基于鞍点法与互易性的远探测波场模拟∗

In the acoustic wave remote detection, the wave field is non-axisymmetric. Using numerical algorithms to calculate the wave field consumes a large amount of time and cannot meet the requirements for real-time processing of actual logging data. To solve this problem, this paper uses an analytical method to calculate the radiation field and the in-well response excited by the reflection wave outside the well respectively. Firstly, the far-field radiation wave field of the in-well sound source is obtained by using the saddle point method and compared with the accurate result obtained by the integration along the real axis to verify the correctness of the solution. Then, the reflection wave is equivalent to the radiation wave of a concentrated force, and the in-well wave field solution excited by the reflection wave is obtained by using the reciprocity relationship between the concentrated force and the in-well sound source. This solution is consistent with the finite difference simulation result. This method provides an effective means for the forward simulation of remote detection and the timely evaluation of remote detection results.

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.