Basis Pursuit Anisotropic Inversion Based on the L1-L2-Norm Regularization

Prestack seismic inversion for VTI media (transversely isotropic with vertical axis of symmetry) is a technique that can be useful to obtain the properties (velocity, density, and anisotropy parameters) of shale reservoirs. Since conventional inversion with smooth constraints (e.g., L-2-norm) is not appropriate, we propose a basis pursuit inversion (BPI) extended to VTI media, where: 1) we decompose the five elasticities into basis pursuit pairs by a dipole decomposition; 2) instead of the commonly used L-1-norm, the L-1-L-2 is implemented as a regularization constraint to achieve higher resolution and stability; and 3) alternating direction method of multipliers (ADMM) is used to obtain the solutions. Since the problem is highly ill-posed, we perform the inversion using PP and PS multicomponent seismic data. The examples (synthetic and real data) verify the higher resolution and better antinoise performance of the proposed method.