瞬变电磁波场转换算法的改进

地球物理电磁场数据与虚拟地震波场数据之间存在数学上的等效转换关系，通过这种等效转换，可有效提高地球物理电磁法对地下目标体分界面的辨识度.但是这种转换在数学上属于不适定问题，可采用奇异值分解法处理.由于大奇异值控制计算矩阵的主要信息，小的奇异值控制计算矩阵的次要信息，传统的截断奇异值分解法只保留大奇异值，而忽略小的奇异值，导致数值解不够精确.本文提出一种新的修正方案——改进截断奇异值法，采用岭估计方法计算由小的奇异值引起的虚拟波场.模型计算结果表明：改进截断奇异值法比传统的奇异值分解法得到的波场转换结果更好，对某煤矿采空区探测数据进行了处理，成功分辨出采空区分界面.

An improvement to the transformation algorithm for the transient electromagnetic field

Mathematically, there exist an effective transformation relationship between the electromagnetic (EM) and virtual seismic data fields, by which one can effectively to identify the underground target's interfaces using the EM method. Such transformation is a uncertain problem, which can be treated by the singular value decomposition (SVD) method. Because large singular values control main information of inversion matrix, small singular values are usually less important. So one usually ignores small singular values during singular value decomposition caluculation, leading to low precision results. To solve this problem, a new algorithm named the modified truncated singular value decomposition method was proposed, in which the ridge estimation method is used to calculate the virtual wave field caused by small singular values. The results of model calculation show that the improved truncated singular value method is better than the traditional singular value decomposition method. Using this new method, the survey data from a gob area of a coal mine was processed, and the interface of this area was successfully identified.