位场向下延拓的相关系数法

摘要

The downward continuation of potential fields plays an important role not only in gravity and magnetic data interpretation, but also in geomagnetic navigation. The downward continuation problem is essentially the solution of the Fredholm integral equation of the first kind. This paper presents a correlation coefficient method for downward continuation of potential fields adapted from the principle of probability tomography. Model experiment and real data application arrives at following conclusions: 1) when the downward-continuation distance reaches 10 grid intervals, the RMS error is about 0.23% of the maximal theoretical potential value; 2) adding white noise of MSE amplitude 1% and 5% of the maximal potential value to the theoretical potential field, MSE propagation coefficients 1. 18 and 0. 54 are obtained; 3) the result of real-data downward continuation by 10 grid intervals proves that the method has high precision, strong anti-noise ability and good stability.%位场向下延拓的研究不仅仅是在重磁资料的解释中,而且在导航方面也有着重要的作用.位场的向下延拓归结于求解一个第一类Fredholm型的积分方程,笔者借鉴概率成像的思想,通过计算已知场与待延拓点位置之间的相关系数来求解向下延拓的方程组,实现了位场的向下延拓.对该方法进行检验:1)理论数据向下延拓10倍点距时,均方误差为理论异常最大值的0.23％；2)理论数据含均方误差为理论数据最大值的1％与5％的白噪声时,向下延拓结果的均方误差传播系数分别为1.18与0.54；3)实际资料向下延拓10倍点距时,相对平均误差为4.9％.