For this, we propose to introduce three terms in the definition of the FWI misfit function: the data misfit itself, the first-order Tikhonov regularization term acting as a smoothing operator, and a prior model norm term. This last term is the way to smoothly introduce prior information into the FWI workflow. On a selected target of the Marmousi synthetic example, significant improvement was obtained when using the prior model term for noise-free and noisy synthetic data. The prior model term may significantly reduce the inversion sensitivity to incorrect initial conditions. The limited range of spatial wavenumber sampling by the acquisition may be compensated with the prior model information, for multiple-free and multiple-contaminated data. Prior and initial models play different roles in the inversion scheme. The starting model is used for wave propagation and therefore drives the data-misfit gradient, whereas the prior model is never explicitly used for solving the wave equation and only drives the optimization step as an additional constraint to minimize the total objective function. Thus, the prior model is not required to follow kinematic properties as precisely as the initial model, except in zones of poor illumination. In addition, we investigate the influence of a simple dynamic decreasing weighting of the prior model term. Once the cycle-skipping problem has been solved, the impact of the prior model term is gradually reduced within the misfit function to be driven by seismic-data only.

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