Seismic Acoustic Impedance Inversion Using Mixed Second-Order Fractional ATpV Regularization

Abstract

Seismic acoustic impedance (AI) inversion is widely used in geophysics as AI can indicate rock characteristics and facilitate stratigraphic analysis. However, traditional AI inversion suffers from a multi-solution problem. To overcome this barrier, anisotropic total p-variation (ATpV) regularization has been applied in inversion as it can improve the accuracy by Lp quasi-norm. Nevertheless, this regularization results in the staircase effect and the scattering effect. To reduce these two effects, we introduced the mixed second-order variations and the fractional difference in AI inversion based on ATpV and proposed a novel AI inversion method using mixed second-order fractional anisotropic total p-variation (MS_FATpV) regularization. Moreover, the alternating direction method of multipliers (ADMM) algorithm is used to build the inversion framework. Numerical experiments demonstrate that the fractional difference and the mixed second-order variant can reduce the staircase and scattering effects. The proposed method reduces the multiplicity and improves the accuracy than some state-of-the-art methods based on anisotropic total variation (ATV).