基于混合正则化的最小二乘三维电阻率反演成像

Least square method based on hybrid regularization for 3D resistivity inversion imaging

基于经典Tikhonov正则化(classical Tikhonov regularization)的最小二乘反演是三维电阻率反演的主要方法。对于电阻率分片连续的地质体,由于光滑反演解的光滑性使得目标区域与背景区域间边界模糊,不能很好地体现异常体的形态信息和位置信息,成像效果不好。将总变分正则化(total variation regularization)与经典Tikhonov正则化结合,提出混合正则化反演方法,通过模型分析比较经典Tikhonov正则化、TV正则化、混合正则化在反演结果上的不同,证明了引入混合正则化约束的最小二乘反演既保持了经典Tikhonov正则化方法解的稳定性,又具有TV正则化方法解的保边缘性,有效地改善了三维电阻率成像效果。最后将混合正则化的反演方法应用到实际工程,验证了该方法的有效性和实用性。

The smooth least-squares method based on the classical Tikhonov regularization method is the main method in 3D resistivity inversion. For the geological body whose resistivity is piecewise continuous, this method however fails to distin-guish the target area from the background due to the smooth nature of the solution. In order to solve this problem, the classi-cal Tikhonov regularization and the total variation regularization ( TV regularization ) were combined and introduced into the least squares inversion method. Three inversion results based on classical Tikhonov regularization, total variation regulariza-tion and the new hybrid regularization were compared. It is shown that the least square method based on hybrid regularization retains both the stability of the classical Tikhonov regularization and the edge-protected property of the total variation regulari-zation. The improvement in 3D resistivity mapping is immediate, and then the method is further verified in practical engi-neering problems.