An invariant representation for the magnetic transfer function in magnetotellurics

Abstract

The magnetic transfer function in the magnetotelluric (MT) method can be represented by two simple complex functions that possess special properties in 3-D environments. This representation is obtained by means of a complex rotation matrix applied to the field measurements. One of the resulting functions is invariant with respect to rotations of the coordinate system and is closely related to the traditional concept known as tipper. The magnitude and phase of this new representation are invariant in a 3-D earth and unambiguously reduce to the corresponding formulas for 2-D cases. With these properties, the proposed representation overcomes the existing limitations of the current definition of the tipper. In the second complex function, the traditional concepts of rotation angle and skew appear naturally in the function’s real and imaginary parts, respectively. We test the new representation using the response of a 3-D model. The results are compared with those obtained using current definitions.