Abstract

The numerical solution of a wave equation plays a crucial role in computational geophysics problems, which forms the foundation of inverse problems and directly impacts the high-precision imaging results of earth models. However, common numerical methods often lead to significant computational and storage requirements. Due to the heavy reliance on forward-modeling methods in inversion techniques, particularly full-waveform inversion, enhancing the computational efficiency and reducing the storage demands of traditional numerical methods have become key issues in computational geophysics. We develop the deep Lax-Wendroff correction (DeepLWC) method, a deep-learning-based numerical format for solving 2D hyperbolic wave equations. DeepLWC combines the advantages of traditional numerical schemes with a deep neural network. We provide a detailed comparison of this method with the representative traditional Lax-Wendroff correction method. Our numerical results indicate that the DeepLWC significantly improves the calculation speed (by more than 10 times) and reduces the space needed for storage by more than 10,000 times compared with traditional numerical methods. In contrast to the more popular physics-informed neural network method, DeepLWC maximizes the advantages of traditional mathematical methods in solving partial differential equations and uses a new sampling approach, leading to improved accuracy and faster computations. It is particularly worth pointing out that DeepLWC introduces a novel research paradigm for numerical equation solving, which can be combined with various traditional numerical methods, enabling acceleration and reduction in the storage requirements of conventional approaches.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.