| 胥利文,陈浩,张秀梅,王秀明.一维Marchenko自聚焦算法的数值解与解析解研究*[J].,2019,38(5):757-766 |
| 一维Marchenko自聚焦算法的数值解与解析解研究* |
| Numerical and analytical solution of one-dimensional Marchenko auto-focusing algorithm |
| 投稿时间：2018-11-09 修订日期：2019-09-03 |
| 中文摘要: |
| 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，本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。 |
| 英文摘要: |
| 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. |
| DOI：10.11684/j.issn.1000-310X.2019.05.001 |
| 中文关键词: Marchenko方程，卷积，相位调制，解析解 |
| 英文关键词: Marchenko equation, Convolution, Phase modulation, Analytical solution |
| 基金项目:国家自然科学基金项目 |
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