Modeling of the Seismic Scalar Wave Field Using the Symplectic Scheme and Singular Kernel Convolutional Differentiator

Abstract

This work adopts both the symplectic difference scheme and singular kernel convolutional differentiator for modeling of the seismic scalar wave field. In this method the computational accuracy and stability have been greatly improved with a slight increase of calculation amount. Compared with other non‐symplectic numerical methods, major advantages of the method presented in this paper are the structure‐preserving property and a strong capability of long‐time tracing. This approach provides a new and effective choice for high‐accuracy modeling of large‐scale and long‐time history seismic wave fields.

Optimal Symplectic Scheme and Generalized Discrete Convolutional Differentiator for Seismic Wave Modeling

“…2) to test the efficiency and accuracy of OSGCD in practical seismic wave simulations. Four methods are employed to compare with our method, which are (1) PRK Lobatto III A-III B [32−35] in combination with GCD (PRK-GCD), (2) Iwatsu three-stage and third-order symplectic scheme [15,[28][29][30]36] in combination with GCD (TO-GCD), (3) optimal two stage and second order symplectic scheme in combination with SCD [15,[28][29]41] (OS-SCD) and (4) optimal second-degree and secondorder symplectic scheme in combination with FDM (OS-FEM). In this numerical experiment, we choose V P =2000 m/s, V S =1250 m/s and ρ=2000 kg/m 3 .…”