Vol.5, No.8A1, 38-45 (2013) Natural Science
Model of the singular current source—The indicator
of geodynamic processes in Japan in 2009-2011
Ludmila F. Moskovskaya
Saint Petersburg Branch of the Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation,
Russian Academy of Sciences, Saint Petersburg, Russia; lf_mosc@mail.ru
Received 13 June 2013; revised 13 July 2013; accepted 20 July 2013
Copyright © 2013 Ludmila F. Moskovskaya. This is an open access article distributed under the Creative Commons Attribution Li-
cense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The calculation method of the location of the
singular generalized current source according
to synchronous measurements of the magnetic
field in the remote points is proposed. It is de-
signed for the continuous monitoring of chan-
ges of the degree of electromagnetic heteroge-
neity of the geophysical environment. Regular
fluctuations of the apparent distance to the ef-
fective single source were recorded according
to the magnetic data of the observatories in Ja-
pan 2009-2011. They are connected with the
rhythm of the geodynamic processes in the vi-
cinity of the station Kakioka. The most signifi-
cant decrease in the apparent distance was
registered in connection with the seismic acti-
vation of the region, including the catastrophic
earthquake of March 11, 2011 with a magnitude
of M = 9.1. The anomalous behavior of the ap-
parent parameters of the generalized source
was displayed not less than two weeks before
the earthquake. Characteristic changes of the
curves were registered in the period of three
Keywords: Precursors of Eart hq uakes; Proces s ing
of Magnetic Field Measurement; Geody namics
Tectonic activity is associated with the transformation
and the release of enormous energies and is accompanied
by abnormal changes of different physical fields. A wide
complex of geophysical research is applied to studying the
phenomena occurring and diagnostics of seismic activa-
tion of the region. It is primarily direct method: seismic
survey and registration of radiation associated with the
deformation and crushing of rock—the acoustic and
low-frequency electromagnetic radiation, gas emanations
[1-5] Preparation processes are reflected variations of
anomalies of temperature and pressure, electrical resis-
tivity of the earth's crust [6-11]. Due to the close interac-
tion of geophysical shells, the Earth abnormal physical
fields of the lithosphere in the process of earthquake
preparation excite anomalies in the atmosphere and
ionosphere. Precursor of large earthquakes was detected
by satellite measurements [12-14]. Long-term monitor-
ing of various fields in earthquake-prone regions gives
an opportunity to develop new and improve the tradi-
tional approaches to data analysis, based on the real field
experiment. We can speak about the methods of registra-
tion fields of direct change in the environment and
changes in the fields-consequences caused by primary.
So anomalies of pressure, temperature, gas emanations
can be considered as the core of electromagnetic re-
In this article, we proposed a model of the singular
source for the joint processing of synchronous measure-
ments of the magnetic field in spatially separated points.
This approach in a sense is similar to the mediated regis-
tration of changes in the environment. It simplifies the
analysis of the material. The apparent distance to the
singular source is connected with electromagnetic proc-
esses occurring in the environments of the earth. This
transformation reduces the decision dimension and thus
simplifies the analysis of temporal intervals of anoma-
lous behavior.
2.1. Data and Sources
We used measure of the magnetic field of the World
Data Center for Geomagnetism of Kyoto University
(http://wdc.kugi.kyo to-u.ac.jp/) and The Advanced Na-
tional Seismic System catalog by the Northern California
Earthquake Data Center (http://www.ncedc.org/anss/cata
Copyright © 2013 SciRes. OPEN ACC ESS
L. F. Moskovskaya / Natural Science 5 (2013) 38-45 39
log-search.html). We analyzed the time series of the vec-
tor of the magnetic field (H, Z-component) of the three
observatories Japan: Kanoya, Kakioka, Memambetsu.
The sample rate is 1 second, an accuracy of 0.01 nT. The
stations form a triangle, extending in the meridional di-
rection (Figure 1). Seismic catalog contains medium and
large earthquake M 4. The paper presents the results of
studies of monitoring from 1 January 2009 to 30 Sep-
tember 2011.
