Seismic impedance inversion using approximation zero-norm minimization with SQP method

Inversion for seismic impedance is an inherently complicated problem. It is ill-posed and band-limited. Thus the inversion results are non-unique and the inversion process is unstable. To take the sparsity of the seismic reflectivity into consideration, the inversion problem can be transformed into an l₀ norm constraint optimization. The resulting minimization problem is proposed to be efficiently solved by the trust region based Sequential Quadratic Programming (SQP) method in this paper, which possesses global convergence and local quadratic convergence rate under suitable assumptions. Null space technique is considered to reduce the computational complexity and greatly accelerate computation speed. Numerical experiments for both synthetic and field seismic data are given. The results illustrate that the proposed approach can invert the acoustic impedance with high-resolution and good spatial continuity. The proposed algorithm also has the advantages of robustness to noise and fast calculation.