从瞬变电磁扩散场到拟地震波场的全时域反变换算法

A new algorithm for full-time-domain wave-field transformation based on transient electromagnetic method

将瞬变电磁满足的扩散方程转变为波动方程,然后利用地震类成像方法实现瞬变电磁虚拟波场成像,是实现瞬变电磁三维反演的有效手段之一.为了实现由扩散场到虚拟波场的转换,文中采用预条件正则化共轭梯度法求解波场反变换问题.首先,对几种离散方式进行比较,采用条件数最小的离散方式进行离散;然后选择最优的正则化参数,并利用超松弛预条件技术对系数矩阵进行预条件处理;最后,利用共轭梯度法进行迭代求解.超松弛预条件有效降低了系数矩阵的条件数,正则化方法使得反变换得到的波场稳定、可靠,共轭梯度法能够保证计算快速收敛.将反变换结果与已知虚拟波场函数对比,证明算法稳定、可信.将文中算法结果与前人研究结果进行对比,说明方法效果.通过实测数据的波场变换处理给出了文中方法的实际应用效果.结合反变换算法,对不同参数模型进行分析,总结了虚拟波场在色散介质中的传播规律.

The wavefield conversion is a useful way to achieve pseudo-seismic interpretation for Transient Electromagnetic Method （TEM）. We adopt the precondition regularization conjugate gradient method to realize the full-domain wavefield transformation from diffusion equation to wave equation. The over relaxation pre-conditioned process effectively reduces the condition number of the coefficient matrix, while Regularized Conjugate Gradient Method （RCG） helps run the inverse transformation of wave-field in full time-domain. The comparison between the results of inverse transformation and the known wave-field functions shows that the algorithm is stable and reliable. Comparison of the results with those of previously proposed sectionalized regularizationshows that the method in this paper is very effective. Combined with the algorithm of inverse transformation, we analyse the characteristics of the virtual wave-field for layered earth models and summarize its propagation properties. The wave-field transformation of the survey data processing results illustrates the effect of the practical application of this method.