Waveform inversion using a logarithmic wavefield

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The seismic reflection inverse problem (2009, background): “…the very natural error minimization or optimization formulation of the inverse problem, promoted extensively by Tarantola and others in the 1980s (Tarantola 1984, 1986, 1987), is not amenable to solution by descent or Newton-type methods (Gauthier et al 1986, Bunks et al 1995, Shin and Min 2006).”
Source-independent time-domain waveform inversion using convolved wavefields: Application to the encoded multisource waveform inversion (2011, methodology): “In addition, we can also obtain the gradient of misfit function with respect to velocities by using the backpropagation algorithm based on the adjoint-state technique (Laily, 1983; Tarantola, 1984; Gauthier et al., 1986; Zhou et al., 1995; Pratt et al., 1998; Shin and Min, 2006; Choi et al., 2008).”
Waveform inversion in the Laplace domain (2008, methodology): “Therefore, the wavefield in the Laplace domain can be so small that the waveform inversion using a logarithmic wavefield (Shin & Min 2006) turns out to be most effective.”
An overview of full-waveform inversion in exploration geophysics (2009, methodology): “…phase and amplitude inversions (cid:1) Bednar et al., 2007; Pyun et al., 2007 (cid:2) from a frequency-domain FWI code using a logarithmic norm (cid:1) Shin and Min, 2006; Shin et al., 2007 (cid:2) , the use of which leads to the Rytov approximation in the framework of local optimization problems.”