3D numerical studies have shown that the vertical voltage above the Baikal deep-water fault is detectable and that respective transfer functions, Ez-responses, are sensitive to the electrical resistivity changes of the fault, i.e.
these functions appear actually informative with respect to the resistivity «breath» of the fault. It means that if the fault resistivity changed, conventional electromagnetic instruments would be able to detect this fact by measurement
of the vertical electric field, Ez, or the vertical electric voltage just above the fault as well as horizontal magnetic field on the shore. Other electromagnetic field components (Ex, Ey, Hz) do not seem to be sensitive to the resistivity changes in such a thin fault (as wide as 500 m). On the other hand, such changes are thought to
be able to indicate a change of a stress state in the earthquake preparation zone. Besides, the vertical profile at the bottom of Lake Baikal is suitable for electromagnetic monitoring of the fault electrical resistivity changes.
Altogether, the vertical voltage above the deep-water fault might be one of earthquake precursors

Avdeev, D. B.

Kuvshinov, A. V.

Pankratov, O. V.

Shneyer, V. S.

Trofimov, I. L.

Earth-prints Repository

151
ANNALS  OF  GEOPHYSICS, VOL.  47, N.  1, February  2004
Key  words Baikal rift zone – electromagnetic mon-
itoring – transfer functions – resistivity changes of
the fault
1. Introduction 
It is generally accepted that one of the pos-
sible precursors of earthquake in the seismical-
ly active Baikal region may be the change in the
electrical resistivity of the saturated porous
rock in deep-water rift faults. In accordance
with the modern concept of the Baikal region
geoelectrical structure (Merklin et al., 1979),
there is a narrow fault there that is galvanically
connected with a deep-seated conductor. Berdi-
chevsky et al. (1989) showed that for two-di-
mensional (2D) model of marine deep magne-
totelluric investigations the vertical electric
field at the ocean bottom is highly sensitive to
the resistivity of the underlying cross-section.
Besides, Berdichevsky et al. (1996) showed
that certain 2D Earth models would generate
considerable vertical electrical currents if the
models include vertical faults of low resistivity.
These authors used horizontal magnetotelluric
field as an incident field. The latter work deals
with magnetotellurics in the Lesser Caucasus
but the first one deals with deep marine magne-
totellurics. Meanwhile, Baikal water is fresh
and much more resistive as compared with the
oceanic water, however, Shneyer et al. (1998)
proved that in 2D model of Southern Baikal the
vertical electric field, Ez, is again sensitive to
the presence of thin vertical fault of low resis-
tivity. Though these results are valuable, we de-
cided to explore the behaviour of Ez for a three-
dimensional (3D) Baikal model, bearing in
mind that the fault is a body of limited length
but not of an infinite one. In this paper we build
Ez-response as a monitor of a Baikal rift
fault electrical resistivity:
3D modelling studies
Oleg V. Pankratov, Alexei V. Kuvshinov, Dmitry B. Avdeev, Vitaly S. Shneyer and Igor L. Trofimov
Geoelectromagnetic Research Institute, Russian Academy of Sciences, Moscow Region, Russia
Abstract
3D numerical studies have shown that the vertical voltage above the Baikal deep-water fault is detectable and
that respective transfer functions, Ez-responses, are sensitive to the electrical resistivity changes of the fault, i.e.
these functions appear actually informative with respect to the resistivity «breath» of the fault. It means that if
the fault resistivity changed, conventional electromagnetic instruments would be able to detect this fact by meas-
urement of the vertical electric field, Ez, or the vertical electric voltage just above the fault as well as horizontal