2.2. Pre-Processing of the Measurements of
the Magnetic Field
The problem was to detect changes in magnetic fields
associated with seismic activity of the region. We used
night segments of the time series, minimally contami-
nated by man-made noise. On a three-hour interval of the
day (from 1:30 to 4:30 hours local time) were calculated
average values of the horizontal (H) and vertical (Z)
component. Each function of the mean values was di-
vided into the time trend and anomalous components,
that contains the local variations of the field. The split-
ting was made by the method of adaptive robust filtration
[15,16] in a sliding window 61 days. It turned out that
the horizontal projection of the anomalous fields has the
form is functionally identical index Dst-variation of
the magnetic field (http://wdc.kugi.kyoto-u.ac.jp). Verti-
cal components of anomalous field at all three stations
are also functionally similar. Amplitude component of
anomalous field decreases with increasing distance of the
station from the equator.
The discovery of a close functional relationship
anomalous components at all stations made us try to
analyze the material using a single model of interpreta-
3.1. Rationale Model of Interpretation
The ring current is the leading physical process which
specifies the form of variation of the anomalous fields.
Variations of the magnetic field penetrate all the physical
space, initiating secondary currents in the environment.
Physical carrier of current systems can be electromag-
netically active environments of the Earth: plasma,
ionosphere, lithosphere. The distance between the ob-
servatories is 900 - 1800 km. Distance to the nearest ob-
servatories conducting environment, the crust of the
earth and the ionosphere, much less. Electromagnetic
properties of environment change as a vertically so later-
ally. Large spatial dimensions of the electromagnetic
disturbances, their proximities to surface observations re-
quire to describe the electromagnetic characteristics of
conducting environments of the use of multivariate
model. At the same time the number of registration
points of field very little. It is known that the solution of
inverse problems of geophysics not single [17]. There are
equivalent distributions of anomalous sources, creating a
specified morphology of the field. For example, the po-
tential field of the layer can be simulated by object of
another class models—singular source. In result, the
number of model parameters is reduced.
The geometry of the current systems of planetary scale
for the low latitudes: the ring current, equatorial current
have a latitudinal direction. Diurnal variation of the
magnetic field is modulated Sq - current variations that
are connected with a wind movement of air masses. Ac-
cording to the experimental data in 4 hours local time on
the latitude 40˚, vector wind currents are mainly directed
to the West with a small projection on the North [18].
We used a simple model of interpretation: a homoge-
neous nonconducting space where parallel to the plane of
observation (in the latitudinal direction) flows horizontal
current. The magnetic field is measured in points located
perpendicular to the current stream (on meridian). Effec-
tive singular source we call horizontal line current, which
is equivalent to the real current distribution relative se-
lected parameters of the magnetic field in the given
points of observation. The problem consists in determin-
ing the coordinates of a source in the plane perpendicular
to the line current. We used in the calculations only ver-
tical (Z) and horizontal (H) anomalous components.
The practical application of such a schematic model
lies in the transformation of several signals of the
anomalous magnetic field to the functions of the coordi-
nates of the effective current source. And investigation of
the regularities of changes of parameters of the model
over time.
3.2. Ways to Calculate the Coordinates of
the Singular Current Source
We used three ways of calculation. We will briefly the
main ideas.
1) Geometric method (Figure 2(a)). Line current gen-
erates a magnetic field lines which lie in the perpendicu-
lar plane. The magnetic field lines lie on the tangent to a
circle perpendicular to the radius of the source. The
height 0
of the line current is determined by the ex-
cos cos
Hd 2
 , (1)
arctg Hi
 
 
 ,,,;
where 1i
—the vertical and horizontal compo-
nents of the anomalous magnetic field on the two sepa-
rated stations; d—distance between stations.
The ratio of angles 12
corresponds to sequen-
Copyright © 2013 SciRes. OPEN AC CESS
L. F. Moskovskaya / Natural Science 5 (2013) 38-45
Figure 1. The layout of magnetic observato-
ries Japan. KNY—Kanoya (φ = 31.424˚, λ =
130.880˚), KAK—Kakioka (φ = 36.232˚, λ =
140.186˚), MMB—Memambetsu (φ = 43.910˚,
λ = 144.189˚). The asterisk marks the earth-
quake M=9.1, 11 March 2011.
cing of observation points fields 1.2 left to right and the
position of the source above.
