Resistivity Inversion Research Based On Hybrid Norms

The resistivity inversion of geophysics is a important ill-posed problem. In this paper, we investigate the reconstruction of a piecewise constant resistivity in 2D by using a hybrid regularization. The hybrid regularization we used combines a total variation regularization and a classical Tikhonov regularization, and it contained the advantages of two single regularization method. In this paper, the interior point method is considered for solving the hybrid regularization model. Based on derivation and simulation,the interior point method can be applied to the hybrid regularization. Other than the fast gradient descent method, the stability and veracity of the the interior point method is very good. So it avoided the impaction of variable parameter. The interior point method solved the problem of hybrid regularization very well, and make the result of the problem better.