Couple-stress asymmetric wave equations modelling with an optimal finite-difference scheme

Abstract

The asymmetric wave equation encompasses the influence of the actual fine structure inside the medium on the wave field, which can better represent the complex seismic wavefield excited by the complex source and reflect the scale effects of the seismic wave response under equal computational power. However, when the finite-difference (FD) operator is applied to implement the numerical modelling using the asymmetric wave equation, numerical dispersion appears due to the use of difference operator to approximate the differential operator, which negatively affects the analysis of the seismic wavefield. To suppress the numerical dispersion, this paper proposes an improved Dung Beetle Optimization (IDBO) algorithm to obtain the optimized FD operators. The IDBO algorithm adopts an improved Tent map and the Opposition-Based Learning strategy to initialize the population, which improves the diversity of the population. The nonlinear function adaptive control strategy is introduced to adjust the population allocation ratio and boundary selection Parameter R to achieve an adequate balance between global exploration and local exploitation. In addition, adaptive weights and the Levy flight mechanism are combined to improve the ball-rolling dung beetle position updating strategy to avoid falling into local extremes. Numerical dispersion analysis and numerical modelling results demonstrate that the optimization of FD operators based on the IDBO algorithm can effectively suppress numerical dispersion. It is of great significance to extract the wave field perturbation caused by heterogeneity due to the complex microstructure in the medium and analyze the influence of the microstructural properties in the medium on seismic wave propagation.