黏弹性介质瑞雷波有限差分模拟与特性分析

摘要

本文通过数值模拟研究了介质黏弹性对瑞雷波传播的影响.模拟采用结合了交错Adams-Bashforth时间积分法、应力镜像法和多轴完美匹配层的标准交错网格高阶有限差分方案.通过模拟结果和理论结果对比,测试了方法的精度,验证了结果的正确性.在均匀半空间模型中,分别从波场快照、波形曲线及频散能量图三个角度,对黏弹性介质瑞雷波衰减和频散特性进行了详细分析.两层速度递增模型被用于进一步分析瑞雷波在黏弹性层状介质中的特性.结果表明:由于介质的黏弹性,瑞雷波振幅发生衰减,高频成分比低频成分衰减更剧烈,衰减程度随偏移距增大而增强;瑞雷波相速度发生频散,且随频率增大而增大,频散能量的分辨率有所降低;黏弹性波动方程中的参考频率,不会影响瑞雷波振幅衰减和相速度频散的程度,但决定了黏弹性和弹性介质瑞雷波相速度相等的频率位置.本研究有助于人们更好地理解地球介质中瑞雷波的行为,并为瑞雷波勘探的应用和研究提供了科学和有价值的参考.%Effects of viscoelasticity of media on Rayleigh waves propagation are studied by numerical simulation based on a standard staggered grid high-order finite-difference (FD) scheme,which combines the staggered Adams-Bashforth time integrators,stress image method,and the multiaxial perfectly matched layer.Accuracy of the FD algorithm is tested and correctness of results is verified by comparison of modeling and theoretical results.In a homogeneous half-space,attenuation and dispersion characteristics of viscoelastic Rayleigh waves are analyzed in term of wavefield snapshots,waveform curves and dispersive images,respectively.Then,the two-layer models with increasing velocity are used to further analyze the characteristics of Rayleigh waves in the viscoelastic layered media.Results show that due to the viscoelasticity of media,amplitude of Rayleigh waves is decreased,and the high-frequency waves are attenuated more severely than the lower-frequency waves.The attenuation degree grows with offset increasing.The phase velocities of Rayleigh-wave are dispersed,which becomes stronger with frequency growing.The resolution of dispersion energy is reduced;reference frequency in the viscoelastic wave equation does not affect the amplitude attenuation and the phase velocity dispersion of Rayleigh waves,but determines the frequency position of the Rayleigh-wave phase velocity equivalent between viscoelastic and elastic media.This work will help further understand the behavior of Rayleigh waves in Earth's media and provide a valuable reference for the application and research of Rayleigh waves exploration.