Elastic reverse time migration using an efficient and accurate adaptive variable grid discretization method

The conventional reverse time migration utilizes regularly sampled computational grids to simulate wave propagation. Selecting the appropriate grid sampling is important for computational accuracy and efficiency. In general, the uniform-size grid cannot represent the complexity of the geology well. The grid may appear sparse in the low-velocity zone, especially in shallow depths where dispersion may occur. Conversely, it may appear excessively dense in the high-velocity zone, such as at greater depths or within a salt body, which results in higher computational memory and time consumption. To overcome these issues, we developed an efficient and accurate adaptive variable grid discretization method that automatically selects the vertical grid size based on the velocity, depth, and dominant frequency of the wavelet in elastic medium. Then we reformulated the elastic equations based on the adaptive variable grid by introducing a mapping relationship. To test the effectiveness, accuracy, and efficiency of the equation, we implemented it to both the forward propagation and migration of elastic wavefield. Synthetic numerical examples demonstrate that our proposed method can achieve elastic wavefield separation and no significant dispersion phenomenon. The multi-component imaging accuracy of reverse time migration is nearly equivalent to the traditional method, while significantly improving computational efficiency and saving storage space.