Double-difference traveltime tomography with edge-preserving regularization and a priori interfaces

Conventional traveltime seismic tomography methods with Tikhonov regularization (L2 norm) typically produce smooth models, but these models may be inappropriate when subsurface structure contains discontinuous features, such as faults or fractures, indicating that tomographic models should contain sharp boundaries. For this reason, we develop a double-difference (DD) traveltime tomography method that uses a modified total-variation regularization scheme incorporated with a priori information on interfaces to preserve sharp property contrasts and obtain accurate inversion results. In order to solve the inversion problem, we employ an alternating minimization method to decouple the original DD tomography problem into two separate subproblems: A conventional DD tomography with Tikhonov regularization and a L2 total-variation inversion. We use the LSQR linear solver to solve the Tikhonov inversion and the split-Bregman iterative method to solve the total-variation inversion. Through our numerical examples, we show that our new DD tomography method yields more accurate results than the conventional DD tomography method at almost the same computational cost.