magnetic field on the shore. Other electromagnetic field components (Ex, Ey, Hz) do not seem to be sensitive to
the resistivity changes in such a thin fault (as wide as 500 m). On the other hand, such changes are thought to
be able to indicate a change of a stress state in the earthquake preparation zone. Besides, the vertical profile at
the bottom of Lake Baikal is suitable for electromagnetic monitoring of the fault electrical resistivity changes.
Altogether, the vertical voltage above the deep-water fault might be one of earthquake precursors.
Mailing address: Dr. Oleg V. Pankratov, Geoelectroma-
gnetic Research Institute, Russian Academy of Sciences,
142190 Troitsk, P.O. Box 30, Moscow Region, Russia; e-
mail: o.pankratov@mtu-net.ru
152
Oleg V. Pankratov, Alexei V. Kuvshinov, Dmitry B. Avdeev, Vitaly S. Shneyer and Igor L. Trofimov
a simple 3D model of Southern Baikal and ver-
ify: 1) whether Ez is detectable over the fault,
and 2) whether Ez-response is sensitive to the
resistivity changes of the fault. 
2. Model 
Lake Baikal is located in the southern part of
Eastern Siberia (see fig. 1). It is the oldest exist-
ing freshwater lake on Earth (20-25 million years
old), being the deepest continental body of water.
It is 636 km long and 48 km wide. Baikal lies in
a deep structural hollow surrounded by rock. The
fault that we are interested in, is located at the
southern part of Lake Baikal, not far from the
town of Slydyanka. A simplified 3D resistivity
model of the Baikal deep fault is shown in figs.
2 and 3. The geometry of the model was taken
mainly from seismic data by Merklin et al.
(1979), whereas the resistivity data were taken
from electromagnetic data by Popov (1977), and
Kieselev and Popov (1992). In the model the
2 km thick, 40 Ω⋅m water layer is underlain by
Fig. 1. Map of the region of Lake Baikal. Modelling region is marked with a rectangle. The fault is marked
with a thick line.
153
Ez-response as a monitor of a Baikal rift fault electrical resistivity: 3D modelling studies
the 1 km thick, 60 Ω⋅m sedimentary layer. Both
layers are surrounded and underlain by 1000
Ω⋅m rock. Below, at a depth of 15 km, there is a
10 km thick conductive layer of 10 Ω⋅m. As for
the fault in the model, it is 28 km long in y-di-
rection (parallel to the shore) and 0.5 km wide in
x-direction (perpendicular to the shore). The ver-
tical size of the fault is 13 km. The fault outcrop
is located at lake bottom exactly where the 35°
steep slope of the north-western shore of the lake
is ending. The shape of the south-eastern shore
slope has been proved not to affect the electro-
magnetic (EM) field calculated in the vicinity of
north-western shore. Thus, the fault appears to
be galvanically connecting the deep conductive
layer under the lake and the lake itself. 
3. Numerical modelling
In the 3D resistivity model proposed we
have performed a series of simulations of the
Fig. 2. 3D resistivity model of the Baikal Fault (side view). Line A-B is the profile where behaviour of Ez is
studied. C is the coast site where components Hx and Hy are taken to obtain Ez response (see details in the text).
Fig. 3. 3D resistivity model (plane view).
154
Oleg V. Pankratov, Alexei V. Kuvshinov, Dmitry B. Avdeev, Vitaly S. Shneyer and Igor L. Trofimov
vertical electric field, Ez, along vertical profile
A-B as well as horizontal magnetic field on the
shore. This 2 km long profile (from lake surface
to the bottom) is located just over the center of
the fault (see fig. 2). The amplitude of the inci-
dent plane wave electric field is chosen to be
equal to 10 mV/km, resembling typical ampli-
tudes of mid-latitude disturbances. Period of
the incident field is taken to be 100 s and 1 h.
While modelling, we varied the fault resistivity,
ρfault, the values taken to be 10, 11 and 20 Ω⋅m.
To perform the simulations we used X3D code
which is based on the solution of modified scat-
tering equation by the Krylov subspace itera-
