Magnetotelluric (MT) and magnetovariational (MV) sounding are two principal geophysical methods used to determine the electrical structure of the earth using natural electromagnetic signals. The complex relationship between the alternating electromagnetic fields can be defined by transfer functions, and their proper selection is crucial in a 3-D inversion. A synthetic case was studied to assess the capacity of these transfer functions to recover the electrical resistivity distribution of the subsurface and to evaluate the advantages and disadvantages of using the tipper vector W to complement the impedance tensor Z and the phase tensor Φ. The analysis started with two sensitivity tests to appraise the sensitivity of each type of transfer function, which is calculated for an oblique conductor model, showing that the resistivity perturbation of the same model will produce distinct perturbations to different transfer functions; the transfer function sensitivity is significantly different. A 3-D inversion utilizing the quasi-Newton method based on the L-BFGS formula was performed to invert different transfer functions and their combinations, along with quantifying their accuracy. The synthetic case study illustrates that a 3-D inversion of either the Z or Φ responses presents a superior ability to recover the subsurface electrical resistivity; joint inversions of the Z or Φ responses with the W responses possess superior imaging of the horizontal continuity of the conductive block. The appraisal of the 3-D inversion results of different transfer functions can facilitate assessing the advantages of different transfer functions and acquiring a more reasonable interpretation.

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