On the Phase Constraint of the Magnetotelluric Impedance; discussion and reply

In his paper, Loewenthal presents what he calls a “simple proof” that the phase of the one-dimensional magnetotelluric modified impedance lies between -π/4 and π/4. A much simpler proof exists (Eckhardt, 1968). My proof is buried as a rather minor feature of an obscure (alas) paper, and some of its sign conventions differ from standard, so I believe it appropriate to restate the proof here.