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

Wang Yu, Peng Suping, Lu Yongxu, Cui Xiaoqin, Li Dong, Xu Zihe, Hu Yaoquan, Yao Di

Acta Geophysica

2026

vol. 74, no. 3

art. no. 178, s. 1--30

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 equation, 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 equation (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.

Conditional stability estimate for an ill-posed elliptic equation by using nonlocal conditions

Benrabah Abderafik

Journal of Applied Mathematics and Computational Mechanics

2022

Vol. 21, nr 3

5--17

We consider an ill-posed linear homogeneous fourth-order elliptic equation. We show that the problem is ill-posed in the sense of Hadamard, i.e., the solution does not depend continuously on the given data. We propose a regularization method via nonlocal conditions and under some a priori bound assumptions different estimates for the regularized solution are obtained. Numerical examples for a rectangle domain show the effectiveness of the new method in providing highly accurate numerical solutions as the noise level tends to zero.

On a Regularization Method for Variational Inequalities with P0 Mappings

Konnov I., Mazurkevich E., Ali M.

International Journal of Applied Mathematics and Computer Science

2005

Vol. 15, no. 1

35-44

We consider partial Browder-Tikhonov regularization techniques for variational inequality problems with P0 cost mappings and box-constrained feasible sets. We present classes of economic equilibrium problems which satisfy such assumptions and propose a regularization method for these problems.