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

Key words:  total variation regularization  classical Tikhonov regularization  hybrid regularization  3D electrical resistivity inversion

Abstract:

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 distinguish the target area from the background due to the smooth nature of the solution. In order to solve this problem, the classical 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 regularization 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 regularization. The improvement in 3D resistivity mapping is immediate, and then the method is further verified in practical engineering problems.