For layered models with a low-velocity half-space, Rayleigh waves can exhibit inversely dispersive patterns and thus are advantageous for providing useful information on the seismic properties of such structures. However, the calculation of dispersion curves usually encounters some difficulties such as root skipping or numerical instability due to the presence of leaky modes. The full-wavefield method and spectral element method can offer better solutions but at the cost of a significant computational effort. For practical applications, most researchers treat the zeros of the real part of the secular function as an approximation to the leaky modes, which may lead to relatively large errors that cannot be ignored. Instead, in this paper, we propose a simple and efficient method to approximate the leaky mode based on the local minima of the absolute value of the secular function. Compared with the dispersion curve generated from the real part of the secular function, the proposed method can provide a more accurate approximation. We further apply a new efficient Monte Carlo search technique to two synthetic datasets and a permafrost example. Results show that our forward and inverse methods are effective, efficient, and robust. Moreover, our numerical experiments indicate that the modified Thomson-Haskell method is more suitable for calculating leaky modes compared with the fast delta method and the generalized reflection/transmission method, and that the inversion results are less sensitive to the effect of the limited spread length on the measured dispersion curves. The present study emphasizes the high efficiency of the proposed method in imaging permafrost structures and foundation features of buildings or roads.

对于具有低速半空间的分层模型，瑞利波可以表现出逆色散模式，因此有利于提供有关此类结构的地震特性的有用信息。然而，色散曲线的计算通常会遇到一些困难，例如由于泄漏模式的存在而出现跳根或数值不稳定等问题。全波场法和谱元法可以提供更好的解决方案，但代价是大量的计算工作。对于实际应用，大多数研究人员将长期函数实部的零点视为泄漏模式的近似，这可能会导致不可忽视的相对较大的误差。相反，在本文中，我们提出了一种简单而有效的方法来基于长期函数绝对值的局部最小值来近似泄漏模式。与从长期函数实部生成的频散曲线相比，该方法可以提供更准确的近似。我们进一步将一种新的高效蒙特卡罗搜索技术应用于两个合成数据集和一个永久冻土示例。结果表明，我们的正向和逆向方法是有效、高效且稳健的。此外，我们的数值实验表明，与快速Delta方法和广义反射/透射方法相比，改进的Thomson-Haskell方法更适合计算泄漏模式，并且反演结果对有限扩展长度的影响不太敏感在测量的色散曲线上。本研究强调了所提出的方法在对建筑物或道路的永久冻土结构和地基特征进行成像方面的高效性。