基于非降阶汉密尔顿算子的三维立体层析反演

不同于前人在射线中心坐标系下基于降阶汉密尔顿算子建立立体层析矩阵，本文详细讨论了在三维直角坐标系下，基于非降阶汉密尔顿算子通过射线扰动理论导出三维立体层析所需的数据空间对模型空间的一阶线性关系，进而建立三维立体层析矩阵.在建立这个庞大且稀疏的系数矩阵后，实施规则化使得该矩阵方程的求解能够收敛到一个合理的结果.理论数据的严格测试证实了三维立体层析矩阵建立的正确性，为实际应用奠定了理论基础.

3D stereo-tomography based on the non-reduced Hamiltonian

Stereo-tomography is a very attractive tomography method with which the position of reflector, the dip of the reflector and the velocity structure can be inverted simultaneously. Differed from the previous 3D stereo-tomography derived in the ray-centered coordinate, in this paper, a detailed investigation of the setup, solution and regularization of the 3D stereo-tomographic matrix equation, which is based on the ray perturbation theory in 3D Cartesian coordinate system, is presented. After this sparse and huge 3D tomographic matrix is setup, some regularization techniques have to be applied to guarantee a proper convergence. The 3D synthetic data examples demonstrate the correctness of the set-up of the 3D stereo-tomographic matrix and the necessity of the related regularization techniques, from which a solid foundation for the real applications of 3D stereo-tomography is constructed.