Phases greater than 90° in MT data: Analysis using dimensionality tools

Abstract

An example of magnetotelluric data is discussed which has distinctive phase values out of quadrant, and for which the Zxx element of the measured tensor is greater than the Zxy element in both real and quadrature parts. Mohr circle plots and principal value decompositions of the real and quadrature parts of the tensor clarify its understanding. An analysis of rotational invariants of the data suggests a case of galvanic distortion of a 2D structure. Results from phase tensor analysis are included, and the example is seen to be a dramatic instance of phase tensor analysis reducing an apparently 3D example to 2D characteristics. The Mohr circles of this example do not capture the axes origin, although there are phases out of quadrant. Extra intrigue is thus added to the question, noted in Lilley, F.E.M., 1998. Magnetotelluric tensor decomposition: part I, theory for a basic procedure. Geophysics 63, 1885-1897 and arising independently in Caldwell, T.G., Bibby, H. M., Brown, C., 2004. The magnetotelluric phase tensor. Geophys. J. Int. 158, 457-469 and Bibby, H.M., Caldwell, T.G., Brown, C., 2005. Determinable and non-determinable parameters of galvanic distortion in magnetotellurics. Geophys. J. Int. 163, 915-930, whether the determinant values taken separately of the real and quadrature parts of a magnetotelluric tensor should both never be negative. For data whose Mohr circles do not capture the axes origin, simple conditions are derived regarding phase. These conditions govern whether or not it is formally possible for observed phases of Zxy to exceed 90°, for any rotation of the observing axes.