The retrieval of physical properties of the Earth’s interior using seismic data has always been challenging for both academy and industry. As such it has been subject to intensive research for the last decades. In parallel, because of the increase of computational power, complex forward modelling have become more affordable. One of the methods that potentially allows to extract more information from seismic data is Full Waveform Inversion (FWI). Theoretically, it can provide models of physical parameters with a higher spatial resolution than other methods such as travel-time tomography.

FWI is commonly formulated as an iterative process that seeks to improve the model by minimizing the differences between the synthetic traces obtained using a reference model (which can be poor in high-frequency content) with the real seismic trace recorded experimentally, hereafter referred to as “data”, by means of a cost functional. Nevertheless, and given the number of parameters to be inverted, statistical methods such as Monte-Carlo are still not applicable for large 3D problems. In this sense the center piece of FWI is the so-called adjoint method, which allows us to obtain the gradient of the misfit function for the current model by cross-correlating both incident and back-propagated wavefield (Tarantola,1984).