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第 38 卷 第 3 期                                                                       Vol. 38, No. 3
             2019 年 5 月                          Journal of Applied Acoustics                      May, 2019

             ⋄ 2018年度检测声学会议优秀论文 ⋄



                      基于鞍点法与互易性的远探测波场模拟                                                          ∗






                                                   许家旗 胡恒山            †


                                              (哈尔滨工业大学力学系       哈尔滨    150001)

                摘要 声波远探测中波场是非轴对称的，采用数值算法计算波场会耗费大量时间，无法满足实际测井数据实
                时处理的需求。为了解决这一问题，该文采用解析法分别计算辐射场和井外界面反射波激发的井内响应。首
                先利用鞍点法获得井内声源的远场辐射波场，并与实轴积分获得的精确结果进行比较验证解的正确性。然后
                将反射波等效为集中力的辐射波，利用集中力与井内声源的互易关系获得反射波激发的井内波场解，该解答
                与有限差分模拟结果一致。该方法为远探测的正演模拟和远探测结果的及时评价提供了有效手段。
                关键词 声波远探测，鞍点法，互易性，渐近解
                中图法分类号: P631.8+14           文献标识码: A         文章编号: 1000-310X(2019)03-0293-08
                DOI: 10.11684/j.issn.1000-310X.2019.03.002




                  Wave filed simulation of single-well imaging based on method of steepest
                                               descent and reciprocity




                                                 XU Jiaqi HU Hengshan

                              (Department of Mechanics, Harbin Institute of Technology, Harbin 150001, China)

                 Abstract  The wave field of single-well imaging is asymmetric. It takes a lot of time to calculate the wave field
                 by numerical algorithm, which cannot meet the needs of real-time processing of logging data. In this study,
                 the analytical solution to the radiation wave from the source in a borehole and the borehole wave excited
                 by reflections from the interface outside the borehole is obtained. Firstly, the far-field radiated wave field of
                 borehole acoustic source is obtained by steepest descent method, and the correctness of the solution is verified
                 by comparing with the exact results obtained by real-axis integration. The reflected wave is taken as equivalent
                 to the radiated wave of a concentrated force. The asymptotic solution to the wave field in the borehole excited
                 by reflected wave is obtained using the reciprocal relationship between the concentrated force and the source
                 in the borehole. The results agree with those obtained by finite difference method. This method provides an
                 efficient tool for feasibility study for downhole acoustic distant detection and quick evaluation of the detection
                 results.
                 Key words Single-well imaging, Steepest descent method, Reciprocity, Asymptotic solution






             2018-12-24 收稿; 2019-02-20 定稿
             国家自然科学基金项目 (11734017)
             ∗
             作者简介: 许家旗 (1994- ), 男, 河南商丘人, 博士研究生, 研究方向: 弹性动力学。
              通讯作者 E-mail: hhs@hit.edu.cn
             †
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