Vol. 4, No. 3, June 2002

*V. S. Yakupov and S. V. Yakupov*

**Institute of Research in Space Physics and Aeronomy, Siberian Division
of the
Russian Academy of Sciences, Yakutsk, Russia**

The geomagnetic field experiences both planetary and local time
variations differing in periodicity and rate. Most difficult to
study are slow variations of the field such as its westward drift,
secular variations and decreases in its main (dipole) component.
These difficulties are overcome by means of repeated magnetic
surveys carried out over large time intervals. Generally they
cannot resolve the detailed time-space structure of field
variations that are still slow but faster than their types
mentioned above. Of particular interest are comparatively
slow variations of the geomagnetic field (more specifically,
the magnetic flux through sufficiently large areas of the
Earth's surface) in volcanic and rifting zones; such variations
are related to the magma movement and thereby to the motion of
the Curie point surface of magnetite (the most widespread ferromagnetic
mineral in the crust). They can provide constraints on the state of
dormant, active, extinct and embryonic volcanoes and are, in the long
run, helpful for predicting volcanic eruptions and/or earthquakes.
This prediction is particularly valuable because local variations in
temperature and magnetic field intensity above a developing magma
chamber undoubtedly antedate the related variation in the stress
state of the overlying rocks giving rise to seismic events. The
integral variations of the magnetic field above an active volcano
and its vicinities are also interesting. Field variations in this
case can be either fast or slow, due to the diversity of their
origins: a change in the position of the Curie point surface under
the volcano; volcanic ejection of a flow varying in density and
velocity including rock fragments that carry remanent and inductive
magnetization; flying rotating rocks fragments possessing a remanence
(with an average magnetization possibly close to zero); possible
presence of a deformable and moving magnetite Curie point surface
in the ejecta cloud and fluctuations in the amount and distribution
of the ejecta cooling below the Curie point above the volcano and
in their magnetization if the material is heterogeneous; fall of
magnetized volcanic products, fluctuations in the direction, velocity
and density of their flux, and inhomogeneous spatial distribution of
the latter; fluctuations in the flux velocity and density of ionized
particles ejected by the volcano, ionization and recombination
processes in the flux (in particular, outflow of ionized gases
and cinder from the neck asymmetrical relative to the crater);
lightning discharges in the ejecta cloud and other possible
effects of electrification of particles during their detachment
from a rock mass and due to mutual friction (prior to the shock
wave resulting in the fracture of rocks with their possible
ejection from the crater); electric discharges in a rock mass
("black lightning") increasing the electric field intensity to 10
^{7} V/m
[*Vorobyev,* 1980];
enhancement of telluric currents due to changes in the electrical conductivity below
and above
the volcano; and so on. The study of processes activating the
volcanic eruption and the eruption itself should be based on
a combined approach using seismic, electrometric and magnetic
methods and peripheral volcanic stations for assessing the
space-time inhomogeneity of volcanic processes; filming for
observation of airglow and evolution of the ejecta cloud;
observation of space-time variations in the amplitude of the
radar pulse reflected from various parts of this cloud and/or
its attenuation in the cloud with the help of an aircraft with
a high-precision positioning system; estimation of the
temperature, electric charge and electric field intensity
distribution in the cloud; and so on. However, all of the
aforementioned phenomena are primarily due to the formation
and development of the magma chamber; therefore, the observation
of geomagnetic flux variations above the chamber is of primary
importance.

Rapid variations in the magnetic flux through surface
loops caused by lightning discharges and passage of meteorites were observed by
* Kalashnikov* [1948],
but these were relative measurements.

We propose an effective method for measuring the modulus of the
magnetic flux through an arbitrary area of the Earth's surface.
Let a closed loop with
*n* coils of a preferably regular (but
generally arbitrary) shape lie at a given time moment on a flat
surface of the Earth (at moderate and high latitudes in both
hemispheres where the vertical component contributes much to
the geomagnetic field intensity). Then, the magnetic flux
through the loop
*F* is equal to
*nSB* = *n**F*_{0}, where
*B* is the average vertical component of the geomagnetic field
induction within the loop of the area
*S*, and
*F*_{0} is the flux
through one coil of the loop. We assume that the loop encompasses
a volcano. Let the magnetic flux changes with time due to the
varying magnetic induction and continuously changing (alternately
decreasing and increasing) number of coils, with the loop remaining
close. Then, an emf is induced in the multicoil closed contour of
the loop:

(1) |

Since the rate of variation in the number of
coils
*dn*/*dt* can and must be maintained large and the magnetic
induction variation rate
*dB*/*dt* is either small or zero during
the measurement period, the first (parenthesized) term in (1)
can be neglected. Thus, the relation

