几种优化方法在频率域全波形反演中的应用效果及对比分析研究

Comparisons and analyses of several optimization methods in the application of frequency-domain full waveform inversion

全波形反演方法是一个有效求解参数重建问题的方法,其本质是一个寻找最优解的优化问题,目前多用局部最优方法求解,如最速下降法、共轭梯度法、高斯-牛顿法、拟牛顿法等.文中给出了常用的优化方法,基于二维声波方程,将这些方法应用于部分overthrust模型的反演,通过对各方法所得反演模型的精度和计算时间的对比分析,对各个方法的优缺点进行总结,为后续多参数反演或高维方程参数反演提供方法选择上的参考;针对所要求解的反问题,选用的优化方法需要在收敛速率、计算存储量和算法的稳定性之间进行权衡,以得到一个最优的反演结果.

Full-waveform inversion method is a useful method in parameter reconstructing which is essentially an optimization problem to find the optimal model to reach the minima of the misfit function. By now, local optimization methods are commonly used to solve this problem, such as the steepest-descent method, conjugate gradient method, Gauss-Newton method, quasi Newton method, et al. In our study, commonly used optimization methods are hsted~ based on the frequency domain 2D acoustic equation, these methods are applied in the inversion of part of the SEG/EAGE overthrust model, then the inverted results obtained are compared and analyzed. Through the comparisons of the methods from the point view of accuracies of the final models and inversion time, we summarize the advantages and disadvantages of the methods, which are helpful for our further multi-parameter inversion or higher dimension equation parameter inversion in optimization methods selecting. For the solved problem, the method used needs to balance the rate of convergence, calculation storage and the stability of the algorithm to reach an optimal result.