An explicit split-step algorithm of the implicit Adams method for solving 2-D acoustic and elastic wave equations

作者：Yang Dinghui^*; Wang Lei; Deng Xiaoying

来源：Geophysical Journal International, 2010, 180(1): 291-310.

DOI：10.1111/j.1365-246X.2009.04407.x

• Numerical solutions
• Numerical approximations and analysis
• Seismic anisotropy
• Computational seismology
• Wave propagation

P>We first transform the seismic wave equations in 2-D inhomogeneous anisotropic media into a system of first-order partial differential equations with respect to time t. And then we develop a new explicit split-step algorithm (SSA) to solve the transformed equations through using the implicit Adams method and high-order interpolation approximation. Our algorithm enables wave propagation to be simulated in two dimensions through generally isotropic and anisotropic models. The high-order space derivatives in this SSA are determined by using the wave displacement, particle-velocity and its gradients simultaneously, while the time advancing of modelling seismic propagation uses the slit-operator algorithm based on the third-order implicit Adams method. On the basis of such a structure, the so-called SSA can suppress effectively the numerical dispersion and source-generated noises caused by discretizing the wave equations when too-coarse grids are used, and is third-order accuracy in time and fourth-order accuracy in space. We explore the theoretical properties of the SSA including the stability criteria of the SSA for solving 1-D and 2-D scalar wave equations, numerical dispersion, theoretical error and numerical error and computational efficiency when using the SSA to model the acoustic wave fields. Meanwhile, we also present the synthetic seismograms generated by the SSA in the three-layer isotropic medium and the 2-D elastic two-layer isotropic and anisotropic wavefield snapshots computed by the fourth-order Lax-Wendroff correction (LWC) scheme and the SSA, respectively. Numerical calculations of the relative errors show that the numerical error of the SSA is less than those of the conventional finite difference (FD) method and the fourth-order LWC scheme. Promising numerical results further illustrate that the SSA has less numerical dispersions and can suppress effectively the source-generated noises, further resulting in both increasing the computational efficiency and saving the space storage.

• 出版日期2010-1
• 单位清华大学