张建明,
韩佩恩
同济大学海洋地质国家重点实验室, 上海 200092
基金项目: 国家重点研发计划项目(2019YFC0312004)以及国家自然科学基金项目(41874127)和上海市科技创新行动计划项目(19DZ1201702)联合资助
详细信息
作者简介: 董良国, 同济大学海洋与地球科学学院教授, 博士生导师, 主要从事地震波传播理论与数值模拟、地震波反演等方面的研究.E-mail: dlg@tongji.edu.cn
中图分类号: P631 收稿日期:2020-11-06
修回日期:2021-01-11
上线日期:2021-03-10
The improved first-arrival traveltime tomography based on the adjoint-state method
DONG LiangGuo,ZHANG JianMing,
HAN PeiEn
State Key Laboratory of Marine Geology, Tongji University, Shanghai 200092, China
MSC: P631
--> Received Date: 06 November 2020
Revised Date: 11 January 2021
Available Online: 10 March 2021
摘要
摘要:目前，有关伴随状态法初至波走时层析成像方法的文献，基本上都是基于面积分来定义目标函数，由此得到的伴随方程也都依赖于地表的法向量.这样，一方面会因为伴随变量计算的不准确而造成梯度的不合理，另一方面也无法合理地处理井中观测问题.本文从理论或数值试验角度指出了这些问题，并提出了不依赖地表法向量的改进的伴随状态法走时层析成像方法.主要改进包括：(1)采用体积分定义目标函数，避免了传统方法不能较好处理井中观测数据的缺陷，可以适应任意地表或井中观测系统.(2)采用摄动法得到了新的伴随方程，克服了传统方法中伴随场计算需要依赖于地表法向量的缺陷，使得检波点处的走时残差可以正确地反传播至地下，进而得到更加合理的速度修正方向，提高了速度反演的精度.
关键词: 初至波/
走时层析/
伴随状态法/
伴随方程/
目标函数/
程函方程
Abstract:In the currently-used first-arrival traveltime tomography based on adjoint state method,the boundary normal vectors of the computational domain must be used to compute the adjoint field. As one result,it will get inaccurate gradients and produce unreasonable inversion results in the situation with complex topography. On the other hand,it cannot correctly deal with the problems for borehole observations. These limitations are discussed in this paper by theoretical analysis and numerical experiments. Furthermore,an improved adjoint state based first-arrival traveltime tomography method is proposed. Major improvements include: (1) The data of any observation geometry can be processed by this improved method,including surface and borehole observations simultaneously. (2) New adjoint equation is derived by perturbation method. It does not depend on the boundary normal vector so that the traveltime residuals of the receivers can be correctly back-propagated to the underground and a correct gradient can be obtained. As a result,the velocity inversion accuracy can be increased.
Key words:First-arrival/
Traveltime tomography/
Adjoint-state method/
Adjoint equation/
Objective function/
Eikonal equation
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http://www.geophy.cn/data/article/export-pdf?id=608009f9c23e67607ae103e3
