电性源瞬变电磁法虚拟波场解析推导

Deriving analytical solution of the pseudo wavefield from transient electromagnetic data

瞬变电磁场至虚拟波场的转换是瞬变电磁拟地震处理的基础,瞬变电磁场满足扩散方程,而虚拟波场满足波动方程,二者之间通过Q变换相互转换。将瞬变电磁数据转换成虚拟波场属于积分反变换,具有典型的不适定特性,以往主要采用数值方法求解该积分反变换。在数值求解中,需对求解方法和参数进行优化,以获得最佳求解效果。为此,本文推导了电性源瞬变电磁法电场响应的虚拟波场解析解。从均匀半空间电磁场响应的解析解出发,借助于拉普拉斯变换对,得到了阶跃响应和脉冲响应的解析表达式,从而建立起瞬变电磁场和虚拟波场的解析变换对。该解析变换对能够用于测试数值求解方法的准确性和稳定性,还能用于检验虚拟波场特性,从而形成有效的虚拟波成像方法。

The transform from transient electromagnetic(TEM)field to pseudo wavefield is the basis for using the imaging technique.The TEM field follows the diffusion equation,while the pseudo wavefield follows the wave equation.These two can be transformed into each other via the Q-transform.As the integral transformation from TEM field to pseudo wavefield is ill-posed,numerical method is used to get the desired pseudo wavefield.As a result,it is often the case that the methods and parameters are need to be optimized to get a optimal pseudo wavefield.Therefore,here in this paper,we derived the analytical solution of the pseudo wavefield from the TEM field.We start from the analytical formula of TEM field,and utilize the Laplace transform to establish the analytical solution pairs.The pairs can be used to test the accuracy and stability of the numerical method,as well as examining the features of the pseudo wavefield to get an effective imaging method.