Full Waveform Inversion by Adaptive Tikhonov-Total Variation Regularization

Summary To stabilize an ill-posed inverse problem such as full waveform inversion (FWI), prior information must be added to the objective function in the frame of regularization techniques. Established regularization methods such as Tikhonov and total variation (TV) regularization assume certain statistical assumptions about the structural properties of the desired model to be recovered. Tikhonov regularization promotes smoothness of the model and TV regularization is suitable for models with piecewise constant (blocky) structures. Thus, neither of these regularization techniques is able to recover models that contain both smooth and blocky features. In such a case, the objective function can be reformulated as a combination of Tikhonov and TV (TT) regularizations. However, the balancing parameter that gives a weight to combine these terms need to be chosen carefully. In this study, we propose a TT regularization method for the FWI problem that automatically determines the balancing parameter (at each FWI iteration) using robust statistics. Through numerical example for the 2004 BP model, we demonstrate the success of the proposed method in deriving high-quality images.