地下瞬变电磁法全区视电阻率核函数算法

Kernelfunction algorithm of all-time apparent resistivity used in underground transient electromagnetic method

全区视电阻率的求解方法是地下瞬变电磁理论体系的重要组成部分.在对全空间核函数分析的基础上,提出了全空间全区视电阻率的核函数算法,采用理论数据对其计算效果进行了验证,同时将其应用效果与半空间瞬变电磁法平移算法进行了比较.结果表明:当采样时刻大于10μs和回线边长大于5m时,全空间核函数随电导率具有单调递增特性,井中多匝小回线装置的等效边长和采样时刻均满足此要求;由核函数算法获取的视电阻率在早期、过渡区及晚期均能反映出模型的真电阻率;在电阻率为10Ω.m的全空间模型中,该方法与平移算法计算结果的均方根误差分别为6.945 1×10-4和1.030 0×10-2,因而具有更高的精确性.实测资料处理结果显示核函数算法具有更好的应用效果,丰富了全空间瞬变电磁法理论体系,为井下实测资料的处理提供了参考.

All-time apparent resistivity calculation method is an important component in theoretical system of underground transient electromagnetic method （TEM）. Based on analysis of full-space kernel function, kernel function algorithm （KFA） was put forward to calculate fullspace all-time apparent resistivity in this paper, and its calculating effect was verified using the- oretical data. Meanwhile, its application effect was compared with translation algorithm, which was used to solve all-time apparent resistivity in half-space TEM. The results indicate that, full-space kernel function is a monotonically increasing function of electric conductivity when sampling instant is later than 10 gs and side length of transmitting loop is longer than 5 m. The equivalent side length and the sampling instant of multi-turn coils used in mine all meet this requirement. All-time apparent resistivity obtained from KFA reaches model＇s ＂real＂ resistivity whether it is in early time, in transition region, or in later time. RMS errors of KFA and Translation algorithm are 6. 945 1 × 10-4and 1. 030 0× 10-2 with a 10Ω· m homogeneous full-space model, which indicates that KFA has a higher accuracy and stability. The interpreta-tion of measured data shows that, KFA can achieve a better application effect, which enriches the theoretical system of full-space TEM and provides a reference for measured data processing in mine.