tions (Avdeev et al., 1997, 2000). The model-
ling region of 44 km × 80 km × 15 km is divid-
ed into 440 × 100 × 14 cells.
Figure 4 presents the vertical electric field,
Ez, along vertical profile A-B for Ex-polarized
incident plane wave, with fault resistivity being
10 Ω⋅m. Left and right panels of the figure re-
veal the results for the periods of 100 s and 1 h
respectively. The figure demonstrates that the
values of |Ez| are ranging, depending on depth,
from zero (at the surface) up to 9 mV/km (at the
bottom). In practice during the future experi-
ment we are going to measure the vertical volt-
age, V(A, B), between points A and B. In our
model, V(A, B) can be calculated as
.,V E z dzA B z
A
B
= #^ ]h g .
The left plot in fig. 4 implies that the vertical
voltage, V(A, B), should exceed 5 mV, which is
very promising, since 5 mV could be readily de-
tected by conventional EM instruments, their
measurement precision accounting for 0.01 mV.
In addition, it is also seen from the figure that
Fig. 4. Electric field components Ez and Ex along profile A-B. The source is Ex-polarized plane wave. The re-
sults are presented for periods 100 s (left panel) and for 1 h (right panel). The fault resistivity is 10 Ω⋅m.
155
Ez-response as a monitor of a Baikal rift fault electrical resistivity: 3D modelling studies
near the fault outcrop, Ez-field even dominates
the primary field Ex. Note that only real parts of
the components are discussed, since imaginary
parts are two orders of magnitude less.
It can be seen from fig. 4 Ez(z) that can be
approximated as follows:
hE z E b ez z
z b. -] ] ]g g g (0< z ≤ b) (3.1)
when we evaluate integral
,V E z dz E z dzA B z z
b
A
B
0
= =# #^ ] ]h g g .
Here b = 2 km is the bottom depth. Also, h = 621
m and h = 586 m for period of 100 s and 1 h re-
spectively. As a consequence, the vertical volt-
age is directly proportional to the vertical elec-
tric field measured at the bottom
,V k E bA B z$=^ ]h g (3.2)
where proportionality coefficient is k = h (1−e−b/h).
We can show that coefficient k does not depend
on the amplitude of the incident field.
The other consequence: higher values of the
vertical electric field are accumulated near the
bottom, so that it is not necessary to locate point
A exactly at the surface. We can locate point A,
say, 100 or 200 m deeper without significant
change in the value of V(A, B).
As for the other polarization of the incident
field (Ey-polarized plane wave), the vertical
electric field is at least two orders of magnitude
less than that for Ex-polarized incident field.
So far we demonstrated the amplitudes of
the fields themselves. But it is known that while
monitoring, the external field should be exclud-
ed from consideration. For this purpose, we in-
troduce Ez-response as the expansion coeffi-
cients in
,V u H u HA B zx x
r
zy y
r= +^ h (3.3)
where Hxr and Hyr are the horizontal magnetic
field components at the coastal reference site
(site C, see figs. 2 and 3). 
Expansion (3.3) can be used in the following
way. Let V1(A, B) and V 2(A, B) be the vertical
voltage values measured for any two different
polarizations of the incident field. Let (Hx1, Hy1)
and (Hx2, Hy2) be the horizontal magnetic fields
measured at the coastal reference site for the
first and for the second polarization respective-
ly. From expansion (3.3) it follows that:
,
,
V u H u HA B
A B
zx x zy y
zx x zy y
1 1 1
2 2 2
= +
.V u H u H= +
^
^
h
h (3.4)
Therefore, we obtain final formulae for transfer
functions uzx and uzy as follows
,
,detu
u
H
H
H
H
H
V
V
A B
A B
1
zy
zx y
x
y
x
2
2
1
1
1
2= -
-d e ^^en o hho (3.5)
where detH = (Hx1Hx2 − Hy1Hy2). Then these
transfer functions uzx and uzy are called the Ez-
responses because bigger values of the vertical
electric field, Ez, are accumulated near the bot-
tom and because V(A, B) is proportional to Ez(b)
(eq. (3.2)). 
Table I presents the absolute value of the Ez-
