Post‐stack impedance blocky inversion based on analytic solution of viscous acoustic wave equation

ABSTRACT The conventional impedance inversion method ignores the attenuation effect, transmission loss and inter‐layer multiple waves; the smooth‐like regularization approach makes the corresponding impedance solution excessively smooth. Both fundamentally limit the resolution of impedance result and lead to the inadequate ability of boundary characterization. Therefore, a post‐stack impedance blocky inversion method based on the analytic solution of viscous acoustic equation is proposed. Based on the derived recursive formula of reflections, the 1D viscous acoustic wave equation is solved analytically to obtain zero‐offset full‐wave field response. Applying chain rule, the analytical expression of the Fréchet derivative is derived for gradient‐descent non‐linear inversion. Combined with smooth constraints, the blocky constraints can be introduced into the Bayesian inference framework to obtain stable and well‐defined inversion results. According to the above theory, we firstly use model data to analyse the influence of incompleteness of forward method on seismic response, and further verify the effectiveness of the proposed method. Then the Q‐value sensitivity analysis of seismic trace is carried out to reduce the difficulty of Q‐value estimation. Finally, the real data from Lower Congo Basin in West Africa indicate that the proposed approach provide the high‐resolution and well‐defined impedance result. As a supplement and development of linear impedance inversion method, the non‐linear viscous inversion could recover more realistic and reliable impedance profiles.