A fast hybrid algorithm for spectral inversion

Abstract

Summary A matrix equation of spectral inversion was derived, which is essentially a simultaneous inversion of nonlinear problem aiming at layer positions and linear problem aiming at reflection coefficients. If linearization inversion techniques are used to invert these parameters, the ultimate solution is heavily dependent on the choice of initial model. If global inversion techniques are used, not only is the accuracy low, but also the convergence speed is slow. In view of these defects, a fast hybrid algorithm for spectral inversion was proposed. As to reflection coefficients, generalized inverse method, which makes the parameters need searching globally reduced by half, was adopted. By doing this, inversion speed can be improved greatly. Meanwhile, Particle Swarm Optimization (PSO) with constriction factor was adopted to globally invert layer positions for the purpose that the probability of converging to global solution can be improved. In this process, if particles hardly update to the vicinity of global solution as iteration time increases, random scattering was conducted. On the basis of best-so-far layer positions and reflection coefficients, Levenberg-Marquardt (L-M) algorithm was followed so as to make the accuracy further higher. The model results validated the fast hybrid algorithm’s feasibility and efficiency. Compared with pure PSO and pure L-M method, it has the attributes of faster convergence speed as well as higher accuracy.