response, |uzy|, shown with respect to the fault
resistivity and period. Table I shows |uzy| trans-
fer function alone, since response uzx appears to
be negligibly small compared to uzy. This is due
to the fact that only TM-polarized incident field
generates major vertical electrical current
through the fault. 
Although electromagnetic field components
Ex, Ey, Hx, Hy, Hz appear to be insensitive to the
Table I. Absolute value of Ez-response, |uzy|, with
respect to the fault resistivity and period.
Ez-response (mV/nT)
100 s                 1 h
ρfault=10 Ω⋅m 776 ⋅10 −9 186 ⋅10 −9
ρfault=11 Ω⋅m 743 ⋅10 −9 180 ⋅10 −9
ρfault=20 Ω⋅m 526 ⋅10 −9 128 ⋅10 −9
precision of 14 ⋅10 −9 5 ⋅10 −9
experimental
Ez-response
156
Oleg V. Pankratov, Alexei V. Kuvshinov, Dmitry B. Avdeev, Vitaly S. Shneyer and Igor L. Trofimov
resistivity of the fault, we still need components
Hx and Hy on the shore in order to obtain trans-
fer functions uzx and uzy. Indeed, transfer func-
tions uzx and uzy do not depend on the polarization
of the incident field but the vertical voltage does.
The second row of table I shows that for a
100 s period, an operator should measure the
values of 776, 743, and 526 and distinguish
them from each other having the measurement
precision equal to 14. Obviously it is possible.
For a 1 h period, the measurement precision is
just enough to distinguish the 10 Ω⋅m fault
from the 11 Ω⋅m fault; and it is far enough to
distinguish the 11 Ω⋅m fault from the 20 Ω⋅m
fault. Altogether, for both periods the changes
in the fault resistivity lead to detectable changes
in Ez-responses. More explicitly, 10% and
100% fault resistivity changes result in 4% and
30% Ez-response changes, respectively. It
should be also stressed that traditional imped-
ance responses (simulated but not shown here)
have appeared to be practically insensitive to
the changes of the fault resistivity. Further nu-
merical modelling (performed but not shown
here) reveals that the link between the Ez-re-
sponses and the fault resistivity holds valid for
bigger resistivity values. Namely, for the values
ρfault=10, 11, 12, 20, 40, 80, 160 and 320 Ω⋅m
we calculated the Ez-responses and found that|uzy(ρfault)| can be approximated as follows:
uzy fault fault$.t o t
c_ i (3.6)
where γ = γ (T) and ν =ν (T) depend on the peri-
od, T, of the incident field. Approximation (3.6)
now follows that though we could hardly distin-
guish the 10 Ω⋅m fault from the 11 Ω⋅m fault at
1 h period, the 10 Ω⋅m fault can easily be distin-
guished from the 14 Ω⋅m fault at this period.
Though our model is an estimate, we realize
that the link between the Ez-responses and the
fault resistivity is rough enough and it must be
detected while in situ measurements.
4. Conclusions 
3D numerical studies have shown that the
vertical voltage is detectable above the Baikal
deep fault, and that Ez-responses are sensitive to
the resistivity changes of the fault, i.e. Ez-re-
sponses appear actually informative with re-
spect to the resistivity «breath» of the fault.
Further studies should include more detailed
modelling and field operations. It should an-
swer the question whether changes in Ez-re-
sponses (and ρ fault) are connected with changes
in a stress state in the fault vicinity and whether
Ez-responses can be used as one of earthquake
precursors.
Acknowledgements
The research has been partly made possible
through grants No. 00-05-64182 and No. 00-05-
64677 from the Russian Foundation for Basic
Research. We are also grateful for both review-
ers’ valuable comments.
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Ez-response as a monitor of a Baikal rift fault electrical resistivity: 3D modelling studies

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Ez-response as a monitor of a Baikal rift fault electrical resistivity: 3D modelling studies

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