基于一种反余切紧凑约束的电磁波走时层析研究

电磁波走时层析可用于空洞和孤石等离散块体异常的探测中.在传统电磁波走时层析中,通常采用一个低阶差分泛函来稳定反演过程,而这类泛函都具有光滑约束的性质,在成像结果中难以对此类离散块体异常进行准确的解释.本文基于Tikhonov正则化思想,提出了一种反余切泛函,该泛函具有紧凑约束的性质且无需选择一个聚焦因子.结合弯曲胖射线层析理论和重加权正则化共轭梯度反演算法,对两个理论模型进行了成像效果研究.与低阶差分泛函和最小支撑泛函的成像结果相比,该方法能够更好地突出异常的边界,成像结果中的虚假异常也要更少.同时,还分析讨论了激发电磁波的中心频率以及数据噪音对成像结果的影响.此外,针对一个地下连续墙墙体内部缺陷的现场模型,利用该方法取得了理想的成像结果,良好地揭示了缺陷的形态和位置.

Traveltime tomography of electromagnetic waves based on an anti-cotangent compactness constraints

The traveltime tomography of electromagnetic waves can be used to detect discrete blocky anomalies, such as voids and boulders. The traditional traveltime tomography of electromagnetic waves usually uses the low-order differential operator with smooth constraints to stable the inversion process, finally resulting in a smooth solution, but leading to uncertainties in data interpretation. Here, we propose an anti-cotangent functional based on Tikhonov' regularization theory, which has the property of compactness constraints and no longer requires the user select a focusing parameter. We invert two theoretical models by the bending fat ray theory and Reweighted Regularized Conjugated Gradient (RRCG) algorithm. Compared to the result by low-order differential and minimum support functional, the proposed approach can better highlight the boundary of anomalies and suppress artifacts. In addition, some influence factors to the tomography results, including central frequency of excited electromagnetic waves and the noise contained in the data are also discussed. Furthermore, we apply the proposed method to a diaphragm wall model and obtain an interpreted image, which well reveals the shape and location of the defects distributed in the wall.