巷−孔瞬变电磁自适应波场反变换及虚拟波场特征

Self-adaptive inverse wavefield transform and derived pseudo-wavefield characteristics under roadway-borehole observation of transient electromagnetic data

  • 摘要:
    目的 针对巷道开挖轮廓线外侧含水层不易被探查的难题,采用巷−孔瞬变电磁观测抵近探查与波场变换相结合的方式,同时接收来自前方与开挖轮廓线外的探测信号并突出含水层的边界信息。为获取波场运动学特征合理、对地层电性结构变化敏感的虚拟波场,提出一种自适应波场反变换算法,从而提高巷−孔瞬变电磁数据波场反变换的精度与效率。
    方法 针对瞬变电磁波场变换核函数动态范围大、反变换方程病态程度高的固有难题,利用波场变换核函数在无穷区间上的解析解,提出一种根据瞬变电磁采集时间等参数自动求取波场反变换积分区间的方法,最大程度压制核函数的动态范围;进而基于精细积分方法建立积分步长与迭代过程自适应的波场反变换方程求解算法,将病态方程组的求解转化为稳定的积分求解问题。对开挖轮廓线外侧的含水层,采用有限体积法对其响应信号进行正演模拟并获取其垂直磁场分量的虚拟波场记录;同时也对井下实测数据采用同样的算法进行波场反变换。
    结果 获取的虚拟波场记录具有合理的波场运动学特征,虚拟波场记录中的反射波轨迹与单炮地震记录的时距曲线存在合理的相似度;在数值精度方面,虚拟波场的回代数据与正演/实测数据具有较高的吻合度,其最大相对误差均小于10%。
    结论 在巷−孔观测模式下,所提出的自适应波场反变换方法能够获取物理意义明确、数值精度可靠的虚拟波场记录,虚拟波场对于电性差异明显的含水层边界响应敏感,从而为进一步开展虚拟波场成像提供了可靠的数据支持。

     

    Abstract:
    Objective  To address the challenge of detecting aquifers outside the roadway excavation contour, this study combined the close-range detection via roadway-borehole transient electromagnetic (TEM) method with the wavefield transform. This will help simultaneously receive detection signals in front of the mining face and outside the roadway excavation contour while also highlighting the boundary information of aquifers. Moreover, to obtain a pseudo-wavefield featuring both reasonable kinematic characteristics and high sensitivity to changes in the electrical structures of strata, this study proposed a self-adaptive algorithm of inverse wavefield transform, thereby improving the accuracy and efficiency of the inverse wavefield transform of roadway-borehole TEM data.
    Methods The TEM wavefield transform faces some inherent limitations, such as a large dynamic range of the kernel function and high ill-posedness of the inverse transform equation. To address these challenges, this study, using the analytical solutions of the kernel function of wavefield transform over an infinite interval, proposed a method to automatically determine the interval of integration for inverse wavefield transform based on parameters such as the acquisition time of TEM data. The proposed method can minimize the dynamic range of the kernel function. Furthermore, using the precise integral method, this study developed an algorithm for solving inverse wavefield transform equations based on a self-adaptive step size of integration and iteration process, thus converting the solving of the ill-conditioned system of equations into solving an integral stably. For aquifers outside the roadway excavation contour, their TEM response signals were determined through forward modeling using the finite volume method. Accordingly, the pseudo-wavefield records of their vertical magnetic field components of TEM data were obtained. Moreover, the inverse wavefield transform of measured TEM data from boreholes was also conducted using the same algorithm.
    Results  The results indicate that the obtained pseudo-wavefield records exhibited reasonable kinematic characteristics. The reflected wave trajectories in the pseudo-wavefield records were reasonably similar to the time-distance curves in the single-shot seismograms. Regarding numerical accuracy, the back substitution results of the pseudo-wavefield data were highly consistent with the forward modeling-derived or measured data, with the maximum relative errors all below 10%.
    Conclusions  Under the roadway-borehole observation mode of TEM data, the proposed self-adaptive algorithm of inverse wavefield transform enables the acquisition of pseudo-wavefield records with clear physical significance and reliable numerical accuracy. Furthermore, the obtained pseudo-wavefield is highly sensitive to the aquifer boundaries with significant electrical contrasts, providing robust data support for further pseudo-wavefield imaging.

     

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