Regularized elastic full-waveform inversion using deep learning

Obtaining high-resolution models of the earth, especially around the reservoir, is crucial to properly image and interpret the subsurface. We have developed a regularized elastic full-waveform inversion (FWI) method that uses facies as the prior information. Deep neural networks (DNNs) are trained to estimate the distribution of facies in the subsurface. Here, we use facies extracted from wells as the prior information. Seismic data, well logs, and interpreted facies have different resolution and illumination to the subsurface. Besides, a physical process, such as anelasticity in the subsurface, is often too complicated to be fully considered. Therefore, there are often no explicit formulas to connect the data coming from different geophysical surveys. A deep-learning method can find the statistically correct connection without the need to know the complex physics. In our deep-learning scheme, we specifically use it to assist the inverse problem instead of the widely used labeling task. First, we conduct an adaptive data-selection elastic FWI using the observed seismic data and obtain estimates of the subsurface, which do not need to be perfect. Then, we use the extracted facies information from the wells and force the estimated model to fit the facies by training DNNs. In this way, a list of facies is mapped to a 2D or 3D inverted model guided mainly by the structure features of the model. The multidimensional distribution of facies is used either as a regularization term or as an initial model for the next waveform inversion. Our method has two main features: (1) It applies to any kind of distribution of data samples and (2) it interpolates facies between wells guided by the structure of the estimated models. Results with synthetic and field data illustrate the benefits and limitations of this method.