瞬变电磁扩散场到虚拟波场的精细积分变换算法

现有的瞬变电磁解释与反演方法主要对电阻率参数进行解释,较难给出准确的地质构造信息.为了能够较多获得地质构造信息,可将瞬变电磁扩散场信号转换为虚拟波场信号,提高瞬变电磁法的分辨率.本文采用精细积分法,实现了瞬变电磁扩散场到虚拟波场的转换.将一个高度病态的线性方程组转换成求积分的过程,大大降低了解决病态问题的难度.积分步长...

A precise integration transform algorithm for transformation from the transient electromagnetic diffusion field into the pseudo wave field

The existing transient electromagnetic interpretation and inversion methods focus on the resistivity parameters, which are difficult to give accurate geological structure information. To solve this problem, the transient electromagnetic diffusion field signal can be transformed into a virtual wave field signal to improve the resolution of the transient electromagnetic method. In this paper, a precise integration method is proposed to realize the conversion of the transient electromagnetic diffusion field to the virtual wave field. It is found that by converting a highly ill-conditioned system of linear equations into an integration process, the difficulties related to solving ill-conditioned problems are greatly reduced. Besides, based on the premise of ensuring high accuracy results, the integration step lengths are exponentially increased by 2, and high computational efficiency is achieved. The applicability of the method proposed in this study is further improved by setting reasonable iteration stopping conditions. The calculations of the typical geoelectric models show that this method has high precision. Then, by reducing the distances between two wave peaks, it was proven that the method introduced in this study had better resolution. Furthermore, through the wavefield inverse transformations of diffusion fields containing noise, it is confirmed that the proposed method also has better noise-resistant capability. Finally, calculations of the pseudo wave fields of 3D models and field data permit to identify well the interfaces of 3D geological bodies, which further demonstrates that the method proposed in this study is stable and reliable. Compared with the preconditioned regularization method, the efficiency of the proposed method is improved by about 4 times. The relative error of the method in this work is within 5%, while the maximum relative error of PRCG can reach 40%~50%, and the accuracy can be improved by 10 times. In terms of resolution and stability, this method also shows better performance.