Seismogram Registration via Markov Chain Monte Carlo Optimization and Its Applications in Full Waveform Inversion
Cycle skipping is a serious issue in full waveform inversion (FWI) since it leads to local minima. To date, most FWI algorithms depend on local gradient based optimization approaches, which cannot guarantee convergence towards the global minimum if the misfit function involves local minima and the starting model is far from the true solution. In this study, I propose a misfit function based on non-stationary time warping functions, which can be calculated by solving a seismogram registration problem. Considering the inherent cycle skipping and local minima issues of the registration problem, I use a Markov chain Monte Carlo (MCMC) method to solve it. With this global optimization approach, I am able to directly sample the global minimum and measure non-stationary traveltime differences between observed and predicted seismograms. The a priori constraint about the sparsity of the local warping functions is incorporated to eliminate unreasonable solutions. No window selections are required in this procedure. In comparison to other approaches for measuring traveltime differences, the proposed method enables us to align signals with different numbers of events. This property is a direct consequence of the usage of MCMC optimization and sparsity constraints. Several numerical examples demonstrate that the proposed misfit function allows us to tackle the cycle skipping problem and construct accurate long-wavelength velocity models even without low frequency data and good starting models.