均匀半空间三维体的三频激电相对相位法积分方程模拟

Tri-Frequency Induced Polarization Relative Phase Modeling of Three- Dimensional Bodies in Homogeneous Half-Space in Integral Equation

利用三频激电相对相位可以快速、直观地区分金属硫化矿与碳质岩石引起的激电异常.针对三维电磁场,研究了均匀半空间的张量格林函数,导出了该函数不含索末菲积分的张量格林函数解析表达式,由张量格林函数求解Fredholm积分方程,将异常体划分为一系列立方单元,并将该积分方程转化为矩阵方程,从而计算出空间任一点的电场.给出了中梯装置下三维异常体的三频激电相对相位的计算实例,并将计算结果与实验模拟结果进行了对比分析.结果证明,当相对相位Φ1-2>Φ2-3时,可能是金属硫化矿引起的异常,当相对相位Φ1-2<Φ2-3时,可能是石墨引起的异常.

Tri-frequency induced polarization is a new geophysical method put forward by He Jishan.Using tri-frequency induced polarization relative phase,the anomalies of induced polarization aroused by pyrite or graphite can be distinguished quickly and directly. In this paper, the tensor Green's function of homogeneous half-space is studied for three-dimensional electromagnetic field.An analytical formula of tensor Green's function that does not involve the Sommerfeld integrals is presented.The fredholm equation is solved using tensor Green's function. The anomalous body is divided into a number of cubic cells and the integral equation is deduced to matrix equation.The electric fields of any point in the earth can be calculated.An example of tri-frequency induced polarization relative phase of anomalous body using middle gradient arrays is provided, and the result is compared with water tank experiment result. All results prove that the relative phase anomalies of range Φ_(1-2)>Φ_(2-3) may be caused by pyrite,and the anomalies of range Φ_(1-2)<Φ_(2-3) may be caused by graphite.