An invariant representation for the magnetic transfer function in magnetotellurics

The magnetic transfer function in the magnetotelluric (MT) method can be re presented by two simple complex functions that possess special properties i n 3-D environments. This representation is obtained by means of a complex r otation matrix applied to the field measurements. One of the resulting func tions is invariant with respect to relations of the coordinate system and i s 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 unam biguously reduce to the corresponding formulas for 2-D cases. With these pr operties. 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 fun ction's real and imaginary parts, respectively. We test the new representat ion using the response of a 3-D model. The results are compared with those obtained using current definitions.