Full Waveform Inversion in Migration Based Travel-time Formulation

The common knowledge now is that standard least squares Full Waveform Inversion is unable to reconstruct macrovelocity for reasonable frequency band of input data but claims unpractically low time frequencies. There are a range of different approaches to overcome this weakness and among them Migration Based Travel Time reformulation of the cost function. Here we compare SVD for linear approximation of standard least squares Full Waveform Inversion with its Migration Based Travel Time reformulation. In order to do that we start with linearization of both nonlinear forward maps with subsequent computations of singular spectra (singular values and right/left singular vectors) for corresponding linear operators. The next step is to construct the two families of linear spans of right singular vectors corresponding to a set of fixed values of the condition number and to analyze their mutual disposition. Our computations demonstrate the reliable reconstruction of the smooth velocity component by full waveform inversion in migration based travel-time formulation.