全波形时间域航空电磁响应三维有限差分数值计算

摘要

全波形时域航空电磁测量具有解释精度高、分辨率高等优点,已成为新一代时域航空电磁探测发展的趋势.为此,本文基于无源有限差分法,将发射电流离散为若干梯形脉冲元,将脉冲元在时间上产生的电磁场转换为空间初始场,在差分迭代过程中分时引入差分方程,逐步将有源有限差分方程转换为无源有限差分方程,最终实现了发射电流为任意波形时,全波形时间域航空电磁响应的三维数值计算.计算结果表明:在梯形波发射时,对于典型地电模型的航空时间域电磁响应,计算稳定时间大于10 ms；与积分方程法相比,发射线圈中心点二次场响应平均误差小于1％.任意源三维全波形数值计算的实现为全波形三维反演和仪器设计奠定了基础.%The full waveform airborne electromagnetic exploration has become a trend of new-generation airborne electromagnetic exploration, due to its advantages of high-precision interpretation and high-resolution. This paper is based on the passive finite-difference solution to decompose the transmitter current into several small trapezoid impulses, and transform the electromagnetic field excited by these trapezoid impulses in time-domain into initial field in space. During the iteration step, finite-difference equations are introduced in the finite-difference equations. It transforms the active finite-difference equations into passive finite-difference equations gradually. It will work out the calculation of full-waveform airborne electromagnetic response with three-dimension finite-difference solution in time-domain eventually, when the transmitter current is in arbitrary waveform. The results show that the stabilization time of calculation for the airborne electromagnetic response of typical geoelectric models in air time-domain can exceed 10 ms with trapezoid-wave transmitting. Compared with the integral equation solution, the average error of response of second field in the center of transmitter coil is less than 1%. The realization of full-waveform three-dimension finite-difference solution provides arnfoundation for full-waveform three-dimension inversion and equipment design.