3D adaptive internal multiples modeling based on globally optimised Fourier finite-difference method

Abstract

Numerical methods have been widely applied to simulate seismic wave propagation. However, few studies have focused on internal multiples modeling. The formation mechanism and response of internal multiples are still unclear. Therefore, we develop a weighted-optimised-based internal multiples simulation method under 3D conditions. Using a one-way wave equation and full-wavefield method, the different-order internal multiples are computed numerically in a recursive manner. The traditional Fourier finite-difference (FFD) method has low numerical accuracy in a horizontal direction. A globally optimised FFD (OFFD) method is used to improve the lateral propagation accuracy of the seismic waves. Meanwhile, we adopt an adaptive variable-step technique to improve computational efficiency. The 3D internal multiples modeling technique is capable of calculating the different-order multiple reflections in complex structures. We use the present method to simulate internal multiples in several models. Theoretical analyses are consistent with the numerical results. Numerical examples demonstrate that the 3D internal multiples modeling technique has superior performance when adapting to lateral velocity changes and steep dip. This also implies that our method is fit for the simulation of internal multiples propagation in a 3D complex medium and can assist in identifying the internal multiples from full-wavefield data.