Love波变分原理与Love面波法的反演技术

The Variation Principles of Love Waves and the Inversion Technique for Love Surface Waves Methods

本文从Ｌｏｖｅ波的变分原理出发，导出了非均质地基土参数（如剪切波速度β、质量密度ρ）的微小扰动引起Ｌｏｖｅ波相速度ｃ或波数ｋ的微小变化的解析关系式，进而求得相速度或波数对土层参数（β、ρ）的偏微商．在利用面波法（即ＳＡＳＷ法）反演土层参数时，若以上述偏微商代替以往的割线法［１］［２］计算偏导数迭代矩阵Ａ＿Ｋ，不仅准确，而且可大大减少计算量，节约机时，提高反演速度．文末给出的实例证明了此法的合理性和实用性。

The small change in phase velocity c or wave number k due to small perturbations in parameters of nonhomognous soil (such as β or ρ) is derived by using the variation principles of Love waves. This leads to analytic expressions of phase velocity or wave number partial derivations with respect to soil parameters. In the inversion process for surface wave methods(i. e. SASW methods),the computional time will decrease significantly by using these partial derivations. At the end of this paper,an actual example is given to demonstrate the effectivness and applicability of the presented method.