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无线电波透视法是常用的工作面地质构造探测方法之一,目前煤矿上多采用基于射线理论的联合代数重建(SIRT)层析方法反演介质电磁波衰减系数.由于发射的电磁波频率范围在几百千至几兆赫兹,基于高频近似的射线理论在模拟电磁波传播时存在局限性,而SIRT方法本身受矿井观测方式的限制,在垂直测线方向反演分辨率不高.本文研究基于菲涅尔带理论的正演方法,电磁波频率越高其第一菲涅尔带半径越小,即越接近射线条件;采用约束正则化方法进行层析成像,推导了Tikhonov正则化的最小化问题表达式,说明了正则参数的作用和意义,利用迭代反演法求最优折衷解.对不同异常模型及实际资料进行了层析成像实验,结果表明对于低频电磁波菲涅尔带理论分辨率优于射线理论,正则化方法具有更好的分辨率,识别出的异常构造基本吻合已知疑似构造位置,说明了其在实际应用中的可行性.
Radiowavefield perspective method is one of the most commonly used methods to detect the geologic structure of the working face, and the SIRT tomography method is often used in coal mines to inverse the electromagnetic wave attenuation coefficient of the medium.As the frequency range of the emitted electromagnetic wave is in the hundreds Thousand and several megahertz, ray theory based on high-frequency approximation has limitations in simulating electromagnetic wave propagation, but the SIRT method itself is limited by the observation mode of the mine and the inversion resolution in the vertical line direction is not high.In this paper, For the forward method of the band theory, the higher the frequency of the electromagnetic wave, the smaller the radius of the first Fresnel zone, that is, the closer to the ray conditions, the constrained regularization method is used for tomographic imaging. The minimization problem of Tikhonov regularization is derived , Illustrates the role and significance of the regular parameters and uses the iterative inversion method to find the optimal compromise.The tomographic imaging experiments on different abnormal models and actual data show that the theoretical resolution of the Fresnel zone is better than that of the radiation Theory, regularization method has a better resolution, the identified anomalous structure basically consistent with the known position of the suspected structure, indicating its actual Feasibility of use.