论文详情
在地震学中,真实的地球表面是一个强阻抗突变界面,可以通过自由表面边界条件对其进行描述。自由表面边界条件在数值模拟中的准确表达是目前地震波有限差分数值模拟的研究热点之一。为解决直接针对自由表面边界条件进行数值近似处理带来的稳定性和精度方面的问题,从平均介质理论出发,结合极限思想,推导了自由表面的另一种新的自适应数学表达方式。本质上,新的自由表面自适应表达方式是对原始弹性波方程中的密度和本构关系的修正,并且在计算过程中不会增加额外的CPU和内存需求。理论分析和数值实验表明,新的自由表面自适应表达方式是泊松比自适应的,对于不同泊松比值的有限差分数值模拟均能给出较为精确的模拟结果,从而可以应用于实际近地表不均匀风化层内的复杂波场的模拟和分析。
The surface of the earth is a strong impedance-discontinuity boundary and has a significant impact on the propagation of seismic waves.In seismology,this boundary is commonly described by free-surface boundary conditions,which are applicable for finite-element and spectral-element methods.However,when applying free-surface boundary conditions to the finite-difference method,the results may suffer from instability or low accuracy because of the numerical approximation for free-surface boundary conditions.To address this issue,an adaptive free-surface expression is proposed based on an averaged medium method and limit theorem,which can be viewed as an alternative to the free-surface boundary conditions.Essentially,the proposed free-surface expression is a modification of density and constitutive relations for the original first-order elastodynamic equation at the free surface,which would cost nearly no extra CPU and memory when applied to finite-difference modeling.Both the theoretical analysis and numerical examples demonstrate that this expression can adaptively handle the finite-difference modeling with various Poisson’s ratios,which implies its potential for wave field modeling in near-surface areas with complex weathered zones.
国家自然科学基金(41474104,41674132)资助。