Static shift estimation in magnetotelluric data using horizontal magnetic tensor

Interpretation of magnetotelluric data in the presence of galvanic distortions, caused by small-scale near-surface structures, can lead to unreliable results. The simplest manifest of these distortions, while limited only to the changes in the amplitude of electric fields, is vertical displacement of the apparent resistivity curves or static shift phenomenon that constitutes non-determinable part of the distortion matrix. Due to the boundary conditions governing components of the electric and magnetic fields, the occurrence of charge accumulation and therefore the static shift of apparent resistivity curves, affects only TM-mode data in the case of two-dimensional models. Thus, we can use the information available in the TE-mode- impedance phase (tipper and horizontal magnetic data) which are independent of this phenomenon.
In this study, geomagnetic transfer functions have been used to estimate this displacement and recover the undistorted TE-mode apparent resistivity based on the Faraday induction law. Ledo et al. (2002) show that tipper data can be used to estimate static shift of magnetotelluric data, if the horizontal variations of the horizontal components of the magnetic field can be ignored. This assumption may be violated in complex situations. We estimate static shift while incorporating such variations and taking into account the horizontal magnetic transfer functions. Estimation of static shift through mathematical methods is only relatively possible and requires the selection of a reference station that has the minimal effect of galvanic distortion. The relations between different components of electric and magnetic fields are integrated and characterized by their mean values. To incorporate the horizontal magnetic tensor, array magnetotelluric data are required, so that components of the magnetic field at the reference and measurement sites are simultaneously provided.
Considering two consecutive sites, impedance tensor at one site is written in terms of tipper and horizontal magnetic tensor at that site and the impedance at the adjacent site. By ignoring other types of distortions that can generally exist and using some algebra, the problem of determining the frequency-independent static shift factor becomes a linear fit problem. A set of data points covering different frequency ranges is selected and the quality of their linear fitting is examined through soling procedure.
Considering the horizontal variations of the horizontal components of the magnetic field, the method has been applied to two synthetic models. Using two different approaches, the distortions caused by small-scale three-dimensional structures are simulated and added to the model responses. In the first approach, the distortion matrix is considered as the product of four parameters of gain factor, anisotropy, and twist and shear angles in the decomposition model then the distortion simulation is performed by selecting some numerical values of these four parameters and multiplying the resulted distortion matrix by the impedance tensor. In the second approach, some part of the top-layer of the model is replaced by a Gaussian distribution of resistivity with known selected mean and standard deviation. In this way, the effects of various geological processes, such as weathering, erosion- and to some extent- the nature of the deposited sediments are involved. The obtained results confirm that the estimated static shift parameter is more accurate than that of the case in which horizontal magnetic transfer functions are ignored and only the vertical magnetic transfer functions are considered.