慢度平方三角网格立体层析反演方法

Stereo-tomography in squared-slowness triangulated model

三角剖分模型是一种稀疏的模型描述方式.在慢度平方三角剖分模型中,界面可以得到自然的描述,射线追踪在一个三角块内存在解析解.基于慢度平方三角剖分模型下的射线扰动理论,实现了立体层析数据空间对慢度平方三角剖分模型要求的所有模型分量的偏导数求取.相比常规的B样条或者大网格模型描述方式,慢度平方三角剖分模型下的立体层析FRECHET导数矩阵规模被大幅压缩,求解精度得到良好保证的同时计算成本得到大幅降低.理论数据算例证实了上述观点.

The triangulated mesh based representation could be the most sparse manner to represent a geologic model. In 2D triangulated model, interfaces are naturally described and the slowness can be of strongly contrast on the both side of the interface. In every triangular mesh, an analytic solution of ray-tracing can be obtained. Based on the theory of ray perturbation in the 2D triangulated model, we derive all the Frechet derivatives of the data components with respect to the model components. Compared with the B-spline or conventional rectangular grid model description, the scale of Frechet matrix of triangulated model is greatly compressed. Not only the accuracy of the tomographic linear system is improved, the computational cost of stereo-tomography is also significantly cut down. The synthetic data examples demonstrates the above points.