Joint Data- and Physics-driven Pre-stack AVA Elastic Parameters Inversion

Elastic parameters such as P- and S-wave velocity and density are of great significance for subsurface quantitative interpretation and reservoir prediction. Current pre-stack amplitude-versus-angle (AVA) inversion methods have been widely used in industry to obtain subsurface elastic parameters. Conventional AVA inversion methods are theoretically based on a linearized physical model formulating the relationship between pre-stack seismic reflection coefficients and subsurface model elastic parameters, called physical model-driven inversion. However, the linearized physical models lead to low accuracy and high uncertainty of inversion results. In recent years, several neural network-based pre-stack AVA inversion methods, called data-driven inversion, have been developed to address this issue. But these methods typically require a large amount of labeled data for training network, and the process does not have a clear physical mechanism. So the data-driven inversion results lack physical interpretability. To address these issues, a joint data- and physics-driven inversion of pre-stack AVA elastic parameters is proposed. Under the framework of semi-supervised learning, a two-dimensional convolutional neural network and a recurrent neural network are used to establish the mapping between several adjacent pre-stack AVA gathers and one-dimensional elastic parameters in time domain. The full Zoeppritz equation is used as a physical model constraint to the neural network, and loss functions are constructed using both well-logging data and pre-stack AVA seismic data. This approach can perform training network using small labeled data and increase physical interpretability of the inversion process. The inverse distance weighted correlation coefficient of seismic data is proposed to weight the loss function of seismic data and well-logging data. Synthetic and field data examples show that the joint data- and physics-driven pre-stack AVA elastic parameters inversion improves the accuracy and resolution, and provides an estimation of uncertainty of the inversion results.