石油物探2017，Vol.56Issue(4)：491-499,9.DOI:10.3969/j.issn.1000-1441.2017.04.004
直角坐标系下立体层析FRECHET导数求取修正问题探讨
On the correction of the Frechet derivatives of stereotomography in Cartesian coordinate
摘要
Abstract
The Frechet derivative of stereotomography in the Cartesian coordinate system is a first-order derivative of disturbance quantity observed in surface to initial model space.If the endpoint of the paraxial ray has to be corrected to the surface,a significant error will be introduced into the Frechet derivative.The inversion accuracy will be reduced and should be modified.Differing from the conventional method to solve this problem by tracing the central ray a little longer,we use the triangular relationship among the coordinates of the emergence point for the central ray at the surface,the endpoint of the paraxial ray at the surface and the lateral difference between the endpoint of the paraxial ray and the expected emergence point at the surface,to convert a linear relationship between the endpoint coordinate difference of the central ray and paraxial ray in the surface and the initial perturbation of the ray start-point.Then the correct Frechet derivatives can be achieved based on this conversion.The method presented is exactly equivalent to the previous method with a lower computational cost.Numerical examples demonstrate the correctness and the necessity of the presented correction for stereotomography in the Cartesian coordinate system.关键词
立体层析反演/傍轴射线/FRECHET导数/直角坐标系Key words
stereotomography/linear relationship/Frechet derivatives/Cartesian coordinate分类
天文与地球科学引用本文复制引用
周嘉欣,熊凯,杨锴..直角坐标系下立体层析FRECHET导数求取修正问题探讨[J].石油物探,2017,56(4):491-499,9.基金项目
国家自然科学基金面上项目(41574098,41630964)资助.This research is financially supported by the National Natural Science Foundation of China (Grant Nos.41274117,41574098). （41574098,41630964）
