A property of the determinant of a 2 x 2 tensor relevant to magnetotellurics

Abstract

Where a 2×2 tensor relates two geophysical quantities that are measured in the field as time-varying vectors, its determinant is shown to be positive when, for two different events occurring at different times, a step clockwise in the direction of one vector from the first event to the second is accompanied by a step clockwise in the direction of the other vector from the first event to the second. The determinant would be negative were the azimuths of the two field vectors to "counter step," i.e., change in opposite directions. In magnetotellurics (MT), the technique known as phase-tensor analysis brings a focus on the determinant signs of MT impedance tensors and telluric distortion tensors, and the azimuth-stepping rules should apply to both categories. Any determinants which may be negative are then seen in the light that they imply a counter stepping of the azimuths of the two relevant field vectors.