水平层状模型中多模式瑞雷波和拉夫波相速度频散曲线的灵敏度分析

以瑞雷波和拉夫波为主要研究对象的高频面波方法，在地下水、环境及工程等领域被广泛应用。对于水平层状模型，横波速度是影响多模式瑞雷波和拉夫波相速度频散曲线的最重要参数。文中利用雅可比矩阵探究多模式瑞雷波和拉夫波相速度对不同深度地层横波速度的灵敏度。研究表明：①不同模式的面波对相同地层横波速度的灵敏度不同；无论是瑞雷波还是拉夫波，低频面波比高频面波对较深层横波速度更灵敏；同时，整个高频段都是多模式面波相速度频散曲线对表层横波速度改变的灵敏频段。②基于对速度递增模型和两种速度异常层（含低速夹层或高速夹层）模型进行的测试分析，认为多模式瑞雷波和拉夫波相速度频散曲线对低速层横波速度的灵敏度高，而对高速层及速度异常层（低速层或高速层）下伏地层横波速度的灵敏度低。③相同模式拉夫波相速度频散曲线对同一地层横波速度的高灵敏度频段范围比瑞雷波的更宽，瑞雷波和拉夫波相速度频散曲线对相同地层横波速度的灵敏度峰值存在差异，因此联合反演多模式瑞雷波和拉夫波相速度频散曲线有利于获得高精度的浅地表横波速度。

Sensitivity analysis of multi-mode Rayleigh and Love wave phase-velocity dispersion curves in horizontal layered models

High-frequency surface-wave method with Rayleigh wave and Love wave as the main study objects is widely applied in various fields such as underground water,environment and engineering.For horizontal layered models,S-wave velocities are the most important parameters for estimating multi-mode Rayleigh wave and Love wave phase-velocity dispersion curves.In this paper,the Jacobian matrix was used to infer the sensitivities of multi-mode Rayleigh wave and Love wave phase-velocity dispersion curves to S-wave velocities of the formations at different depths.The following conclusions were drawn.①The sensitivities of surface waves of different modes to the S-wave velocity at a certain depth are different.For both Rayleigh wave and Love wave,low-frequency surface wave is more sensitive to the S-wave velocities in deep formations,compared with high-frequency surface wave.Moreover,multi-mode phase velocities with a broad high-frequency range are sensitive to surface S-wave velocity.②Based on a velocity-increasing layered model and two layered models with velocity anomalies (containing low-velocity interlayer and high-velocity interlayer),the analysis results suggested that the phase-velocity dispersion curves of both Rayleigh wave and Love wave are sensitive to S-wave velocity in low-velocity layer,and they are both not sensitive to the S-wave velocity in high-velocity layer or below velocity-anomaly layer (low-velocity layer or high-velocity layer).③For surface wave of a certain mode,the frequency band of Love wave,in which phase-velocity dispersion curves are sensitive to S-wave velocity of a specific layer,is wider than that of Rayleigh wave.In addition,the sensitivity peaks of Rayleigh wave and Love wave phase-velocity dispersion curves to S-wave velocity of a certain layer are different.Therefore,joint inversion of multi-mode Rayleigh wave and Love wave phase-velocity dispersion curves can be applied to obtain high-precision shallow subsurface S-wave velocity.