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.


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