Local 1-D interpretation of magnetotelluric B-polarization impedances

It is shown that magnetotelluric impedances from the B-polarization (magnetic field in the strike direction of a 2-D resistivity structure) share a number of properties with 1-D impedances: all B-polarization impedances satisfy the same phase constraints as 1-D data, i.e. the impedance phase always lies between 0° and 90°. As a consequence the B-polarization impedances are minimum phase and thus allow conversions between apparent resistivity and phase. The constraints hold for an arbitrary 2-D topography of the air–earth interface. By examining the spectral function it is found that the B-polarization impedances for a number of models admit an exact 1-D interpretation. For two quarter-spaces this holds for all points and resistivity contrasts. The resulting 1-D model gives the correct resistivity down to a depth of half the distance to the interface. For the dyke model as the next complicated structure, 1-D interpretability requires that the host resistivity does not exceed the dyke resistivity by more than a factor of 60. B-polarization data of more complex structures investigated in this paper show either no, or only a marginal, violation of 1-D interpretability. A necessary condition constraining the frequency dependence of B-polarization and 1-D data in terms of their Mellin transform is derived in the final section.