波动方程反演的全局优化方法研究

Study on global optimization methods for wave equation inversion problems

复杂介质波动方程反演是地球物理研究中的重要问题,通常表述为特定目标函数最优化,难点是多参数、非线性和不适定性.局部和全局优化方法都不能实现快速全局优化.本文概述了地震波勘探反演问题的理论基础和研究进展,阐述了反演中优化问题的解决方法和面临的困难,并提出了一种确定性全局优化的新方法.通过在优化参数空间识别并划分局部优化解及其附近区域,只需有限次参数空间划分过程就能发现所有局部解(集合);基于复杂目标函数多尺度结构分析,提出多尺度参数空间分区优化方法的研究方向.该方法收敛速度快,优化结果不依赖初始解的选取,是对非线性全局优化问题的一个新探索.

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.