1D scalar full waveform inversion inferring convergence properties with analytic and numerical examples

Wenyong Pan, Kristopher A. Innanen

Formulated as a least-squares form, Full waveform inversion (FWI) seeks to minimize the difference between the modeling data and the observed data and estimate the subsurface parameters. It has been widely studied in recent years, but some problems still remain to be addressed. In this research, we performed the analytic analysis of 1D scalar FWI. The analysis to this simplest condition can help us achieve some new ideas and discoveries in FWI. A simple two-interface model and a homogeneous background model are used as the true velocity model and initial velocity model respectively. And two iterations are performed for analysis based on some optimal assumptions. We found that: (1) after the first iteration, the placement error at the second interface is influenced by the velocity contrast and interfaces distance; (2) after the second iteration, the placement error at the second interface become smaller for small velocity contrast, but may become larger for large velocity contrast; (3) and the noises produced in the cross-correlation have a negative influence to the amplitude recovery of the second interface, which will decrease the convergence rate of FWI; (4) but the noises have no significant influence to the placement error of the second interface.