Invariant TE and TM impedances in the marine magnetotelluric method

SUMMARY The magnetotelluric (MT) impedance tensor has a nil diagonal when one of the axes of the coordinate system coincides with the strike of a 2-D structure. In general, real data are full tensors either because of 3-D effects or measurements not aligned to the geological strike. The usual practice to adapt the field tensor to the 2-D assumption is to rotate to a new system of coordinates. In most cases, there is no single angle of rotation that warranties that the diagonal elements become zeros as in the ideal 2-D case. Even maximizing the off-diagonal elements does not necessarily produce a nil diagonal. Consequently, the 2-D inversions proceed by neglecting whatever there is left in the diagonals. In this work, we explore an alternative that places no constraints on direction but assures a nil diagonal. We use two rotational invariants that compact the four elements of the tensor into only two and reduce in 2-D to the TE and TM impedances. These are obtained readily by solving a quadratic equation. We explore four different scenarios: (1) using the invariants, (2) rotating the tensor perpendicular to the profile, (3) rotating to the average maximum orientation for each station and (4) maximizing the off-diagonal elements of the tensor for each site, frequency to frequency. These approaches were applied to 3-D synthetic and field data. The field data correspond to two marine magnetotelluric surveys in the Gulf of California. In one of them, there is no information on the instrument orientation because the compasses failed. In this case, the rotational invariants come handy to overcome the problem. In the other survey, there was orientation information and the 2-D inversions illustrate the better performance of the invariants relative to the traditional approaches.