Study on global optimization methods for wave equation inversion problems
波动方程反演的全局优化方法研究

The wave equation inversion in complex media is an important research in geophysics.This problem is usually described as objective function optimization,which has many difficulties such as multi-parameter,nonlinear in the parameter and ill-posedness.Both local-optimization and global-optimization methods are unable to achieve fast global optimization.This paper gives a brief introduction of theoretical foundation and research advances in seismic exploration inversion problem.The optimization solutions of inversion problem are discussed and the difficulties are analyzed.Finally,a new deterministic optimization method is presented.All the local optimization solutions(sets) can be determined after finite times of parameter space identification and partition procedures.Based on multi-scale landscape analysis of complex objective functions,a multi-scale parameter space partition method is proposed.The new method has a very fast convergence speed and the optimization solution is independent on the selection of initial solutions.This is a new research direction of nonlinear global optimization methods.