Deriving analytical solution of the pseudo wavefield from transient electromagnetic data
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.
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