弹性波层析成像及其在土木工程中的应用

对弹性波层析成像理论和算法进行系统研究。射线追踪是建立在几何光学近似的基础上,合理选择弹性波源使之在介质中有较大的波速梯度,则在土木工程中应用弹性波层析成像能够满足其理论前提;提出二阶段射线追踪的快速方法,第一阶段采用改进的扫描法初选射线路径,第二阶段对初选射线路径进行扰动分析确定最终射线路径;讨论离散反演问题解的性质,特别是对于混定问题采用奇异值分解理论可获得满意的解估计,在减小解方差的同时也降低解的分辨半;研制弹性波层析成像系统,数值仿真表明软件正确可靠,工程实例表明该技术在土木工程中有显著的推广应用价值。

ELASTIC WAVE TOMOGRAPHY AND ITS APPLICATION TO CIVIL ENGINEERING

The elastic wave tomography and its application to the civil engineering are studied in the paper. It is found that the theory of ray tracing is based on the geometric optics approximation. A two-step of ray tracing is proposed to be a fast technique. In the first step, the initial ray paths are searched by a modified scan method. Then, the final ray paths are confirmed by perturbation analysis for the initial ray paths. It can be realized that the algorithm is satisfied on the reciprocity; it is an effective algorithm with high accuracy. An example for illustration the proposed technique is given. At last, the discrete inverse problem is also discussed.