The Improved Nearly Analytic Discrete Method For 3D Elastic Equations And Its Numerical Simulation

The type of nearly analytic discrete methods (NAD-type) is a new class of numerical simulation methods for wave propagation. These methods are based on the truncated Taylor expansion with respect to the time. According to the partial differential equation (PDE), we convert the high-order temporal derivatives to the high-order spatial derivatives. Meanwhile, the high-order spatial derivatives can be approximated by the interpolations of the original values and their gradients. Theoretical and numerical results show that NAD-type can effectively preserve the information of the wave fields by suppressing numerical dispersion and improving numerical accuracy and efficiency.From theoretical and numerical aspects, this paper systemically studies the algorithms of the NAD-type, and several main results are obtained. We have improved the ONADM for the 3D case and explored its stability condition. Extending the 2D RNADM to the 3D case, we discuss its computational accuracy and stability condition. We also present a newly proposed algorithm: SNADM and analyze its properties including computational accuracy and numerical dispersion.Comparison with the classical fourth-order LWC scheme shows that the NAD-type methods have many advantages. They can generate clearer snapshots of wave fields without any visible dispersion. To obtain the results without any numerical dispersion, the time cost by the LWC schemes is about 559, 1222 and 1955 times of that taken by ONADM, RNADM and SNADM, receptively. Besides, the storage space of ONADM is roughly about 3.3% of that needed for the fourth-order LWC scheme, while of RNADM and SNADM is about 5.8‰.