罗飞,,
王华忠
同济大学海洋与地球科学学院, 波现象与智能反演成像研究组, 上海 200092
基金项目: 国家自然科学基金（41774126，41574098，41604091，41704111），国家科技重大专项（2016ZX05024-001，2016ZX05006-002）资助
详细信息
作者简介: 冯波, 男, 1984年生, 博士, 主要从事地震波偏移成像与反演成像等理论与应用研究.E-mail:ancd111@163.com
通讯作者: 罗飞, 男, 1990年生, 博士在读, 主要研究地震波传播理论以及速度建模.E-mail:luofei19901217@126.com
中图分类号: P631收稿日期:2018-09-11
修回日期:2019-04-03
上线日期:2019-06-05
Wave equation traveltime tomography using Rytov approximation
FENG Bo,LUO Fei,,
WANG HuaZhong
Wave Phenomena and Intelligent Inversion Imaging Group(WPI), School of Ocean and Earth Science, Tongji University, Shanghai 200092, China
More Information
Corresponding author: LUO Fei,E-mail:luofei19901217@126.com
MSC: P631--> Received Date: 11 September 2018
Revised Date: 03 April 2019
Available Online: 05 June 2019
摘要
摘要:传统的波动方程走时核函数（或走时Fréchet导数）多基于互相关时差测量方式及地震波场的一阶Born近似导出，其成立条件非常苛刻.然而，地震波走时与大尺度的速度结构具有良好的线性关系，对于小角度的前向散射波场，Rytov近似优于Born近似.因此，本文基于Rytov近似和互相关时差测量方式，导出了基于Rytov近似的有限频走时敏感度核函数的两种等价形式：频率积分和时间积分表达式.在此基础之上，本文提出了一种隐式矩阵向量乘方法，可以直接计算Hessian矩阵或者核函数与向量的乘积，而无需显式计算和存储核函数及Hessian矩阵.基于隐式矩阵向量乘方法，本文利用共轭梯度法求解法方程实现了一种高效的Gauss-Newton反演算法求解走时层析反问题.与传统的敏感度核函数反演方法相比，本文方法在每次迭代过程中，无需显式计算和存储核函数，极大降低了存储需求.与基于Born近似的伴随状态方法走时层析相比，本文方法具有准二阶的收敛速度，且适用范围更广.数值试验证明了本文方法的有效性.
关键词: Rytov近似/
有限频走时敏感度核函数/
波动方程走时层析/
初至波/
隐式矩阵向量乘/
Gauss-Newton方法
Abstract:The conventional wave-equation traveltime sensitivity kernel (TSK) or traveltime Fréchet derivative is derived from the Born approximation and cross-correlation measurement, which has a very narrow valid condition. In fact, the seismic traveltime has a more linear relationship with the large-scale velocity structure. For small-angle forward scattered wavefield, Rytov approximation is proved to be superior to Born approximation. Based on the Rytov approximation and cross-correlation measurement, a new wave-equation traveltime sensitivity kernel is derived. Meanwhile, an implicit matrix-vector product method is proposed, which can directly calculate the product of a matrix (TSK) and a model-space vector as well as the product of a matrix transpose and a data-space vector, eliminating the need of calculating TSK explicitly. Based on the proposed implicit matrix-vector product method, traveltime tomography using the Gauss-Newton inversion algorithm is implemented efficiently by solving the normal equation iteratively using a conjugate gradient method. Compared with the conventional TSK method, the proposed inversion strategy is free of TSK calculation and storage, making it more practical for large-scale problem. Compared with the adjoint traveltime tomography, the proposed method has a quasi-second-order convergent rate and a broader valid condition. Numerical examples demonstrate the effectiveness of the proposed method.
Key words:Rytov approximation/
Finite-frequency traveltime sensitivity kernel/
Wave-equation traveltime tomography/
First-arrival/
Implicit matrix-vector product/
Gauss-Newton method
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http://www.geophy.cn/data/article/export-pdf?id=dqwlxb_15018
