An improved ONAD algorithm based on a modified nearly analytic discrete operator for solving 2D scalar wave equation

Abstract

High resolution seismic imaging requires high accuracy forward numerical modeling method. However, most of existing methods suffer from strong numerical dispersion when a coarse grid is used and energy shifts after long-time calculations. The optimal nearly analytic discrete method (ONADM) can effectively suppress the numerical dispersion, but still leads to serious energy distortion after long time integration. In this paper, to further reduce the numerical dispersion, we suggest an improved spatial approximate operator which is called modified nearlyanalytic discrete (MNAD) operator, by minimizing the energy error. The temporal operator uses the traditional central difference. Promising numerical experiments show that: (1) the MNAD can significantly reduce the computational costs because it can provide clear wave fields on a coarse grid like the traditional NAD operator; (2) the MNAD is stable and only has a less than 1.4% energy error after 300-second seismic wave field simulation (150000 temporal iterative steps) on a coarse grid with a spatial step of 30m; (3) For complex models, like the SEG/Salt model, MNAD can also provide clearer wave fields without any visible numerical dispersion.