(2) |

is valid with a
reasonable (and controllable) accuracy. Hence, if the rate of
variation in the number of coils is kept constant, the
*S* value
is known and
*E* is measured, we find
*F*_{0} = -*E*/*Sdn*/*dt*
(the implementation
of this idea has been developed by the authors and M. V. Yakupov).
Monitoring of magnetic flux (and thereby field) variations using
a single loop or a system of loops can be performed either
continuously (e.g. in the case of active volcanoes) or in
time intervals of the prescribed duration. In particular,
monitoring of variations in the geomagnetic flux through
volcanoes (regardless of the extent of their activity) must
be conducted near large settlements or in densely populated
areas (Vesuvius, the group of volcanoes near the town of
Petropavlovsk-Kamchatski, and others). Among active volcanoes
in Russia, of particular interest is apparently the Karymski
Volcano in the Kamchatka Peninsula, whose activity has
drastically increased in the last years (personal communication
of S. A. Fedotov). A network of stations should be organized in
active volcanic regions such as Iceland and Kamchatka for regular
observations of geomagnetic flux variations. In areas where the
Curie point surface occurs at depths not greater than ~2 km, its
position can be determined using the technique of radar probing
by magnetic field pulses
[*Yakupov and Yakupov,* 2002].
Obviously, the method proposed for measuring the geomagnetic flux is equally
applicable to its component produced by external sources of the
magnetic field; their contribution can easily be eliminated because
they operate over large areas and their monitoring is ensured by
a network of observatories. In the equatorial region and adjacent
areas where the horizontal component of the geomagnetic field
prevails, the measuring loop should lie in the vertical or nearly
vertical plane. For this purpose, it is possible to utilize natural
and artificial relief forms striking E-W; narrow river valleys
striking N-S, with upper parts of the loop fastened to bridges or
special supports; and natural or artificial supports and structures,
as well as relatively deep reservoirs including offshore areas.

In order to gain numerical estimates, we assume that the loop average
is 1 km
^{2}, the average induction of the geomagnetic field is 0.5 Gs
(5
10
^{-5} A/m), and the alternating frequency is 100 Hz. Then,
according to (2) the induced emf is 5
10
^{3} V if self-induction
is neglected. To estimate the possible effect of the self-induction,
we consider the differential equation determining the current strength
*J* in the closed part of the loop
[*Tamm,* 1956]
with the variable number of its
coils, resistivity
*R* = *R*_{0}*n* and self-induction
*L* = *L*_{0}*n*, where
*R*_{0} and
*L*_{0} are the resistivity and self-induction of one coil and
*n* is the number of coils in the circuit at a given time moment:

(3) |

Let at any time moment the loop be a closed circuit with a
number of coils
*n*. We set

We seek for a partial steady-state
solution to (3) in the form
*J* = *E*/*R*_{0}*n* = *J*_{0}/(1 + *vt*).
Substituting it into (3), we obtain

This actually gives
*J* = *E*/*R*_{0} (1 + *vt*) = *J*_{0}/(1
+ *vt*), and the self-induction
emf values due to a change in the current strength and self-induction
of the circuit cancel out and can be neglected. The complete solution
of (3) should include, in addition to its partial solution, the
general solution of the homogeneous equation

(4) |

The solution
of (4) has the form
*A* exp(-*B*/*t*), where
*A* and
*B* are constants, and
therefore rapidly decreases with time, so that its contribution is
negligibly small in a steady-state regime. If
*E* can be reliably
measured starting from a value of 10 mV, a change in the vertical
component of the magnetic field
*D**Z* can be determined starting from
10
^{-6} Oe (0.1
*g* ). We suppose that this change is due to
the
ascent of a magma chamber in the form of a vertical circular cylinder
with a radius
*R*. Let the Curie point surface be located at a depth
*h*3*R* above the chamber. The vertical
component of the geomagnetic
field intensity above the center of the cylinder having a normal
magnetization
*J*_{n} is
-2*p**J*_{n} (1 - *h*/(*R*^{2}
+ *h*^{2})^{1/2}).
Taking logarithm of the increment
*D**h* = *f*(*D**Z*/*Z*),
approximate calculations show that, given
*h* = 1 km,
the magnetic susceptibility
*c* = 10^{-4} and
*J*_{n} = *c**H* = 10^{-6}510^{-5},
a change of
*Z* by 0.1
*g* corresponds to a ~0.1-m shift of the
Curie point surface above the vertical cylinder modeling the magma
chamber. The actual value of this shift should apparently be
estimated at
1 m, if one takes into account fast variations
and disturbances of the magnetic field, surface temperature
variations, difference between the real and model configurations
of the magma chamber, and so on.

A method is proposed
for measuring the modulus (and its time variations) of the
geomagnetic flux through arbitrary areas of the Earth's surface.
Of particular interest are measurements of relatively slow flux
variations in active volcanic areas and rift zones, including
the monitoring of active volcanoes and assessment of processes
in dormant, extinct and embryonic volcanoes for predicting their
possible eruptions and associated seismic phenomena. Theoretical
estimates indicate that, if the magma chamber is modeled by a
vertical cylinder of radius
*R*, the detectable amount of the ascent
of the magnetite Curie point surface overlying the chamber at a
depth
*h*3*R* is ~0.1 m and more; the
real estimate should
apparently be raised to ~1 m.

Kalashnikov, A. G., On a new method for studying weak variations in
the geomagnetic field (in Russian), * Izv. Akad. Nauk SSSR, Ser. Geogr. Geofiz.,
XII,* (2), 137-146, 1948.

Tamm, I. E., * Fundamentals of the Theory of Electricity* (in Russian), GITTL,
Moscow, 1956.

Vorobyev, A. A., * Equilibrium and Energy Conversion in the Earth's Interiors*
(in Russian), Tomsk, 1980.

Yakupov, V. S., and S. V. Yakupov, Sounding of the Earth by magnetic field pulses
(in Russian), * Dokl. Ross. Akad. Nauk, 384,* (6), 2002.