ℓ1–2-norm regularized basis pursuit seismic inversion based on exact Zoeppritz equation

Abstract

Sparsity constraints have been widely adopted in the regularization of ill-posed problems to obtain subsurface properties with sparseness feature. However, the target parameters are generally not sparsely distributed, and sparsity constraints lead to results that are missing information. Besides, smooth constraints (e.g., ℓ2 norm) lead to insufficient resolution of the inversion results. To overcome this issue, an effective solution is to convert the target parameters to a sparse representation, which can then be solved with sparsity constraints. For the estimation of elastic parameters, a high-resolution and reliable seismic basis pursuit inversion is proposed based on the exact Zoeppritz equation. Furthermore, the ℓ1–2 norm is proposed as a constraint, where a regularized function is minimized with the alternating direction method of multipliers (ADMM) algorithm. Numerical examples and real data applications demonstrate that the proposed method can not only improve the accuracy of the inversion results, especially the S-wave velocity and density information, but also increase the resolution of the inversion results. Furthermore, the ℓ1–2-norm constraint has better noise suppression demonstrating great potential in practical applications.