Pre-stack Seismic Inversion with Boundary Inequality Constraints Derived from Prior Elastic Parameters Information

Conventional pre-stack seismic inversion methods based on the Aki-Richards approximation rely on the assumption of weak elastic contrasts, which often leads to inversion distortions at interfaces with high elastic contrasts. This study proposes an innovative pre-stack seismic inversion method that integrates low-frequency bound inequality constraints based on prior elastic parameter information with Lp (0 < p < 1) quasi-norm sparsity constraints. First, low-frequency information constraints and sparsity constraints on reflection coefficients are incorporated into the inversion objective function. Then, by introducing non-negative slack variables and residual variables, the inequality constraints based on prior elastic parameter information are transformed into equality constraints and embedded into an augmented Lagrangian function to effectively reduce the solution space. Finally, the problem is solved comprehensively using the Alternating Direction Method of Multipliers (ADMM) along with a soft-thresholding shrinkage algorithm. Model tests and practical applications demonstrate that the proposed method effectively mitigates the strong dependence of the Aki-Richards linear approximation on the weak elasticity assumption and can accurately characterize gas-bearing reservoir boundaries.