Comparison of stochastic optimization methods on two analytic objective functions and on a 1D elastic FWI

We compare the performance of three different stochastic optimization methods on two analytic objective functions varying the number of parameters, and on a 1D elastic full waveform inversion (FWI) problem. The three methods that we consider are the Adaptive Simulated Annealing (ASA), the Genetic Algorithm (GA), and the Neighbourhood Algorithm (NA) which are frequently used in seismic inversion. The application of these algorithms on the two analytic functions is aimed at evaluating the rate of convergence for different model space dimensions. The first function consists in a convex surface, and the second one is a multi-minima objective function which also permits to verify the ability of each method to escape from entrapment in local minima. Our study shows that among the three optimization methods GA displays the better scaling with the number of parameters. The ASA method is often the most efficient in case of low dimensional model spaces, whereas NA seems to perform less efficiently than the other two and to be more prone to get trapped in local minima. Tests of 1D elastic FWI on synthetic data, inverting for density, P and S-wave velocity for a total of 21 unknowns confirm the conclusions drawn from the previous examples.