Dynamic smoothing in crosswell traveltime tomography

Variable‐size (dynamic) smoothing operator constraints are applied in crosswell traveltime tomography to reconstruct both the smooth‐ and fine‐scale details of the tomogram. In mixed and underdetermined problems a large number of iterations may be necessary to introduce the slowly varying slowness features into the tomogram. To speed up convergence, the dynamic smoothing operator applies adaptive regularization to the traveltime prediction error function with the help of the model covariance matrix. By so doing, the regularization term has a larger weight at initial iterations and the prediction error term dominates the final iterations with a small regularization term weight. In addition, it is shown that adaptive regularization acts by reweighting the adjoint modeling operator (preconditioning) and by providing additional damping. Comparisons of two dynamic smoothing operators, the low‐pass filter smoothing and the multigrid technique, with the fixed‐size (static) smoothing operators show that the dynamic smoothing operator yields more accurate velocity distributions with greater stability for larger velocity contrasts. Consequently, it is a preferred choice for regularization.