Regularized elastic full waveform inversion using deep learning

We present a regularized elastic full waveform inversion method that uses facies as prior information. Deep neural networks are trained to estimate the distribution of facies in the subsurface. Here we use facies extracted from wells as the prior information. There are often no explicit formulas to connect the data coming from different geophysical surveys. Deep learning can find the statistically-correct connection without the need to know the complex physics. We first conduct an adaptive data-selection elastic full waveform inversion using the observed seismic data and obtain estimates of the gradient. Then we use extracted facies information from the wells and force the estimated model to fit the facies by training deep neural networks. In this way, the 1D facies distribution is mapped to a 2D or 3D inverted model guided mainly by the structural features of the model. The multidimensional distribution of facies is used as a regularization term for the next waveform inversion and it can be updated iteratively. The proposed method has two main features: 1) it applies to any kind of distributions of data samples and 2) it interpolates facies between wells guided by the structure of the estimated models.