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第 38 卷 第 5 期                                                                       Vol. 38, No. 5
             2019 年 9 月                          Journal of Applied Acoustics                 September, 2019

             ⋄ 2018年度全国检测声学会议优秀论文 ⋄



               一维Marchenko自聚焦算法的数值解与解析解                                                                  ∗




                                胥利文      1,2,3  陈 浩    1,2,3†  张秀梅      1,3  王秀明      1,2,3



                                              (1 中国科学院声学研究所       北京   100190)
                                                (2 中国科学院大学      北京  100049)
                                         (3 北京市海洋深部钻探测量工程技术中心           北京  100190)
                摘要    Marchenko 自聚焦算法可以构造介质表面到介质内任一点的格林波场，这种算法仅仅需要边界上单边
                记录的反射响应和介质内任一点到介质表面的直达波数据。为了研究算法构造期望波场的具体过程，该文分
                别在数值解和解析解模型中求解耦合 Marchenko 方程组，利用解析解模型中的序列构造解释数值解中波形产
                生的具体原因。方程求解过程主要包括一维时域卷积和利用时间窗算子的截断效应求取聚焦函数和格林函
                数，其中卷积过程可以解释为利用聚焦函数来调制单边记录的波场相位。
                关键词     Marchenko 方程，卷积，相位调制，解析解
                中图法分类号: O429           文献标识码: A          文章编号: 1000-310X(2019)05-0757-10
                DOI: 10.11684/j.issn.1000-310X.2019.05.001




                       Numerical and analytical solution of one-dimensional Marchenko

                                               auto-focusing algorithm


                          XU Liwen 1,2,3  CHEN Hao  1,2,3  ZHANG Xiumei 1,3  WANG Xiuming   1,2,3
                               (1 Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China)
                                   (2 University of Chinese Academy of Sciences, Beijing 100049, China)

                (3 Beijing Engineering Research Center of Sea Deep Drilling and Exploration, Institute of Acoustics, Chinese Academy of
                                                 Sciences, Beijing 100190, China)

                 Abstract  The Marchenko auto-focusing algorithm can reconstruct the Green’s wave-field from the surface
                 to a subsurface point of the medium, it only requires the single-sided surface reflection and direct wave from a
                 point source in the medium to the surface. In order to study the specific process of constructing the desired
                 wave-field by this algorithm, the coupled Marchenko equations are solved in the numerical and analytical model
                 respectively, and the series in the analytical model is used to explain the causes of the waveform generation
                 in the numerical solution. The process mainly includes one-dimensional time-domain convolution and the use
                 of the truncation effect of the time window operator to obtain the focusing function and the Green’s function.
                 The convolution process can be interpreted as the use of the focusing function to modulate the phase of the
                 recorded wave-field.
                 Key words Marchenko equation, Convolution, Phase modulation, Analytical solution


             2018-11-09 收稿; 2019-07-16 定稿
             国家自然科学基金项目 (11574347, 11734017, 91630309, 41274134)
             ∗
             作者简介: 胥利文 (1990- ), 男, 甘肃陇南人, 博士研究生, 研究方向: 声波干涉算法。
              通讯作者 E-mail: chh@mail.ioa.ac.cn
             †
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