新的瑞雷波多模式频散曲线反演目标函数

反演瑞雷波频散曲线能有效地获取横波速度和地层厚度，传统的多模式瑞雷波频散曲线反演需要正确的模式判别.然而，当地层中含有低速软弱夹层或高速硬夹层等复杂结构时，瑞雷波可能会出现"模式接吻"和"模式跳跃"等现象，这些现象极易造成模式误判，进而导致错误的反演结果；同时，传统的频散曲线反演方法需要进行求根运算，进而导致现有的瑞雷波非线性反演速度慢，运算时间长.鉴于此，对传统的Haskell-Thomson频散曲线正演模拟算法进行了改进，提出了一种新颖有效的目标函数.该目标函数直接利用实测频散曲线与迭代更新模型频散函数表面形状进行最佳拟合，无需将多模式频散数据归于特定的模式，可有效避免多模式瑞雷波频散曲线反演模式误识别；同时，该目标函数不需要求根运算，进而大大加快了非线性反演速度.基于粒子群优化算法，利用实际工作中经常遇到的3种典型理论地质模型和某一高速公路路基实测资料进行了理论模型试算和实例分析，检验了本文提出的瑞雷波多模式频散曲线反演新方法的有效性和实用性. 

A New Misfit Function for Multimode Dispersion Curve Inversion of Rayleigh Waves

Inversion of the Rayleigh wave dispersion curve can effectively obtain the shear wave velocity and stratum thickness. And the classical inversion of multimode Rayleigh wave dispersion curve requires correct mode identification. However, there may be "mode-kissing" and "mode-jumping" phenomena in the Rayleigh waves when the stratum contains complex structures such as low-velocity soft intercalations or high-speed stiff sandwich layers. These phenomena can easily lead to mode misidentification, and lead to wrong inversion results. At the same time, the classical dispersion curve inversion method needs to seek the roots, which leads to that the nonlinear inversion of Rayleigh wave is slow and the computation time is long. In view of these, the classical Haskell-Thomson dispersion curve forward modeling algorithm is improved, and a novel and effective misfit function is proposed. The misfit function is directly used to fit the dispersion function surface shape of the iterative updating model by using the measured dispersion curve. It is not necessary to assign the multimode dispersion data to a specific mode, which can effectively avoid the mode misidentification in the inversion of multimode Rayleigh wave dispersion curve. And the misfit function does not require the seeking root operation, thus greatly accelerating the nonlinear inversion speed. In this paper, based on the particle swarm optimization algorithm, three theoretical geological models and a certain roadbed test data often encountered in practical work are used to calculate the theoretical model and analyze the example. And the validity and practicability of the new method of Rayleigh wave multimode dispersion curve inversion are verified.