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

一种用于非对称性波动方程数值模拟的模拟退火混合蜣螂优化算法

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,非对称性波动方程包含介质的特征尺度参数并考虑了微结构相互作用。本文融合了广义连续介质力学的两个理论分支,即修正偶应力理论(M-CST)和单参数二阶应变梯度理论,建立了一种新颖的统一框架下的非对称性波动方程。对统一框架下的非对称性波动方程进行数值模拟可以提供精确准确的反映地下结构,对后续地震波反演和成像工作具有重要意义。但是,采用有限差分(FD)方法进行数值模拟可能会引起数值频散,从而影响数值模拟的准确性。为了提高数值模拟精度并突出尺度效应,最优FD算子的设计至关重要。为此,本文设计了一种称为蜣螂优化(DBO)算法与模拟退火(SA)算法(称为SDBO算法)的混合方案。在此基础上,开发了SDBO算法下的FD算子优化方法,并将该优化的FD算子应用于统一框架下的非对称性波动方程数值模拟。DBO算法和SA算法的结合降低了DBO算法收敛到局部极值的风险。数值频散结果强调,所提出的SDBO算法产生的FD算子的精度误差控制在万分之五以内,同时涵盖更广泛的频谱覆盖范围。这证实了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频散,提高了弹性波数值模拟的精度,从而凸显了尺度效应。这对于提取介质中复杂微结构引起的波场扰动以及分析尺度效应具有重要意义。