水平层状介质条件下的井地电磁场响应计算

Calculation of borehole-to-surface electromagnetic responses on horizontal stratified earth medium

本文以垂直电偶极子矢量磁位的Sommerfeld积分表达式为基础,导出各含源层垂直分段电流源的电磁场沿导线方向的积分计算公式,进而得到各垂直分段电流源的电磁场。对各分段电流源的地面电磁响应进行叠加即可得到其井地电磁响应,从而将一维井地电磁正演问题简化为计算层状介质中垂直有限长电流源的地面电磁场问题。文中给出的算例验证了结果的可靠性,并与常规有限长电流源离散成多个小电偶极子源的近似方法计算时间及计算精度进行了对比,结果验证了算法的可靠性和高效性。

Borehole-to-surface electromagnetic forward modeling for 1D medium can be simplified as a calculation of electromagnetic response on earth surface exited by a vertical line current source with finite-length embedded in stratified medium.The field near the line current source cannot be seen as the response of a vertical electric dipole(VED) source.In order to calculate the electromagnetic fields on the earth surface,the integral formulation to calculate the fields of vertical fragmentation current source in each layer which contains current source is derived based on the Sommerfeld integral formal of magnetic potential of VED.Finally the electromagnetic fields of vertical line current source with arbitrary length can be obtained by way of superposing the electromagnetic fields of each fragmentation current source.The validity of the method is tested in this paper,and the computing time and the accuracy are compared with the results of the conventional approximate calculation method which discretizes the vertical finite-length current source into many small VEDs.The results show that this method is reliable and efficient.