Full Waveform Inversion is an ill-posed problem. As such, it needs mathematical and numerical tools to improve convergence and avoid falling into local minima. This is a crucial issue, especially when using bad starting models for inversion. The question addressed here is whether Full Waveform Inversion should be suitable for seismic imaging. To answer this problem, we simulate a simple seismic experiment that consists in two square velocity anomalies surrounded by a homogeneous medium. The difficulty here results in the homogeneous starting model used for inversion and the acquisition design that is not suitable for inverting this kind of features. Because the physical problem shows mostly reflective behaviour, retrieving model parameters is very challenging. Nevertheless, we will show that the preconditioner presented in this work allows us to recover accurately both position and velocity values of the reservoirs, leading to very precise images of both anomalies after applying Reverse Time Migration.


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