Algorithmic and practical aspects of TV regularization for joint time-lapse FWI
Résumé
Joint time-lapse FWI manages non repeatability artifacts induced by compaction and acquisition changes by jointly inverting the baseline and monitor data for the simultaneous update of the baseline and monitor models. In this framework, model-difference regularization links together the baseline and monitor subproblems. The edge-preserving total-variation (TV) regularization should be suitable to reconstruct localized model changes in the monitor model. TV regularization minimizes the 1-norm of the gradient of the subsurface model and hence is non differentiable. The alternating-direction method of multipliers (ADMM) and proximal methods provide a suitable framework to implement TV regularization in the 1-norm regularized 2-norm time-lapse FWI. The principle of ADMM is to separate the 2-norm and the 1-norm subproblems in the objective with alternating directions and recast the 1norm subproblem as a denoising problem. Within one ADMM iteration, the denoising reduces to an element-wise soft thresholding while model parameters are updated with one or several inner iterations of 2-norm regularized FWI. ADMM however requires the careful tuning of the penalty and thresholding parameters, and raises the issue of the convergence rate. This study reviews the algorithm of ADMMbased TV-regularized joint time-lapse FWI and illustrates the tuning of the hyper parameters with two synthetic examples.