电性源瞬变电磁有限差分偏移成像方法

Finite difference transient electromagnetic migration imaging for grounded sources

目前,瞬变电磁数据的主要处理结果是给出地下介质的(视)电阻率信息,较难给出清晰的地质界面信息.本文基于有限差分偏移成像原理,实现了电性源瞬变电磁虚拟波场的偏移成像技术.根据瞬变电磁扩散场与虚拟波场之间的数学关系,本文使用精细积分法对第一类Fredholm积分方程求解,然后消除直达波,得到只含有地层反射波的虚拟波场.在此基础上,本文从时间域波动方程出发,对上行波的一级近似方程反向外推,得到时间-空间域二维与三维的波场递推公式.通过求解地下空间的波场,并使用反褶积方法削弱虚拟波场的波形展宽效应,从而提高对地质界面的纵向分辨率,获得较为准确的地质界面信息.本文分别采用均匀半空间模型、D型模型、HK型模型以及两层含水采空区模型对本文方法进行验证,并对实测数据进行处理,偏移成像的结果与地质资料相吻合,说明瞬变电磁有限差分偏移成像方法在识别电性界面以及地层特征方面具有可行性.

The currently major interpretation approach of transient electromagnetics is to provide information on the(apparent) resistivity of the underground medium, and it is challenging to provide detailed information on the geological interface. In this paper, based on the finite-difference principle, the migration imaging technology of the transient electromagnetic pseudo wavefield of the grounded source is achieved. According to the mathematical relationship between the transient electromagnetic diffusion field and the pseudo wavefield, the precise integration method is used to solve the first type of Fredholm integral equation, and then the direct wave is eliminated, and the pseudo wavefield containing only the ground reflection wave is obtained. Based on this, the 2D and 3D wavefield recursion equations in the time-space domain are derived by backward extrapolation of the first-order approximation equation for upcoming wave fields. By solving the wave field of underground space and using the deconvolution method to weaken the wave broadening effect of the pseudo wavefield, the longitudinal resolution of the geological interface can be improved and more accurate information of the geological interface can be obtained. The uniform half-space model, the D type model, the HK type model, the two-layer water-bearing goaf model, and field data are all used to verify the approach proposed in this paper. The results of the migration imaging are consistent with the geological data, indicating the transient electromagnetic finite-difference migration imaging method is feasible in identifying electrical interfaces and stratum features.