起伏地形条件下电阻率法三维反演

A discussion on 3D inversion result of the resistivity method under the condition of undulate topography

地形起伏下的三维反演问题是当前电阻率法研究的一个难题。为了更好地解决上述问题,采用加权正则化共轭梯度法实现起伏地形三维电阻率反演算法。该方法引入了加权正则化思想,显著降低了迭代时目标函数发散的问题,提高了反演稳定性。对比了两种消除反演中地形影响的方法,结果表明,直接带地形的电阻率法三维反演具有更好的分辨率,能有效地消除地形所造成的误差,但在起伏角度偏大,如河流、堤坝等接近垂直角度时,使用此方法会使得反演发散得不到满意的结果;此时采用基于地形校正的方法有一定的效果。

3D resistivity inversion under the condition of undulate topography is a difficult problem in the current resistivity method. In order to solve this problem, the authors use a weighted regularized conjugate gradient method to accomplish three-dimensional resistivity inversion algorithm of undulating terrain. The method introduces weighted regularization thought which can significantly reduce the prob-lem of the objective function iteration divergence and improve the stability of the inversion. A comparison of the two methods in elimina-ting topographic influence in the inversion shows that the direct use of the terrain resistivity method of 3D inversion can yield better res-olution, which can effectively eliminate the error caused by terrain. Nevertheless, under the condition that the rolling angle is almost vertical such as the cases of rivers and dams. The continual utilization of this method can hardly get a satisfactory result because it cau-ses the inverse divergence. In such cases, the use of topographic correction method has some advantageous effects.