An improved total variation type regularization for geophysical inverse problems

Different types of regularization have been developed to obtain stable solutions to linear inverse problems. Among these total variation (TV) leads to piecewise constant solutions and has received much attention for solving inverse problems arising in geophysical studies. However, the method shows staircase effects and is not suitable for the models including smooth regions. To overcome the staircase effect, we present a method, which employs a local order difference operator in the regularization term. Experimental result from the real seismic traveltime tomography show that the proposed inversion method is able to retain the smooth regions of the regularized solution, while preserving sharp transitions presented in it.