层状介质二维井间电磁成像

Two-dimensional crosshole electromagnetic imaging of layered media

根据分层介质中波的传播规律,利用均匀介质中的三维张量格林函数推导出二维情况下分层介质的张量格林函数,它是一个对kx的一维Sommerfeld积分。准确求取这一积分后,可以方便地利用迭代等方法反演出井间的电导率。给出了利用上行波和下行波方式表达的界面反射和折射张量函数及其各分量。通过积分方程方法对埋置于有8个分层的两个垂直方向电导率异常体模型进行了计算,反演结果与原模型基本吻合,有效地实现了层状介质中二维井间电磁成像。

The two-dimensional Green tensor for layered media was deduced from the three-dimensional Green dyadic for homogeneous according to the propagation laws of waves in layered media. The tensor is one-dimensional Sommerfeld integral over k\-x. After the integral has been precisely valued, the electric conductivity of the media laying between the holes can be inversed by the methods such as iteration or others. Each component of the tensors representing the reflection and refraction at the interfaces were expressed in the form of upgoing and downgoing wave. Using the integral equation method, a case of two vertical abnormal conductors embedded in a 8-layered medium was calculated. The inversion image well matches the original model, showing that the mentioned method can perform two-dimensional crosshole electromagnetic imaging well for layered media.