Resolving the Ambiguity in Attenuation Imaging

Seismic data enable imaging of the Earth, not only of velocity and density but also of attenuation contrasts. Unfortunately, the Born approximation of the constant-density visco-acoustic wave equation, which can serve as a forward modelling operator related to seismic migration, exhibits an ambiguity when attenuation is included. Different scattering models involving velocity and attenuation perturbations may provide nearly identical data. This result was obtained earlier for scatterers that did not contain a correction term for causality. Such a term will lead to dispersion when considering a range of frequencies. We demonstrate that with this term, iterative migration or linearised inversion will almost but not fully remove the ambiguity. Because the initial update in a gradient-based optimization scheme that minimizes the difference between modelled and observed data is still affected by the ambiguity, the reconstructed model starts to approximate the true model only after a very large number of iterations.