A three-dimensional transient electromagnetic data inversion method based on a time–frequency transformation

Herein,a three-dimensional(3D)inversion method in the frequency domain based on a time–frequency transformation was developed to improve the efficiency of the 3D inversion of transient electromagnetic(TEM)data.The Fourier transform related to the electromagnetic response in the frequency and time domains becomes a sine or cosine transform under the excitation of downward-step current.We established a transformation matrix based on the digital fi ltering calculation for the sine transform,and then the frequency domain projection of the TEM data was determined from the linear transformation system using the smoothing constrained least squares inversion method,in which only the imaginary part was used to maintain the TEM data transformation equivalence in the bidirectional projection.Thus,the time-domain TEM inversion problem was indirectly and effectively solved in the frequency domain.In the 3D inversion of the transformed frequency-domain data,the limited-memory Broyden–Fletcher–Goldfarb–Shannoquasi–Newton(L-BFGS)method was used and modifi ed with a restart strategy to adjust the regularization parameter when the algorithm tended to a local minimum.Synthetic data tests showed that our domain transformation method can stably project the TEM data into the frequency domain with very high accuracy;furthe rmore,the 3D inversion of the transformed frequency-domain data is stable,can be used to recover the real resistivity model with an acceptable effi ciency.