基于谱共轭梯度法的时间域全波形反演

发布时间：2018-02-15 14:38

本文关键词： 全波形反演梯度类优化方法谱共轭梯度法共轭梯度法最速下降法　出处：《吉林大学》2017年硕士论文　论文类型：学位论文

【摘要】：全波形反演(FWI)通过设定和利用相应的优化方法求解一个非线性最小二乘问题,来不断修正初始模型的模型参数,使得假设的初始模型模拟的地震数据与实际观测的地震数据之间的残差不断减小,进而使得初始模型逐渐逼近地下真实构造,最终获得高分辨率的地下速度分布。我们可以看出全波形反演实质上是一个最优化问题,目前求解全波形反演应用比较广泛的优化方法为梯度类局部优化算法,主要包括最速下降法、共轭梯度法等。最速下降法计算量小、计算速度快,但收敛速度较慢;共轭梯度法具有存储需求小、算法简单有效、克服了最速下降法收敛速度慢等优点,非常适合求解大规模无约束优化问题,在全波形反演中应用比较广泛。为了提高共轭梯度法的计算效率,克服共轭梯度法生成上升的搜索方向的缺点,本文将谱共轭梯度法应用到全波形反演中,谱共轭梯度法是谱梯度法与共轭梯度法的结合。相对于共轭梯度法,谱共轭梯度法可以在不依赖任何线搜索的情况下,满足充分下降性,并且结合非线性搜索技术可以实现全局收敛。与共轭梯度法相比谱共轭梯度法具有共轭梯度法全部的优点,而且在计算迭代搜索方向时,谱共轭梯度法比共轭梯度法多了一个谱系数,利用了目标函数的更多信息,所以比共轭梯度法具有更好的数值表现。本文利用最速下降法、共轭梯度法与谱共轭梯度法三种算法对Marmousi模型进行了二维时间域全波形反演试算。首先对比了基于上述三种算法的全波形反演结果,经过对比分析可知相对于其它两种优化方法谱共轭梯度法可以更好地改善反演效果,其反演结果更加接近地下真实构造。然后,又对比了基于上述三种算法的全波形反演的目标函数迭代40次的收敛曲线。收敛曲线中谱共轭梯度法的目标函数值经过40次迭代后明显小于其它两种算法的目标函数值,而且在其它两种算法的目标函数值变化趋势早已趋于水平时,谱共轭梯度法的目标函数值依然具有明显的下降趋势,可知基于谱共轭梯度法的全波形反演相对于其它两种算法不仅反演结果更加接近地下真实情况,而且目标函数收敛速度更快。
[Abstract]:Full-waveform inversion (FWI) is used to modify the model parameters of the initial model by setting and using the corresponding optimization method to solve a nonlinear least square problem. The residual difference between the seismic data simulated by the hypothetical initial model and the observed seismic data is reduced, and the initial model gradually approaches the underground real structure. Finally, the high resolution underground velocity distribution is obtained. We can see that the whole waveform inversion is essentially an optimization problem. At present, the most widely used optimization method to solve the full waveform inversion is the gradient local optimization algorithm. It mainly includes the steepest descent method, conjugate gradient method and so on. In order to improve the computational efficiency of conjugate gradient method, it is very suitable for solving large-scale unconstrained optimization problems and is widely used in full waveform inversion. In this paper, the spectral conjugate gradient method is applied to the whole waveform inversion. The spectral conjugate gradient method is a combination of the spectral gradient method and the conjugate gradient method. The spectral conjugate gradient method can satisfy the sufficient descent property without any line search, and the global convergence can be realized by combining the nonlinear search technique. Compared with the conjugate gradient method, the spectral conjugate gradient method has all the advantages of conjugate gradient method. Moreover, the spectral conjugate gradient method has a more spectral number than the conjugate gradient method in calculating the direction of iterative search, and makes use of more information of the objective function, so it has better numerical performance than the conjugate gradient method. In this paper, the steepest descent method is used. Three algorithms, conjugate gradient method and spectral conjugate gradient method, are applied to the 2-D time-domain full waveform inversion of Marmousi model. First, the full waveform inversion results based on the above three algorithms are compared. Compared with the other two optimization methods, the spectral conjugate gradient method can improve the inversion effect, and the inversion result is closer to the underground real structure. After 40 iterations, the objective function values of the spectral conjugate gradient method are obviously smaller than those of the other two algorithms. Moreover, when the change trend of the objective function value of the other two algorithms has already tended to be horizontal, the objective function value of the spectral conjugate gradient method still has an obvious downward trend. Compared with the other two algorithms, the full waveform inversion based on the spectral conjugate gradient method is not only closer to the underground real situation, but also converges faster with the objective function.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631.4

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