大地电磁测深资料的二次函数逼近非线性反演

将二次函数逼近非线性优化首次应用于大地电磁测深反演问题，该反演方法利用二次函数有唯一最小值的特点进行逼近大地电磁反演模型，从而避免了常规的迭代反演过程中陷入局部极小问题，实现了对目标函数求全局极小，较好地解决了非唯一性问题；同时该方法不用求灵敏度矩阵，且对初始模型无任何要求。通过理论模型检验、井旁MT点反演结果与测井曲线的对比及MT测线的反演电阻率深度剖面与地震测线的时间剖面对比均表明，本文方法取得较好的应用效果。

Non-linear inversion with the quadratic function approaching method for magnetotelluric data.

We present a new technique for inverting magnetotelluric sounding (MT) data by introducing the quadratic function approaching scheme, which is originally used in non-linear optimization. The quadratic function approaching method (QFAM) takes the advantage of that quadratic function has single extreme value. It avoids leading to an inversion solution for local minimum and ensures the solution for global minimization of objective function. The method does not need calculation of the sensitivity matrix and not require a strict initial earth model. In this study, the coefficients of the quadratic function used for the inversion are calculated dexterously by using affine transformation and by adopting an effective method for selecting control points. Examples for synthetic data and field measurement data indicate that the proposed inversion method is effective.