回线源瞬变电磁成像的理论分析及数值计算

THEORETICAL ANALYSIS AND NUMERICAL CALCULATION OF LOOP-SOURCE TRANSIENT ELECTROMAGNETIC IMAGING

为进一步提高瞬变电磁法对地探测的解释精度 ,提出了回线源瞬变电磁成像原理及数值计算方法 .讨论了频率域中水平层状介质中瞬变电磁响应 ,得到一个以波阻抗为积分核的双重积分式 ;然后对水平层介质下电磁场的解进行上、下行波分离 ,得到含有以反射系数序列为未知的线性方程组 ,并给出了求取波阻抗和反射系数的数值解法 :对实测磁场值进行域的变换 ,以均匀半空间下的等效波阻抗代替积分核函数 ,经过线性数字滤波后 ,在频率域求出等效波阻抗 ;把频率域中的波阻抗转换到时间域 ,以此为参数 ,构建方程组 ,在时间域用线性规划法求出反射系数序列 .最终以反射系数为参数进行成像 .对理论模型的数值计算结果表明 ,用本文提出的成像方法可以增强瞬变电磁法识别地下电性分界面的能力 .

In order to improve the prospecting precision to the earth of the transient electromagnetic method(TEM), the principle of TEM imaging technology and a numerical calculation method are put forward. Transient electromagnetic response to the layered earth is discussed in the frequency domain, then a double integral in which the kernel is unknown is obtained. The solution of the electromagnetic field in the medium of layered earth is separated into the forms of upper and down traveling waves. Then a set of linear equations in which reflection coefficients are unknown is reached. The numerical solution of wave-impedance and reflection coefficients is given as follows: Transforming the magnetic field data from time into frequency domain, replacing the kernel of equation with the equivalent wave-impedance of homogeneous half-space, getting the equivalent wave-impedance in the frequency domain after digital filtering, then returning the equivalent wave-impedance into the time domain, constructing equations with it, getting reflection coefficients from the equation with the method of linear programming in the time domain. The imaging result section can be drawn according to it. The imaging result from the theorical model shows that the method proposed in this paper can improve greatly the ability to recognize the underground electric interfaces.