总强度磁异常各阶垂向导数换算新方法

摘要

The vertical derivative of the total field magnetic anomaly （TMA） plays an important role in the interpretation process of magnetic objects. Owing to the filter characteristics of vertical derivative operator in frequency domain, the conversion of vertical derivative is inherently unstable and any high-frequency noise presented in the surveying data gets strongly magnified in the transformed map in such a way to mask any useful signal. Based on the harmonic properties of the vertical integral and derivatives of TMA, an algorithm is presented to perform calculation of vertical derivatives using both frequency and space domain transformations. The effectiveness of the suggested techniques has been illustrated by synthetic sphere magnetic model whose TMA＇s first and second vertical derivative expressions are deduced when the geomagnetic direction is different from magnetization direction. The conclusion indicates that the presented vertical derivatives calculation method provides better results and allows a lower degrading of the signal-to-noise ratio than the standard Fourier method.%总强度磁异常垂向导数换算在磁性目标解释推断过程中具有重要意义。分析频率域总强度磁异常各阶垂向导数转换因子的滤波特性，指出在求解总强度磁异常垂向导数时，常规傅里叶变换法会明显放大观测数据中高频噪声的影响，甚至可能淹没掉真实信息。给出一个重要定理：总强度磁异常沿垂直方向的积分及各阶偏导数均为准调和函数，在此基础上，提出基于拉普拉斯方程的逐步求解法，联合空间域和频率域换算总强度磁异常沿垂直方向的各阶导数。同时，采用球体磁场模型验证所提方法的有效性，并推导地磁场方向和磁化强度方向不一致时，球体总强度磁异常沿垂直方向的一阶和二阶导数表达式。结论表明：利用样条法计算的垂向导数结果精度明显优于常规傅里叶变换法计算结果，且具有较强的抗噪能力。