First-arrival Traveltime Tomography with Modified Total Variation Regularization

Abstract

The first-arrival traveltime tomography is a robust tool for near-surface velocity estimation. A common approach to stabilize the ill-posed inverse problem is to apply Tikhonov regularization to the inversion. However, the Tikhonov regularization method recovers smooth local structures while blurring the sharp features in the model solution. We present a first-arrival traveltime tomography method with modified total variation regularization to preserve sharp velocity contrasts and improve the accuracy of velocity inversion. In order to solve the minimization problem of the new traveltime inversion method, we decouple the original optimization problem into two subproblems: a standard traveltime inversion problem with the traditional Tikhonov regularization and a L2 total variation problem. We use conjugate gradient method and split-Bregman iterative method to solve these two subproblems, respectively. Our synthetic and field data examples show that the new method produces higher resolution models than the Tikhonov method for the models with sharp interfaces.