优化策略的二维大地电磁光滑聚焦反演研究

为了得到快速、稳定的反演结果和清晰的地质界面，在前人研究的基础上，提出一种新的反演目标泛函。采用最光滑模型和最小支撑梯度模型泛函同时对数据目标泛函进行约束，利用高斯牛顿法进行求解，实现了二维大地电磁数据的光滑聚焦反演。光滑聚焦反演既可以得到清晰的地质界面，又可在一定程度上避免聚焦反演可能产生的构造形态畸变。在进行反演迭代的过程中，采用Nelder-Mead优化算法优化Morozov偏差原理选取合适的正则化因子的优化策略，很大程度上加快了反演收敛的速度。最后，结合典型的模型和实测数据对反演方法进行了验证，同时与不同反演策略进行对比分析。反演结果表明，对于典型模型，光滑聚焦反演结果与模型吻合更好，收敛曲线下降速度更快，地质体分界面也更加清晰；实测数据反演结果进一步验证了该算法的有效性和可靠性。

Two-dimensional magnetotelluric smooth focusing inversion based on optimization strategy

On the basis of previous studies, this paper proposes a new inversion objective functional with the purposes of realizing rapid and stable inversion and obtaining clear geological interfaces. It adopts the smoothest model and the minimum support gradient model functional to constrain the data objective functional. Solved by the Gauss-Newton method, the new inversion objective functional enables the smooth focusing inversion of two-dimensional magnetotelluric data. The smooth focusing inversion can not only present clear geological interfaces but also avoid the distortion of structural morphology caused by focused inversion to a certain extent. In the process of inversion iteration, we adopt the optimization strategy of improving the Morozov discrepancy principle with the Nelder-Mead optimization algorithm to obtain the appropriate regularization factor, which greatly accelera-tes the inversion convergence. Finally, the proposed inversion method is verified with a typical model and real data and also compared with other inversion strategies. The inversion results show that for typical model inversion, the algorithm in this paper outperforms the others in agreeing with the model, with the convergence curve decreasing rapidly and the geological body interface being clear. The inversion results of real data further verify the reliability and effectiveness of this algorithm.