“…Full waveform inversion (FWI) (Lailly, 1983;Tarantola, 1984) has been widely used in exploration and global seismology for high-resolution parameter estimation (Virieux and Operto, 2009;Tromp, 2020). With the success of the application of mono-parameter FWI to field data (Sirgue et al, 2010;Warner et al, 2013;Operto et al, 2015;Shen et al, 2018), it becomes more and more attractive to study multiple parameters (Operto et al, 2013), to account for the effect of attenuation (Kamei and Pratt, 2013;Fabien-Ouellet et al, 2017;da Silva et al, 2019;Kamath et al, 2021), density (Yang et al, 2016a;Operto and Miniussi, 2018), anisotropy (Prieux et al, 2011;Alkhalifah and Plessix, 2014), or elastic parameters (Brossier et al, 2009;Köhn et al, 2012;Vigh et al, 2014;Pan et al, 2018;Trinh et al, 2019;Wang et al, 2021). FWI formulates seismic inversion into a PDE-constrained optimization problem.…”