适用于粗糙介质的瞬变电磁法三维正演研究

    Study on 3D forward modeling of transient electromagnetic method for rough media

    • 摘要: 为了分析介质内部孔隙、裂隙等微观空间结构对瞬变电磁场扩散的影响规律,基于频谱法和 Riemann−Liouville 算子在频率域的解析形式,提出一种适用于粗糙介质的瞬变电磁三维正演方法。以半空间模型为例,通过对比一维解析解与三维数值解验证算法正确性,进而以层状、柱状及断层破碎带 3 种三维模型为研究案例,深入探究粗糙度对瞬变电磁场扩散规律及探水工作的潜在影响。相较于传统模型,粗糙均匀半空间模型在瞬变电磁响应早期阶段响应值更低,晚期衰减曲线斜率更小,一定时间后瞬态响应值反超传统模型;特定参数下,粗糙介质模型单点瞬变电磁响应在双对数坐标系中近乎线性衰减,与均匀半空间扩散规律相似,低阻体识别难度大,而传统模型瞬变电磁响应经历缓慢、快速、缓慢衰减 3 个阶段,对低阻体反应更直接;粗糙度越大,对瞬态响应影响越显著,会导致含水区域勘探中异常识别难度增加或反演结果失真。在应用瞬变电磁法开展水文地质调查时,需结合钻井揭示的地层岩性及其岩石分形维数评估地下粗糙度,综合考量其对瞬态响应的影响,可为找水工作者识别含水体提供参考,助力提升煤矿等场景探水工作的准确性与安全性。

       

      Abstract: To investigate the influence of microscopic spatial structures such as pores and fractures inside media on the diffusion law of transient electromagnetic fields, a 3D forward modeling method for transient electromagnetics applicable to rough media is proposed based on the spectral method and the analytical form of the Riemann-Liouville operator in the frequency domain. Taking the half-space model as an example, the correctness of the algorithm is verified by comparing the 1D analytical solution with the 3D numerical solution. Furthermore, three 3D models including layered, columnar and fault fracture zone models are used as cases to deeply explore the potential effects of roughness on the diffusion law of transient electromagnetic fields and water detection. Compared with the traditional model, the rough homogeneous half-space model presents a lower response value at the early stage of transient electromagnetic response and a smaller slope of the attenuation curve at the late stage, and the transient response value exceeds that of the traditional model after a certain time. Under specific parameters, the single-point transient electromagnetic response of the rough medium model attenuates almost linearly in the log-log coordinate system, which is similar to the diffusion law of the homogeneous half-space, making it difficult to identify low-resistivity bodies. In contrast, the transient electromagnetic response of the traditional model undergoes three stages: slow, fast and slow attenuation, with a more direct response to low-resistivity bodies; the greater the roughness, the more significant the impact on the transient response, which will increase the difficulty of anomaly identification or distort the inversion results in water-bearing area exploration. When applying the transient electromagnetic method to hydrogeological surveys, it is necessary to evaluate the underground roughness combined with the formation lithology revealed by drilling and its rock fractal dimension, and comprehensively consider its influence on the transient response. This can provide a reference for water prospectors to identify water-bearing bodies and help improve the accuracy and safety of water detection in coal mines and other scenarios.

       

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