Three-dimensional frequency-domain full waveform inversion with phase encoding

Three-dimensional quantitative seismic imaging methods such as full waveform inversion, still suffer from their prohibitive computational cost. The computational burden mainly results from the computational cost of the forward problem, namely, the seismic full wavefield modeling, that must be performed for a huge number of sources at each iteration of the inversion. Building super-shots by source assembling allows to mitigate the number of simulations per iteration but adds artifacts in the imaging because of interferences between individual shots of the super-shot. These artifacts can be mitigated by using phase encoding technique which consists of applying a deterministic or random phase shift to each individual source at each iteration of the inversion. We have implemented source assembling with phase encoding in acoustic frequency-domain full-waveform inversion and have assessed the performances of the method with a 2D and 3D synthetic case study corresponding to the SEG/EAGE overthrust model.