反演二维弹性波动方程组多参数的渐近展开法

THE MULTI-PARAMETER INVERSION THEORY AND METHOD OF TWO DIMENSIONAL ELASTIC WAVE EQUATIONS

采用摄动法对二维弹性波动方程组的系数反问题进行渐近近似，给出了反演系数的具体计算方法。用摄动法解微分方程组的系数反问题还是首次。此外，还采用了地球物理分层模型，这种分层模型便于更精细地反映地球不同圈层的物理特征，更接近于实际情况。同时对进一步提高反演分辨率、增加反演参数、对病态方程组如何克服不适定性等问题，作了具体阐述，具有重要的理论意义与应用价值。

The perturbation method is used in the paramaters inversion of two dimensional elastic wave equations in this paper. This is first time to use perturbation method in combination with geophysics stratified model to solve the paramater inversion of differential equation. The models application can reflect better the physical characterstics of the different stratum. It is described in the paper how to raise better inversions resolving power, how to increase inversions paramaters and how to overcome improperly posed problem of ill condition system of equations. This study has important theoretical meaning and applied value.