Time-Domain Wavefield Reconstruction Inversion Based on Unbalanced Optimal Transport

Abstract

Wavefield Reconstruction Inversion (WRI) is a novel seismic inversion method with a more expansive search space and reduced non-linearity and is more robust than other conventional techniques (e.g., full waveform inversion, FWI) in terms of local minima. Most of the modifications and applications of WRI are generally employed in the frequency domain, while the current time-domain solutions for WRI are either based on rough approximations, which lead to inaccurate inversion results, or are computationally expensive due to the data-domain Hessian. Here, we will provide another perspective to address time-domain WRI and maintain its effectiveness, namely reducing non-linearity and the effects of “cycle-skipping” while ignoring the data-domain Hessian. On the basis of iteratively solving the inversion problem, the time-domain augmented wave equation is solved by approximating the reconstructed wavefield on the right as the current wavefield. Due to this approximation and the traditional <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> measurement, the reconstructed wavefield based on the poor model will be inaccurate away from the receivers, which will affect the subsequent model inversion. To alleviate this problem, we incorporate the unbalanced optimal transmission (UOT) distance measurement into the inversion. This distance measurement method can accurately obtain the best misfit between two unbalanced signals. Moreover, the accurately measured misfit with low-frequency and long-wavelength acts as an extended source of the subsequent wavefield reconstruction, ensuring the reconstructed wavefield’s accuracy based on the defective initial model without excessive additional computation. The numerical results demonstrate the accuracy and applicability of the proposed method.