| 利用Munk公式和海底反射走时反演深海水体速度:理论 |
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| 引用本文： | 孙建国.利用Munk公式和海底反射走时反演深海水体速度:理论[J].吉林大学学报(地球科学版),2021,51(1):1-12. |
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| 作者姓名： | 孙建国 |
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| 作者单位： | 吉林大学地球探测科学与技术学院, 长春 130026 |
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| 基金项目： | 国家重点研发计划（2019YFC0312004） |
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| 摘 要： | 为解决深海水体速度建模问题,建立了两个利用Munk公式和海底反射走时反演深海水体速度的反演理论,一个是射线走时反演理论,另一个是波动方程走时反演理论。具体地讲,是建立了地震波走时关于Munk参数的Fréchet导数和海森矩阵公式。为得到射线走时的Fréchet导数和海森矩阵,利用了3种不同的方法,即变分法、微扰法和Taylor级数展开法。这3种方法在理论上完全等价,其最终结果也完全相同。为得到波动方程走时反演理论中的Fréchet导数和海森矩阵,利用复合函数求导的链式法则对文献中的有关结果进行变换,以将其从面向速度本身的Fréchet导数和海森矩阵变换为面向Munk参数的Fréchet导数和海森矩阵。此外,还提出了实现利用Munk公式和海底反射走时构建深海水体声速剖面的5个策略,包括利用解析公式计算海底反射走时的由下至上的射线追踪策略,选用最简单的海底边界条件把数值模拟区域限定为水体的策略,用已知的深海声道轴深度和交替反演策略将四参数反演问题转简化为单参数反演问题的策略,由点到面,利用一维声速剖面公式实现深海水体的维速度建模的策略,以及用最简单的算法实现走时反演的最优化计算策略等。与常规走时反演相比,利用Munk公式进行的海底反射走时反演最多只需要反演4个参数,并可利用交替反演将四参数反演化为单参数反演,大大地减少了走时反演的计算量。
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| 关 键 词： | 深海水体 速度建模 海底反射 走时反演 Fréchet导数 海森矩阵 |
| 收稿时间： | 2020-04-16 |
Inversion of the Deep Sea Water Velocity by Using Munk Formula and Seabed Reflection Travel Time |
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| Sun Jianguo.Inversion of the Deep Sea Water Velocity by Using Munk Formula and Seabed Reflection Travel Time[J].Journal of Jilin Unviersity:Earth Science Edition,2021,51(1):1-12. |
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| Authors: | Sun Jianguo |
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| Institution: | College for GeoExploration Science and Technology, Jilin University, Changchun 130026, China |
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| Abstract: | Using ideas from computational electromagnetics and the basic procedure from the domain decomposition method, we present a biaxial parabolic approximation method for enlarging the angle domain in which the parabolic approximation to the acoustic wave equation is multiple applied and that can be used for migrating data with super-wide angles. Mathematically, the biaxial approximation is a special case of the multiaxial parabolic approximation, and thus can be straightforwardly extended to multiaxial approximations. In detail, we first divide the subsurface into several fan-shaped subdomains and use the axis of each subdomain as the local wave propagation direction. Then, we make a parabolic approximation to the wave equation in each subdomain with respect to the corresponding symmetry axis and compute the forward-propagating wave alternately using a high-order parabolic approximated wave equation in two subdomains. Finally, we use the computed forward-propagating wave as the boundary condition for calculating the back-scattered wave and Green's function by applying the thin slab approximation. Compared with most one-way methods, the proposed method can deal with the strong velocity contrast in the horizontal direction at a large scattering angles. Moreover, compared with certain full-wave methods that have been published in recent years, the proposed method is considerably more efficient and sacrifices only a little in terms of accuracy. Numerical results from comparisons with models of different complexities demonstrate that our method is cost-effective and has considerable potential for use in seismic modeling and imaging. |
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| Keywords: | deep sea water body velocity model building seabed reflection traveltime inversion Fréchet derivative Hessian matrix |
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