Elastic full-waveform inversion using tools of neural networks

Abstract In this paper, we investigate the full-waveform inversion (FWI) for elastic wave equation as training a neural network. The forward modeling of the elastic wave equation in the time domain by the staggered-grid difference schemes can be reformulated as a process of a recurrent neural network (RNN). As a result, the FWI problem is equivalent to neural network training, and the parameter of RNN coincides with the model parameter of inversion. Furthermore, a variety of stochastic optimizers including Adgrad, RMSprop, Adam, Nadam and Admax in neural networks can be applied in the training process. The gradient of the objective function with the model parameters is computed by the technique of automatic differentiation instead of the adjoint-state method in the traditional FWI. A new objective function of FWI is also proposed. Compared to the traditional FWI methods, the developed FWI using tools of neural networks has a relatively good robustness. Numerical computations and comparisons with Marmousi model for two and three parameters simultaneous inversion are completed. The results show that the algorithms except Adgrad can yield good inversion results. The FWI framework developed in this paper has potential applications for other complex partial equations.