Theory based machine learning viscoelastic full waveform inversion based on recurrent neural network

Tianze Zhang, Kristopher A. Innanen, Jian Sun, Daniel O. Trad

In this study, we use a recurrent neural network (RNN) to achieve viscoelastic full waveform inversion. The RNN is a typical type of neural network that consists of several RNN cells. In this study, each RNN cell is designed according to the stress velocity viscoelastic wave equation. With the Automatic Differential engine built in the machine learning library, the exact gradient for the trainable parameters, the velocity models and attenuation models, would be given based on the computational graph. Both the simple and complex model numerical inversion tests prove that the inversion based on this theory-guided recurrent neural network can give accurate inversion results. The performance of this RNN based inversion with different objective functions are also tested. Three objective functions are tested here, which are the l1 norm, l2 norm and Huber objective functions. All the three objective functions can provide the right inversion results, however, the l1 norm and Huber objective function have better accuracy to reconstruct the high wavenumber components of the modes. The l2 norm inversion has the best data residual convergence rate, but l1 norm and Huber objective function have better accuracy to reconstruct the models. Compared with Qp and Qs , the inversion for Vp and Vs are more stable with all the three objective functions.