Nesterov's Method and L-BFGS Minimisation Applied to Acoustic Migration

Seismic full waveform inversion based on the acoustic wave equation attempts to find the acoustic parameters of the subsurface from seismic data. Because the least-squares error between observed and modelled data has local minima, a good initial velocity model is<br>required. We therefore prefer the name nonlinear migration. We compared three gradient-based minimisation methods on a two-dimensional acoustic test problem: the limited-memory BFGS method with or without bounds on the model parameters, and Nesterov's method.<br><br>We found that the L-BFGS method without bound constraints performs best on the test problem, followed by Nesterov's method. However, the cost of decreasing the error by a given factor increases dramatically when the error becomes smaller.