Full Waveform Inversion (FWI) is a powerful tool to quantify the Earth's subsurface structure. However, most of the FWI applications have been limited to acoustic media. In geological settings, such as gas clouds, gas sand, melt lens, where the attenuation becomes important, one must use a viscoelastic FWI. Here we present the theory and application of a viscoelastic FWI in the time domain. First, we carried out sensitivity analyses for back-scattered, reflected and transmitted waves. We find that the presence of attenuation has a significant effect on post-critical reflections, but it has little or no effect on near-offset reflection data, suggesting that the inversion of port-critical reflections can help to reduce the cross talks between attenuation and velocity contrast or propagation effects. We have first tested the method on synthetic data and then applied to 15 km long offset data acquired by CGG Offshore central Sumatra, Indonesia. Apart from the recovery of attenuation parameters, the viscoelastic inversion provides sharper P-wave velocity image as compared to the elastic FWI.


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