| 一阶Rytov近似有限频走时层析 |
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| 引用本文： | 冯波,罗飞,王华忠.一阶Rytov近似有限频走时层析[J].地球物理学报,2019,62(6):2217-2226. |
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| 作者姓名： | 冯波 罗飞 王华忠 |
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| 作者单位： | 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 |
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| 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. |
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| 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.
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| 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 |
| 收稿时间： | 2018-09-11 |
Wave equation traveltime tomography using Rytov approximation |
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| FENG Bo,LUO Fei,WANG HuaZhong.Wave equation traveltime tomography using Rytov approximation[J].Chinese Journal of Geophysics,2019,62(6):2217-2226. |
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| Authors: | FENG Bo LUO Fei WANG HuaZhong |
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| Institution: | Wave Phenomena and Intelligent Inversion Imaging Group(WPI), School of Ocean and Earth Science, Tongji University, Shanghai 200092, China |
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| 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. |
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| Keywords: | Rytov approximation Finite-frequency traveltime sensitivity kernel Wave-equation traveltime tomography First-arrival Implicit matrix-vector product Gauss-Newton method |
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