矩形大定源层状介质中感应电动势的数值求解方法

研究地电断面电阻率的变化是瞬变电磁勘探中常用的方法.为了得到地电断面电阻率的变化,一种方法就是在求出感应电动势的基础上进行电阻率的求解.因此,准确而有效的求出感应电动势的值是非常关键的.矩形大定源回线在求解层状介质中,感应电动势的值时分为零偏移距和非零偏移距两种情况.在中心点接收时,采用线性数字滤波方法求解频率域垂直磁场分量;在非零偏移距情况下,为了求解频率域垂直磁场分量,首先采用傅里叶正余弦变换法将双重贝塞尔函数积分转换为正余弦变换形式,再利用折线逼近快速算法对其进行数值计算,最后,根据法拉第电磁感应定律,可得到二次场时间域感应电动势的数值解.其数值模拟结果表明,利用线性数字滤波方法及折现逼近方法可以有效的求出矩形大定源层状介质中感应电动势的值.

Numerical calculation method of induced EMF from rectangular loop over layered medium

Research on the resistivity changes in geoelectric section are one of the mostly used TEM methods.In order to obtain the resistivity changes,one approach is to calculate the value of induced EMF.Therefore,to compute the value of the induced EMF accurately and effectively is critical.The big rectangle loop can be divided into zero offset and non-zero offset in solving the value of the induced EMF over layered medium.In the central point,the linear digital filtering method can be used in the calculation of frequency domain response.In the case of non-zero offset,in order to solve the vertical magnetic field component,double Bessel functions are firstly converted into Fourier sine（or cosine） form and then the poly-line approximation fast algorithm is used for the numerical calculation.Finally,according to Faraday＇s law of electromagnetic induction,the time domain induced EMF can be calculated.The numerical simulation results show that the use of the linear digital filter method and poly-line approximation method can effectively calculate the value of the induced EMF in the rectangular loop over layered medium.