Complex-Valued Imaging with Total Variation Regularization: An Application to Full-Waveform Inversion in Visco-acoustic Media

Full waveform inversion (FWI) is a nonlinear PDE constrained optimization problem, which seeks to estimate constitutive parameters of medium such as phase velocity, density, and anisotropy, by fitting waveforms. Attenuation an additional parameter that needs be taken into account in viscous media exploit the full potential FWI. more easily implemented frequency domain using complex-valued velocities time-harmonic wave equation. These complex are frequency-dependent guarantee causality for dispersion. Since estimating velocity at each grid point space not realistic, generally performed real processing (or slowness) reference attenuation quality factor) separate parameters. This parametrization requires priori empirical relation (such Kolsky-Futterman (KF) or standard linear solid (SLS) models) between two quantities, prone generate modeling errors if it does represent accurately behavior subsurface. Moreover, leads multivariate inverse twice larger than actual size ill-posed due cross-talk classes To alleviate these issues, we present mono-variate algorithm solves directly problem sequence narrow bands frequencies under assumption band-wise dependence sought velocities.