基于流固界面平面波反/透射系数验证海域场地波动模拟方法精度的注记

Notes on the accuracy verification of wave simulation method developed for the ocean-bottom seismic site response analysis using the plane-wave reflection and transmission coefficients

面向基于平面波输入的海域场地效应研究,本文以勒让德谱元波动模拟方法为例,探讨利用流固界面反/透射系数以验证海域场地模拟方法的精度。考虑四阶勒让德谱元(令单元尺寸与目标最小模拟波长一致),就入射角小于临界角情形,基于入射、反/透射模拟波形模的最大值以计算反/透射系数,计算与解析结果的相对误差小于0.5%;超过临界角情形,相对误差可超过20%。相对误差过高的原因为:入射角超过临界角情形,反射、透射与入射波形将存在相位差,仍基于波形模的最大值计算反/透射系数将导致错误结果。本文建议利用Hilbert包络幅值代替波形模的最大值,并论证了这一做法的合理性。改进后模拟所得反/透射系数与解析结果的相对误差保持在0.5%以内。

The accuracy verification of wave simulation method,developed for the ocean site response analysis under oblique plane wave incidence,is discussed in this paper taking the Legendre-spectral-element based wave simulation method as an example.Considering the fourth order Legendre interpolant in each element,the relative errors of computed Reflection/Transmission(R/T)coefficients on basis of the peak absolute value of the simulated R/T waves are less than 0.5%,in case that the incident angle is less than the critical angle.However,the relative error can be bigger than 20%in case that the incident angle is larger than the critical angle.The reason for the generation of large errors are as follows:in case that the incident angle exceeds the critical angle,there will be a phase shift between the R/T waves.In that case,the R/T coefficients must be computed using the peak absolute vale of the Hilbert envelop instead of the direct peak absolute value of the R/T waves,which can also be proved in this paper.With such modification,the relative errors of the computed R/T values using the Legendre-spectral-element based wave simulation method are all kept within 0.5%.