【摘要】 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.更多还原

【Abstract】 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.更多还原