Full waveform inversion reconstructs subsurface structures by matching the synthetic waveform to the observed waveform. Inaccuracy of the source wavelets can, thus, easily lead to an inaccurate model. Simultaneously updating source wavelets and model parameters is a conventionally used strategy. However, when the initial model is very far from the true model, cycle skipping exists, and estimating a reliable source wavelet is very difficult. We propose a combinatory inversion workflow based on seismic events. We apply a Gaussian time window around the first break and gradually increase its width to include more seismic events. The influence of inaccurate source wavelets is alleviated by applying a Gaussian time window around the first break to evaluate the normalized cross-correlation-based objective function. There are inevitable small model artifacts caused by inter-event interactions when calculating cross-correlations. As a result, we switch to the optimal transport function to clean the model and update the source wavelets simultaneously. The combinatory strategy has been applied to models with different types of geological structures. Starting from a crude initial model, we recovered a high-resolution and high-fidelity model and the source wavelets in two synthetic experiments. Finally, we apply our inversion strategy to a real-land seismic dataset in Southeast China and obtain a higher-resolution velocity model. By comparing an inversion velocity profile with well log information and the recorded data with the simulated data, we conclude that our inversion results for the field data are accurate and this new strategy is effective.

Numerically solving seismic wave equations is vital to large-scale forward modeling and full waveform inversion. In this paper, a new modified symplectic discontinuous Galerkin (MSDG) method is proposed to solve the acoustic and elastic equations. The MSDG method employs a symmetric interior penalty Galerkin formulation as the space discretization. The time discretization is based on a modified symplectic partitioned Runge–Kutta scheme with minimized phase error. Thus, the MSDG method has the advantages of high accuracy, being flexible to deal with complex geometric boundaries and internal structures, and stable for long time simulations. The numerical stability conditions, dispersion and dissipation are investigated in detail for the MSDG method. To validate the method, we carry out several numerical examples for solving the acoustic and elastic wave equations in various media. The numerical results show that the MSDG method can effectively suppress the numerical dispersion and is suitable for wavefield simulations.