First arrival travel time tomography has achieved wide application. However, tomographic resolution is insufficient because geometry constraints cause rays to be unevenly distributed in the velocity model. The variable damping constraint method adopts uneven priori information to match uneven data distribution which can lessen the correlation between velocity correction values and ray coverage density. In this paper, we combine the variable damping constraint with a smoothness constraint which is added into the regularization equations in velocity inversion to avoid instability caused by only using the variable damping constraint method. The alpha-trimmed-mean filter is used to smooth and denoise intermediate results in the velocity inversion process. We use the LSQR algorithm to enhance the convergence rate and suppress error propagation in solving linear equations. In this paper, we apply the proposed tomographic method to perform velocity inversion using VSP data. The application in recovery test of the checkerboard model and velocity inversion of real VSP data show that the variable damping constraint method can improve tomographic quality because it can solve the effects of uneven ray coverage. In addition, the examples show that the tomographic result near geophones is much more reliable than other areas in the velocity model.
