基于菲涅尔带理论的无线电波层析正则化方法研究

Regularization method of radio wave tomography based on Fresnel zone theory

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.

Radio-wave penetration method is one of the most popular methods for geological anomaly detection. Based on raybased theory and Simultaneous Algebraic Reconstruction Technique（ SIRT） method,the attenuation coefficients of coal seam are reconstructed. The electromagnetic wave frequency ranges from a few hundred thousand to a few megahertz is adopted,which leads to unsatisfied with high frequency approximation for ray path theory.And the inversion resolution using SIRT method is reduced by low SNR data and the poor geometry in mine tunnel. In our study,Fresnel zone theory,which includes interference effects of wave propagation,is used to compute theoretic field strength. The higher the frequency of the electromagnetic wave is,the smaller the Fresnel zone radius is. The Tikhonov regularization method for minimization problem is derived to inverse the attenuation coefficients. Different regularization parameters are tested to account for effect on model solutions and the trade-off value is used. Conclusions are reached from inversion experiment for theoretical models and field data. The resolution based on Fresnel zone theory is better than that based on ray path theory. The inversion results well confirm to the known geological anomalies,which shows the feasibility and reliability of the above method for the practical application.