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基于鞍点法与互易性的远探测波场模拟*

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许家旗,胡恒山.基于鞍点法与互易性的远探测波场模拟*[J].,2019,38(3):293-301
基于鞍点法与互易性的远探测波场模拟*
Wave filed simulation of single-well imaging based on method of steepest descent and reciprocity
投稿时间：2018-12-24修订日期：2019-04-27
中文摘要:
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，为远探测结果的及时评价提供了有效手段。
英文摘要:
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 for quick evaluation of the detection results.
DOI：10.11684/j.issn.1000-310X.2019.03.002
中文关键词:声波远探测,鞍点法,互易性,渐近解
英文关键词:Single-wellimaging, Methodof steepestdescent, Reciprocity, Asymptoticsolution
基金项目:国家自然科学基金项目 (11734017)
作者单位E-mail
许家旗哈尔滨工业大学力学系 哈尔滨hitgclx_xjq@163.com
胡恒山哈尔滨工业大学力学系 哈尔滨hhs@hit.edu.cn
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