带先验知识的波阻抗反演正则化方法研究

针对波阻抗反演中存在的不适定性问题，本文提出了一种带先验知识的正则化重开始共轭梯度法.该方法的内层循环采用修改的共轭梯度法，并使用重开始技巧；外层循环使用Morozov偏差准则作为停机准则.正则参数的选取采用连续几何选取法.克服了传统共轭梯度法迭代不足或迭代过度的缺点，将迭代步数控制在了合适的范围，使算法能够更快速更准确的收敛.同时考虑了用最速下降法计算先验解和对解施加非均一的规范约束.通过理论模型试算和实际资料处理，并与共轭梯度法进行对比，表明该算法具有精度高、抗病态能力强，运算速度快的优点，具有实用性.

Regularizing method with a priori knowledge for seismic impedance inversion

This paper proposes a regularized restarted conjugate gradient method with a priori knowledge for solving ill-posed problems in impedance inversion. In inner loop，we use a modified conjugate gradient algorithm and a restarted technique; in outer loop, the Morozov’s discrepancy principle is used as a stopping rule. For choice of the regularization parameter, we use a geometric manner. The shortcoming of the traditional conjugate gradient method is that the iterations may be surplus or insufficient. This algorithm can overcome these two shortcomings by controlling the iterations within a reasonable range, so it converges quickly and accurately. A priori knowledge is obtained from the steepest descent method and a non-uniform constraint is considered to impose on the solution. Theoretic simulations are made and compared with the classical conjugate gradient method. Field data applications are performed. It reveals that the proposed algorithm has the advantages of high precision, robustness, fast calculation and practicability.