地磁剖面异常二维拟合算法研究

RESEARCH ON TWO-DIMENSIONAL FITTING ALGORITHM OF GEOMAGNETIC PROFILE ANOMALY

地磁方法在地球物理学研究中具有重要的作用,地磁剖面的异常拟合更是解释地磁问题的重要一步,磁剖面的数据拟合就是去除测量过程中偶然误差及近地表不均匀体的干扰,让曲线圆滑,使得实测曲线与理论曲线的拟合程度达到要求。其中拟合算法的选择最为重要,而最小二乘法是基于一般多项式为拟合函数,具有较大局限性,当拟合阶数过高时,其方程组为病态方程,会很大程度上导致解的不稳定性,从而影响到拟合的精度。所以用广义正交多项式作为基底,用正交多项式的离散正交性来拟合磁异常曲线,由于高阶的拟合函数对于拟合精度具有巨大优势,能够有效拟合测量中不规则波动。

Geomagnetic method plays an important role in geophysical research, and the abnormal fitting of geomagnetic profile is an important step in explaining geomagnetic problems. the data fitting of magnetic profile is to remove accidental errors and the interference of inhomogeneous bodies near the surface in the process of surveying, make the curve smoothed and make the fitting degree between the measured curve and the theoretical curve meets the requirements. Among them, the choice of fitting algorithm is the most important, and the least square method is based on the general polynomial as the fitting function, which has great limitations. When the fitting order is too high, the equations are ill-conditioned equations, which will lead to the instability of the solution to a great extent. thus affecting the accuracy of fitting. Therefore, the generalized orthogonal polynomial are used as the base, and the discrete orthogonality of the orthogonal polynomial is used to fit the magnetic anomaly curve. Because the high-order fitting function has a great advantage in fitting accuracy, it can effectively fit the irregular fluctuations in the measurement.