层状介质上时空展源瞬变电磁响应的计算方法研究

Study on the electromagnetic fields of an extended source over layered models

在瞬变电磁法的实际应用中,由于发射回线和发射波形的不规则性而导致其发射源成为时空展源.展源效应的忽略会造成正反演和数据解释的差错,因此开展展源效应的研究对于瞬变电磁法的实际应用具有重要的意义.对于空间展源,本文以磁偶极子的响应为基响应,应用有源空间的互易定理和第二类曲线积分,提出了一种可基于发射回线数值坐标求取任意形状发射回线响应的计算方法.同时对于时间展源,以阶跃波形的响应为基响应,对阶跃响应的特性进行了分析,提出了一种对发射信号进行非均匀采样的高效时间域计算方法,解决了对数采样的基响应与高密度采样的发射波形之间进行常规卷积时所面临的时间与精度之间的矛盾.通过对层状大地上展源响应的模拟仿真和对比验证显示了本文所提出方法的正确性.最后本文考察了几种常见时空展源在常规近似前后响应的差别,并给出了相关结论.

In practical applications of transient electromagnetic methods, irregularity of the transmitting loop or current waveform makes the source an extended one. Since neglect of the effect of the extended source will cause some errors in both forward modeling and data interpretation, it makes great sense to calculate the responses that take this effect into account. For a spatially extended source over layered medium, step response is firstly calculated and taken as the basic response, then principle of reciprocity and the integral of the second kind are used to propose a new method that can compute the response based on the coordinates of the loop. For an extended source in time, an improved step-function summation method is proposed to deal with the contradiction between the precision of result and consuming of time. Comparisons with the published work have proved the validity and accuracy of our methods. The effect of the traditional approximations of the extended source is also investigated and some analysis for the numerical results is presented for advanced usage.