A numerical study of simultaneous-source full waveform inversion with l1-norm

Abstract

Simultaneous-source techniques have been proposed to reduce the acquisition cost and alleviate the computational overburden of data processing, and they have been applied to full waveform inversion (FWI) in recent years. These techniques are mainly based on the l2-norm objective function (least-squares criterion). However, if we consider that real field data contain noise such as outliers, it would be preferable to use the robust objective function in simultaneous-source FWI. In this study, we propose combining the simultaneous-source FWI with the l1-norm objective function (least-absolute criterion), which is known to be robust to data containing noise, specifically outliers. For the l1-norm-based simultaneous-source (SS-1) FWI, we first verify the crosstalk reduction and the robustness to data containing outliers. The expectations of the gradient direction directly give an evidence for the crosstalk reduction, and a signal-to-noise ratio analysis supports the convergence of our algorithm. The analysis shows that the crosstalk noise of the SS-1 FWI can be suppressed by random phase encoding. In addition, the spectrum of the weighted residuals indicates that the main property of the l1-norm objective function is preserved in the SS-1 FWI. Numerical examples show that the SS-1 FWI produces reliable results as the l2-norm simultaneous-source FWI does, similar to the case of the individual-source FWI. These results support the idea that combining the simultaneous-source FWI with the l1-norm objective function improves the computational efficiency and preserves the intrinsic characteristics of the l1-norm objective function.