An Improved DBO Algorithm Applying for Numerical Modelling Under the Asymmetric Wave Equations

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 has a negative impact on the analysis of seismic wave fields. For the purpose of improving the accuracy and efficiency of numerical modelling of the asymmetric wave equation, this study proposes an improved Dung Beetle Optimization (IDBO) algorithm and an IDBO algorithm-based finite-difference (IDBO-FD) scheme. The IDBO algorithm, which initializes the population using an enhanced Tent map and the Opposition-Based Learning strategy, increases the population’s variety. To achieve a good balance between global exploration and local exploitation, a nonlinear function is used to adaptively alter the population allocation ratio. Additionally, the ball-rolling dung beetle position update approach is enhanced by combining adaptive weights and the Levy fight strategy to prevent falling into local extremes. Numerical dispersion analysis and numerical modelling results indicate that the IDBO-FD scheme can successfully find the optimal FD operators and effectively suppress the numerical dispersion. This is of great significance for extracting wave field perturbations caused by complex microstructures in the medium and analyzing the impact of the microstructural properties of the medium on seismic wave propagation.