Rapid Determination of the Critical Temperature in Simulated Annealing Inversion

Knowledge of the critical temperature, T*, the temperature at which a phase change occurs, greatly improves the efficiency of simulated annealing when used for optimization or inversion. A numerical method of accurately determining T* in a relatively short computation time has been developed. This method is used to recover the seismic soundspeed profile from wavefield data, a problem in which cycle skipping causes many local minima of the energy function and the averaging of the medium by finite length waves results in many states with similar energies. Computations indicate that it is cost-effective to spend about 80 percent of the computing budget looking for T* instead of annealing, and that in the course of finding T* many states with energies near the global minimum will also be found. The a posteriori probability distribution of the solution has been constructed from trial solutions generated at T*.