我国是世界上最大的煤炭生产和消费国家之一。开采过程中煤火导致煤自燃带来的矿井灾害是国家能源战略安全和生态文明建设的重大问题，煤自燃的监测与防治工作迫在眉睫。瞬变电磁法（Transient Electromagnetic Method, TEM）因其具有直接定位高温异常区的技术优势而备受关注。然而，在实际应用中，复杂起伏地形会对TEM的探测效果产生显著影响，使得电磁正演模拟结果与实测数据之间出现偏差，进而影响地质解释的准确性。为此，本文进行三维起伏地形下煤岩分层结构的瞬态电磁响应特性研究，实现高精度三维起伏地形煤岩分层模型的建立与瞬态电磁响应的高效计算。主要内容如下：

（1）基于双向梯度插值、赫斯特指数（Hurst）自适应调整与多尺度分形技术，提出了一种改进的分形布朗运动（Fractal Brownian motion, FBM）地形生成算法，实现了起伏地形的高精度模拟，生成的建模文件可直接应用于电磁计算，无需二次集成。相比于商业软件建模，本文方法建模时间缩短，提升了三维起伏地形的建模速度与模型质量。

（2）基于细化区域自动识别并根据地形确定网格细化程度，提出了一种新型亚网格FDTD（Finite-Difference Time-Domain, FDTD）方法，实现了起伏地表的局部细化。同时，允许在计算区域内根据条件指定位置实施网格加密。与现有的亚网格方法相比，该方法的计算内存占用和计算时间分别减少了42.5%和46%。

（3）基于本文所提的算法，实现了复杂地形条件下电磁场传播特性的精确模拟，并分析了不同复杂地形下模型的瞬态电磁响应。通过系统分析地表形态、煤层形态、地表-煤层双重复杂地形耦合特征及辐射源收发点装置布局等因素对瞬态电磁响应影响规律进行分析与总结。

本研究提出的方法为理解三维起伏地形对瞬态电磁响应的影响提供了高效、可靠的解决方案，对提高地质勘探的精度和有效性具有重要的实用价值。

China is one of the largest coal-producing and consuming countries in the world. The mine disaster caused by spontaneous coal combustion due to coal fire in the mining process is a major issue in the national energy strategy security and ecological civilization construction, and the monitoring and prevention of spontaneous coal combustion is urgent. The transient electromagnetic method (TEM) has attracted much attention because of its technical advantage in directly locating high-temperature anomalies. However, in practical application, the complex undulating terrain will have a significant impact on the detection effect of TEM, resulting in the deviation between the EM simulation results and the measured data, which in turn affects the accuracy of the geological interpretation. For this reason, this paper investigates the transient electromagnetic response characteristics of coal-rock layered structures in three-dimensional undulating terrain and realizes the establishment of a high-precision three-dimensional undulating terrain coal-rock layered model and the efficient calculation of transient electromagnetic response. The main contents are as follows:

(1) Based on two-way gradient interpolation, Hurst index adaptive adjustment, and multi-scale fractal technology, an improved Fractal Brownian motion (FBM) terrain generation algorithm is proposed, which realizes the high-precision simulation of undulating terrain, and the generated modeling files can be directly applied to electromagnetic calculations without the need for secondary integration. Compared with commercial software modeling, the method in this paper shortens the modeling time and improves the modeling speed and model quality of 3D undulating terrain.

(2) Based on the automatic identification of the refinement region and the determination of the mesh refinement degree according to the terrain, a new subgrid FDTD (Finite-Difference Time-Domain, FDTD) method is proposed to realize the local refinement of the undulating terrain. At the same time, it allows the implementation of grid encryption at specified locations within the computational area according to the conditions. Compared with the existing subgrid methods, the computational memory occupation and computation time of this method are reduced by 42.5% and 46%, respectively.

(3) Based on the algorithm proposed in this paper, accurate simulation of electromagnetic field propagation characteristics under complex terrain conditions is realized, and the transient electromagnetic response of the model under different complex terrain is analyzed. The transient electromagnetic response is analyzed and summarized by systematically analyzing the influence laws on the transient electromagnetic response of factors such as surface morphology, coal seam morphology, surface-coal seam double complex terrain coupling characteristics, and the layout of radiation source transceiver point devices.

The method proposed in this study provides an efficient and reliable solution for understanding the influence of three-dimensional undulating terrain on transient electromagnetic response, which is of great practical value for improving the precision and effectiveness of geological exploration.

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