The Magnetotelluric Response Functions - Models and Methods of Magnetotellurics - page 9

the components Z xy and Z yx on the secondary diagonal, while the components
Z xx and Z yy on the principal diagonal indicate the geoelectric asymmetry of the
medium. By way of example consider (1.1) and (1.2) describing the horizontally
homogeneous layered model. Here Z xy =− 0. No wonder

that Z xy and Z yx are sometimes said to be principal impedances, whereas Z xx and
Z yy are referred to as secondary impedances. Such a paradoxical peculiarity of the
impedance tensor [ Z ] can be easily removed by rotating the magnetic field through

Z yx = Z and Z xx = Z yx =

/2 (Adam, 1964) and writing the impedance relation as

[ Z ] H ,

E = [ Z ] H =

− / /

2)] H =

.

[ Z ][ R ( 2)[ R ( (1 16)

where

cos

sin

[ R ( )] =

− sin cos

⎡ ⎤

01 H x

H y

H y
−

H x
H y

⎣ ⎦

H =

[ R ( / 2)] H = = =

− 10 H x

and:

⎡ ⎤

Z xx Z xy 0 Z xy − Z xx Z xy

− 1 Z xx

[ Z ]

⎣ ⎦ .

= [ Z ][ R ( − / 2)] = = =

Z yx Z yy 10 Z yy − Z yx

Z yx Z yy

Here [ Z ]isthe Adam impedance tensor. In this representation, the basic information
on the vertical distribution of the conductivity is given by the components

Z xx

=

Z yy =− Z xy =−

Z xy and Z yx on the principal diagonal, while the components Z xx

Z yx =

and Z yy on the secondary diagonal indicate the geoelectric asymmetry of the

medium. Turning back to the horizontally homogeneous model described by (1.1)
and (1.2), we see that in the representation E = [ Z ] H the electric and magnetic

fields are collinear.
The components of the impedance tensor [ Z ] can be transformed into apparent
resistivities . In the horizontally homogeneous model the transform

2

/ o
gives a vivid qualitative picture of vertical resistivity profile. This useful property
of the one-dimensional impedance is inherited by components Z xy , Z yx of the
impedance tensor (though with some distortions) and hardly by components Z xx ,
Z yy . So, it would appear natural to calculate the amplitude and phase MT-curves
related to x

A = | Z |

, y -axes as

Z xy Z yx

2 2

xy = yx =

(1 . 17)

o o

xy = Arg Z xy yx = Arg Z yx .