Physics Tomorrow Letters

Seismic full-waveform inversion (FWI) uses full seismic recordings to characterize properties of the Earth’s interior, and can provide high resolution images of the subsurface (Tarantola 1984; Gauthier et al. 1986; Tarantola 1988; Pratt 1999; Tromp et al. 2005; Fichtner et al. 2006; Plessix 2006). The method has been applied at industrial scale (Virieux & Operto 2009; Prieux et al. 2013; Warner et al. 2013), regional scale (Chen et al. 2007; Fichtner et al. 2009; Tape et al. 2009; Chen 2 et al. 2015), and global scale (French & Romanowicz 2014; Bozdag et al. 2016; Fichtner et al. ˘ 2018a; Lei et al. 2020). Due to the nonlinearity of relationships between model parameters and seismic waveforms, insufficient data coverage and noise in the data, FWI always has nonunique solutions and infinitely many sets of model parameters fit the data to within their uncertainty. It is therefore important to quantify uncertainties in the solution in order to better assess the reliability of inverted models (Tarantola 2005). FWI problems are traditionally solved using optimization methods in which one seeks an optimal set of parameter values by minimizing the difference or misfit between observed data and model-predicted data. The strong nonlinearity and nonuniqueness of the problem implies that a good starting model is required to avoid convergence to incorrect solutions (generally alternative modes or stationary points of the misfit function). Such models are not always available in practice. To alleviate this requirement a range of misfit functions that may reduce multimodality have been proposed (Luo & Schuster 1991; Gee & Jordan 1992; Fichtner et al. 2008; Brossier et al. 2010; Van Leeuwen & Mulder 2010; Bozdag et al. 2011; Métivier et al. 2016; Warner & Guasch 2016; ˘ Yuan et al. 2020; Sambridge et al. 2022). Nevertheless, none of the standard methods of solution using any of these misfit functions have been shown to allow accurate estimates of uncertainty to be made in realistic FWI problems.