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The anisotropic total variation with overlapping group sparsity (ATV_OGS) regularisation term is an improvement on the anisotropic total variation (ATV) regularisation term. It has been employed successfully in seismic impedance inversion as it can enhance the boundary information and relieve the staircase effect by exploring the structured sparsity of seismic impedance. However, because ATV_OGS constrains only the structured sparsity of the impedance's first-order difference and ignores the structured sparsity of the second-order difference, the staircase effect still occurs in an inversion result based on ATV_OGS. To further fit the structured sparsity of the impedance's second-order gradients, we introduce the overlapping group sparsity into the second-order difference of the impedance and propose a novel second-order ATV with overlapping group sparsity (SATV_OGS) seismic impedance inversion method. The proposed method reduces the interference of the large amplitude noise and further mitigates the staircase effect of the ATV_OGS. Furthermore, the accelerated alternating direction method of multipliers (A-ADMM) framework applied to this novel method. It can increase the efficiency of inversion. The experiments are carried out on a general model data and field data. Based on the experimental results, the proposed method can obtain higher resolution impedance than some impedance inversion methods based on total variation.

Seismic impedance inversion using second-order overlapping group sparsity with A-ADMM