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Using the 3-D axial anisotropy, the dipping anisotropy, and the azimuthal anisotropy as case studies, we investigated the influence of each anisotropic resistivity element on the magnetotelluric surface responses. To justify the strong and weak influence and edge effect, we have introduced the influence indices for the impedance components, and the edge effect indices for the tipper components. Interestingly, for decoupled modes, we found that ρ xx has a strong influence on Zxy, Zyy, and Ty, while ρ yy strongly affects Zyx, Zxx, and Tx. The three elements ρ zz , ρ xz , and ρ yz have only a very weak influence on all types of responses. For the coupled mode, ρ xx , ρ yy , and ρ xy display a strong influence on all responses. Based on our studies on the influence of the anisotropic resistivity elements, we design and propose two practical processes to replace the conventional axial, dipping, azimuthal, and general anisotropic inversions. First, the axial or dipping inversion can be approximately decoupled into ρ x -mode and ρ y -mode inversions. The decoupled mode inversions can be performed either independently and in parallel, or as a joint inversion. Second, since the three resistivity elements always show a weak influence, the general anisotropic inversion can be simplified to just the reduced coupled azimuthal anisotropic inversion with only three resistivity elements as outputs. Both proposed techniques can save a lot of the computational resources. Criteria to choose either the decoupled or coupled modes depend greatly on the magnitudes and distributions of the Zxx and/or Zyy, and Tx and/or Ty responses. [ABSTRACT FROM AUTHOR]