Wavefield reconstruction inversion with a multiplicative cost function. (13th December 2017)

• Record Type: Journal Article
• Authors: da Silva, Nuno V; Yao, Gang
• Is Part Of: Inverse problems. Volume 34:Number 1(2018:Jan.)
• Publication Date: 2017-12-13
• Subjects: wavefield reconstruction inversion -- multiplicative cost function -- seismic inversion -- acoustic inversion -- full waveform inversion; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa9830
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We present a method for the automatic estimation of the trade-off parameter in the context of wavefield reconstruction inversion (WRI). WRI formulates the inverse problem as an optimisation problem, minimising the data misfit while penalising with a wave equation constraining term. The trade-off between the two terms is balanced by a scaling factor that balances the contributions of the data-misfit term and the constraining term to the value of the objective function. If this parameter is too large then it implies penalizing for the wave equation imposing a hard constraint in the inversion. If it is too small, then this leads to a poorly constrained solution as it is essentially penalizing for the data misfit and not taking into account the physics that explains the data. This paper introduces a new approach for the formulation of WRI recasting its formulation into a multiplicative cost function. We demonstrate that the proposed method outperforms the additive cost function when the trade-off parameter is appropriately scaled in the latter, when adapting it throughout the iterations, and when the data is contaminated with Gaussian random noise. Thus this work contributes with a framework for a more automated application of WRI.