L1-Norm Multi-Constraint Inversion Based on N-ADMM with an adaptive penalty

Pre-stack seismic data typically suffer from poor signal-to-noise quality, possibly leading to unstable inversion results. Traditional multi-channel laterally-constrained inversion will blur the steep inclined strata, while noise undermines the reliability of simple structure constrained inversion. We present a new inversion method, L1-norm multi-constraint inversion, to overcome these limitations using the exact Zoeppritz equations method (EZMI). Built upon an L1-norm sparsity-regularized objective function, this method constrains the inversion of three parameters horizontally and vertically and the dip angle of the formation, effectively restores the sparse characteristics of inversion outcomes, protects the amplitude information of the stratum boundary, produces inversion outputs that converge better from trace to trace, and improves inversion precision. When dealing with nonlinear optimization tasks, we use the Nesterov-type accelerated alternating direction method of multipliers with adaptive penalty (N-ADMM) combined with the Levenberg-Marquardt (LM) algorithm to drive the objective toward its minimum, which accelerates convergence speed and ensures good stability of the equation. At the same time, by employing the exact Zoeppritz equations, we further cut the inversion misfit and boost overall accuracy. Synthetic data are employed to benchmark the EZMI approach against the unconstrained inversion based on the exact Zoeppritz equations (EZUI), thereby validating the proposed method. Finally, using the actual data for experimental analysis, results further indicate that EZMI delivers superior inversion quality and offers clear benefits for AVO inversion.