A progressive data assimilation strategy in full-waveform adjoint tomography

Elastic full-waveform inversion (FWI) is powerful in resolving fine-scale structures in complex models, but suffering from strong nonlinearity and slow convergence rate, especially in the presence of cycle-skipping issues when the initial model is not well constrained. We present a progressive data assimilation (PDA) strategy to mitigate the cycle-skipping issue and boost the convergence rate. Specifically, we split each seismogram into several time windows with a constant length after the first arrival. At each iteration, the PDA strategy automatically screens the windows that are not cycle skipped for inversion according to the criteria of similarity measured between the observed and predicted waveform within a given window. Through the iterations, the model improves and more data will automatically be assimilated into the inversion, forming a positive feedback of model update, and speed up the convergence rate. To provide additional constraints and also stabilise the inversion at the beginning, we include low-frequency surface waves and examine their contribution to the inversion. We validate the effectiveness of the PDA strategy in FWI through numerical experiments using the 1D linear gradient velocity model and the Foothill model. Compared with the conventional FWI strategy, the proposed PDA strategy in an elastic FWI can effectively mitigate the cycle-skipping problem and significantly accelerate the convergence rate. We further apply this method to the field data, and it improves the shallow part of the model with only a fraction of the entire dataset, demonstrating the great potential for practical usage.