Elastic TTI full waveform inversion based on theory guided neural network

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

In this study, we use the recurrent neural network (RNN) to achieve TTI elastic full waveform inversion. The motivation for building such a network is that in real media full waveform inversion, the physics of wave propagation is very complex, and implementing insufficient accurate wave equations in such complex media would lead modeling errors. Most fractures are not vertically but with certain dips and azimuths, thus estimating the title angles along with the elastic parameters are important for accurately invert the parameters. The recurrent neural network (RNN) is a typical type of neural network that is consisted of several RNN cells. In this study, each RNN cell is designed according to the staggered grid stress velocity TTI wave equation and the Voigt stiffness parameters and the title angles are considered as the parameters in this inversion. Based on the forward computational graph, the gradients with respect to each parameter are given by the backpropagation of the forward computational graph. In order to mitigate the cross talk, we use high order total variation (TV) regularization to mitigate the cross-talk in the inversion, Numerical inversions using simple models and complex models prove the validation of this method.