Convex constrained optimization for the seismic reflection tomography problem

The nonlinear seismic reflection tomography problem consists on minimizing the function g(p) = ||T − f(p)||22, where p is a vector containing the velocity model parameters and depth position of the reflectors, T contains the travel time of the rays, and f(p) is a nonlinear function that depends on the velocity of the subsurfaces. Recently a new approach, based on the spectral gradient method, was applied to find unconstrained local minimizers of g(p). This new idea requires very low storage and computational cost, but it presents an erratic behavior when applied to ill-conditioned problems. In this work, we combine the new low cost iterative technique with the recently proposed spectral projected method for convex constrained optimization to improve the convergence of the process, and to avoid the erratic behavior by imposing regularity into the optimization problem. Preliminary numerical experiments are also presented on synthetic data sets to illustrate the advantages of the new combined scheme.