Determinable and non-determinable parameters of galvanic distortion in magnetotellurics

Galvanic distortion has long been recognized as an obstacle in the interpretation of magnetotelluric (MT) data. One fundamental problem for distortion removal is that the equations that describe the effects of galvanic distortion on the impedance tensor are underdetermined. We have previously shown that an explicit solution for four of the parameters of the regional (undistorted) impedance tensor can be resolved without any assumptions. These determinable parameters are the components of a tensor (the phase tensor) representing the phase information contained in the impedance. The coordinate invariants of the phase tensor provide a simple and objective guide to the dimensionality of the regional impedance tensor at each measured frequency. Where the regional structure is 2-D, one of the principal axes of the phase tensor will be aligned parallel to the strike of the regional conductivity. The distortion tensor and the parameters of the regional impedance tensor that represent the amplitude information cannot be determined without assumptions. Where the phase tensor shows the regional impedance tensor to be 1-D, the distortion tensor and the regional impedance can be determined to within a single multiplicative constant. Where a 2-D regional structure is indicated, two assumptions are necessary to determine the regional impedance tensor but the solution is not unique, and any choice of assumptions could be made with equal validity. For 3-D structures, the phase tensor provides the direction of greatest inductive response, which is the closest equivalent of a strike direction. In this case four constraints are required for a solution. In practice, a MT sounding may contain sections that display different characteristic dimension and the distortion tensor can be determined from the section of the sounding with the lowest characteristic dimension. The greatest amount of information is determined from a 1-D section. The use of the information contained in the phase tensor overcomes some of the shortcomings of traditional distortion analysis. Illustrating the tensors using an elliptical representation aids the interpretation of the tensor data involved in this analysis.