A Hybrid Dung Beetle Optimization Algorithm with Simulated Annealing for the Numerical Modeling of Asymmetric Wave Equations

In the generalized continuum mechanics (GCM) theory framework, asymmetric wave equations encompass the characteristic scale parameters of the medium, accounting for microstructure interactions. This study integrates two theoretical branches of the GCM, the modified couple stress theory (M-CST) and the one-parameter second-strain-gradient theory, to form a novel asymmetric wave equation in a unified framework. Numerical modeling of the asymmetric wave equation in a unified framework accurately describes subsurface structures with vital implications for subsequent seismic wave inversion and imaging endeavors. However, employing finite-difference (FD) methods for numerical modeling may introduce numerical dispersion, adversely affecting the accuracy of numerical modeling. The design of an optimal FD operator is crucial for enhancing the accuracy of numerical modeling and emphasizing the scale effects. Therefore, this study devises a hybrid scheme called the dung beetle optimization (DBO) algorithm with a simulated annealing (SA) algorithm, denoted as the SA-based hybrid DBO (SDBO) algorithm. An FD operator optimization method under the SDBO algorithm was developed and applied to the numerical modeling of asymmetric wave equations in a unified framework. Integrating the DBO and SA algorithms mitigates the risk of convergence to a local extreme. The numerical dispersion outcomes underscore that the proposed SDBO algorithm yields FD operators with precision errors constrained to 0.5‱ while encompassing a broader spectrum coverage. This result confirms the efficacy of the SDBO algorithm. Ultimately, the numerical modeling results demonstrate that the new FD method based on the SDBO algorithm effectively suppresses numerical dispersion and enhances the accuracy of elastic wave numerical modeling, thereby accentuating scale effects. This result is significant for extracting wavefield perturbations induced by complex microstructures in the medium and the analysis of scale effects.