Multichannel impedance inversion for nonstationary seismic data based on the modified alternating direction method of multipliers

Abstract

We have upgraded the conventional nonconvex optimization algorithm and addressed a new technique to estimate the acoustic impedance (AI) for attenuated seismic data based on the modified alternating direction method of multipliers (ADMM). To eliminate the discontinuity in the inverted AI profiles with the existing single-trace processing strategy, we construct a multichannel framework and a dimensional reduction operation is used with a brief matrix manipulation in the designed forward-simulation model. The [Formula: see text] norm constraint in the inversion function can assist to search a global optimal AI solution. In the promoted ADMM solving procedure, we invoke the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm and the generalized iterated-shrinkage algorithm to solve the relative suboptimization problems. Our new technique could recover an absolute AI from the nonstationary seismic data directly, even though this inversion problem is seriously ill-posed and nonlinear. The inverted AI profile will be satisfied with the assumption that the calculated reflectivity is comparatively sparse corresponding to its minimum [Formula: see text]-norm. Appending this adequate constraint term to the objective function is crucially significant in reducing the number of estimated AI. Due to the consideration of seismic attenuation in the equation, the inversion approach is deployed into the nonstationary reflection data avoiding the drawbacks brought by the energy-compensation processing (e.g., inverse [Formula: see text]-filtering). Using synthetic and field data, we determine the performance of our method.