RESIDUAL STATICS ESTIMATION: SCALING TEMPERATURE SCHEDULES USING SIMULATED ANNEALING1

Linearized residual statics estimation will often fail when large static corrections are needed. Cycle skipping may easily occur and the consequence may be that the solution is trapped in a local maximum of the stack-power function. In order to find the global solution, Monte Carlo optimization in terms of simulated annealing has been applied in the stack-power maximization technique. However, a major problem when using simulated annealing is to determine a critical parameter known as the temperature. An efficient solution to this difficulty was provided by Nulton and Salamon (1988) and Andresen et al. (1988), who used statistical information about the problem, acquired during the optimization itself, to compute near optimal annealing schedules. Although theoretically solved, the problem of finding the Nulton–Salamon temperature schedule often referred to as the schedule at constant thermodynamic speed, may itself be computationally heavy. Many extra iterations are needed to establish the schedule. For an important geophysical inverse problem, the residual statics problem of reflection seismology, we suggest a strategy to avoid the many extra iterations. Based on an analysis of a few residual statics problems we compute approximations to Nulton–Salamon schedules for almost arbitrary residual statics problems. The performance of the approximated schedules is evaluated on synthetic and real data.