Progressive matching optimisation method for FWI

To eliminate the dependency on a good initial model of the traditional full waveform inversion (FWI) method, we propose an optimisation method combining a derivative free optimisation method of modified particle swarm with gradient descent search. We worked with the acoustic wave approximation, in two dimensions, with the synthetic Marmousi velocity model as the test case. We were able to obtain a high-precision inversion of this model, comparable to traditional FWI methods, with the distinct advantage of not using an initial model close to the global optimal, as would usually be required. For this result, we used a progressive inversion scheme by consecutive layers, and a modified particle swarm optimisation algorithm where we introduced the gradient of the misfit function as a local search guide, and other regularization terms.