Applications of dispersion relations to the geomagnetic transfer function

The geomagnetic transfer function is nowadays used to constrain the magnetotelluric inversion procedure given that this function contains complementary information to the impedance tensor. For the models usually employed by inversions, the real and imaginary parts of the geomagnetic transfer function are related by dispersion relations. The computation of the dispersion relations involves the Hilbert transform, and here we discuss different expressions to compute them. This computation was verified using synthetically generated geomagnetic transfer function from 2D and 3D models. The dispersion relations were applied on two cases: (a) to study the consistency between the real and imaginary parts of field recorded data, and (b) to develop a procedure to complete or extend the amount of measured data.