正则化方法在无线电波层析中的应用

无线电波透视法是常用的工作面地质构造探测方法之一，目前普遍使用的SIRT方法层析分辨率不高。本文采用约束正则化方法，推导Tikhonov正则化和全变差正则化的最小化问题表达式，讨论影响层析结果的主要因素，对典型理论模型进行了层析成像实验。结果表明：正则化方法具有比SIRT方法更好的分辨率；射线条数越多、噪声水平越低，层析分辨率越高；Tikhonov正则化在正则参数增大时层析结果更光滑，减小时则更贴近异常，全变差正则化与其相反。最后对实际坑透数据进行层析，识别出的异常构造基本吻合已知疑似构造位置，从而说明正则化方法在无线电波透视应用中的可行性。

Application of Regularization Method in Radio Wave Tomography

Radio-wave penetration method is one of the most popular methods for geological detection. Based on Simultaneous Algebraic Reconstruction Technique (SIRT) method, the attenuation coefficients of coal seam are reconstructed. But the inversion resolution for SIRT tomography method is reduced by the poor geometry and low SNR data acquired in mine tunnel. In our study, the Tikhonov and Total Variation (TV) regularization methods for minimization problem are derived to inverse the attenuation coefficients and the influence factors of inversion results are discussed to account for effect on model solutions. Conclusions are reached from inversion experiment for theoretical models and field data. Regularization methods have better inversion resolution than SIRT method. More fold and higher SNR are important factors to obtain high resolution result. For Tikhonov regularization method, increasing regularization parameter makes the inversion result smoother, while decreasing parameter causes the result closer to the geological anomalies. TV regularization method has opposite property. The inversion result for field data well conform to the known geological anomalies, which shows the feasibility and reliability of the two regularization methods for practical application.