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.

在广义连续介质力学 (GCM) 理论框架中，非对称波动方程包含介质的特征尺度参数，解释了微观结构的相互作用。本研究整合了GCM的两个理论分支，即修正偶应力理论（M-CST）和单参数第二应变梯度理论，在统一框架中形成了一种新颖的非对称波动方程。在统一框架中对非对称波动方程进行数值模拟，可以准确地描述地下结构，对后续地震波反演和成像工作具有重要意义。然而，采用有限差分（FD）方法进行数值建模可能会引入数值离散，从而对数值建模的准确性产生不利影响。最优FD算子的设计对于提高数值建模的准确性和强调尺度效应至关重要。因此，本研究设计了一种称为粪甲虫优化（DBO）算法与模拟退火（SA）算法的混合方案，记为基于SA的混合DBO（SDBO）算法。开发了SDBO算法下的FD算子优化方法，并将其应用于统一框架中的非对称波动方程数值模拟。集成 DBO 和 SA 算法可以降低收敛到局部极限的风险。数值色散结果强调，所提出的 SDBO 算法产生的 FD 算子的精度误差限制在 0.5‱，同时涵盖更广泛的频谱覆盖范围。这一结果证实了SDBO算法的有效性。 最终，数值模拟结果表明，基于SDBO算法的FD新方法有效抑制了数值色散，提高了弹性波数值模拟的精度，从而加剧了尺度效应。该结果对于提取介质中复杂微结构引起的波场扰动以及尺度效应分析具有重要意义。