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摘要: 由于传统的阻尼最小二乘法只适合于模型较少的简单模型，因此当介质的层数较多时，反演就会受到多解性的影响，有时甚至出现不收敛的情况，并且反演十分耗时。为此，使用正则化思想引入模型约束进行反演，且正则化因子通过计算每次迭代的数据目标函数和模型目标函数自适应得到，使反演能够稳定地进行；引入拟牛顿法来更新雅可比矩阵，大大缩短反演所需要的时间，通过典型的3层与多层理论模型的反演试算，证明了拟牛顿法自适应正则化反演算法对初始模型的要求不高，拟合效果好，收敛速度快，适应性强，体现了良好的稳定性和可靠性。Abstract: Because the damping least square method is only suitable for a simple model, when the media has multiple layers, inversion is effected by multiple solutions, sometimes even no convergence occurs, and the inversion is very time-consuming. For this purpose, regularization idea is used to introduce the model-constrained inversion, in the cause of iteration, the adaptive regular factor of the regularized inversion algorithm is calculated adaptively based on the relation of the data objective function and the model objective function; it can result in a stable convergence in the iteration course of the inversion. In this paper, the inversion used quasi-Newton method to update Jacobian matrix, it reduced greatly the time required for the inversion, and the typical spreadsheet three and multi-theoretical model as an example to inversion is proved less demanding on the initial model of the adaptive quasi-Newton regularized inversion algorithm. The inversion result also show that the adaptive regularized inversion is steady and reliable and has good fitting effect, fast convergence and strong adaptability.
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