2) The energy method (Figure 2(b)). Determination of
the position of a concentrated source can be based on the
hypothesis on the rate of decreasing fields, depending on
the distance to a source. We postulate the law downturn
. The decay rate for the point singular
source (Biot-Savart law) is equal to two: 2
. The
integral over the length of the infinite straight line gives
the decay rate 1
.The real distribution of the hori-
zontal current in the volume will lead to the fact that the
provisions of the apparent centres effective current
sources will be shifted closer to the observation points of
the magnetic field. Thus, effective distance to the com-
mon source will become weaker vary. This is equivalent
to reducing the rate of decay of the field. The height 0
of the line current is determined by the expression:
020 12
030 33
XrX dr
 
 
22 2
3213 3
32 11
21 1
drdr R
drdr RR
 
 
 
1, 2, 3.,,
ii ii
 components of the ano-
malous magnetic field in three spaced stations; 1
the distance between the stations.
-exponential quan-
tity of field decay in dependence of distance from the
, where
HH ZZ —the
module of the magnetic field.
3) Geometrically-energy method (Figure 2(a)). Coor-
dinates effective source is evaluated based on the rate of
decay for the fields depending on the distance to the
source and raster corner of the output of an electromag-
netic wave from efficient source.
The height 0
of the line current is determined by
the expression:
Hd rr
 , (3)
 1,2.
Angle, which is opposite the base of the triangle
, where i
, ,
i = 1, 2; 1
—the vertical and horizontal
components of the anomalous magnetic field on the
two separated stations; d—distance between stations.
-exponential quantity of field decay in dependence
of distance from the source:
, where
—the module of the magnetic field.
3.3. Indexes Spatial Homogeneity
Model interpretation assumes that current source is the
same for all three stations. In reality, in the vicinity of a
station may experience additional electromagnetic het-
erogeneity lithospheric or ionospheric. This will cause
the displacement of the estimation of the parameters of a
generalized source. If the field of spatial rather homoge-
neous and can be simulated a singular source, then geo-
metrical orderliness is necessary. For sequence of the
registration points of fields (1, 2, 3) values of the angle
of the direction to the source are an ordered:
 or 123
. Angles are measured
from the vertical. The possibility to solve the problem of
determining the coordinates of a common source ac-
cording to three stations in the energy method is deter-
mined by the energy criterion of spatial uniformity of the
We introduced indexes geometric and energetic ho-
mogeneity to describe the spatial uniformity of the mag-
netic field. If the in current day criterion of homogeneity
was correct or not correct, then the index relies equal to
Figure 2. Parameters of the model. a) variant No. 1—geometric
method, variant No. 3—geometrically-energy method; b) vari-
ant No. 2—energy method.
Copyright © 2013 SciRes. OPEN AC CESS
L. F. Moskovskaya / Natural Science 5 (2013) 38-45 41
either 1 or 0. We also used the generalized index of ho-
mogeneity is defined as the arithmetic average of the first
3.4. Comment about the Choice of the
Model of Interpretation
The homogeneous space is extremely schematic model
of the enclosing environment. In reality, we are dealing
with a system spatially separated electroconductive lay-
ers of the Earth carries of current systems. The solution
to problem of determining the magnetic field from the
source in the environment can be approximated by the
composition of multiple reflections from the boundary
layers [19]. The lithosphere and the ionosphere are the
closest to the points of measurements of the magnetic
field. They are electromagnetically active environments.
Currents generated by a variety of physical processes can
occur here. Current configuration in conducting shells
defines the main energy contribution to the cumulative
result in the given time. Effective singular source can be
either in the lower half-space, or the top.The position of
the generalized source relative to the plane of observa-
tion of the magnetic field is determined by the order of
the changes in angles: 123
—the upper half-
space and 12
 – the lower.
4.1. The Apparent Distance of the
Generalized Singular Source
to the Earth
We estimated the effective distance to the singular
current source for three variants of calculations. Indicator
field decay with distance was set equal to 1
. The
calculations were performed using projections of dis-
tances between the stations at the meridian (Figure 1).
We carried out a separate analysis of the functions of
the distance to sources, caught up in the upper and lower
half space, and the function module distances. It turned
out that the average logarithmic levels for the years
2009-2010 the same name pairs of evaluation differ not
more than 3%. This value significantly is less than the
local fluctuations of the functions.
Generalized source is often in the upper half-space.
The boundary surface-to-air is a physical border, defin-
ing the main geometry reflection. In this article we show
module function of distance to the surface of the earth.
Short-term variations of the magnetic field of the Earth are
generated by external causes: solar-terrestrial relation-
ships. Field changes caused by variations of geoelectrical
parameters of the lithosphere-atmosphere-ionosphere
associated with geodynamic processes are characterized
by longer periods of course. For the best selection of
search effects of geodynamic processes on the fields, the
functions of the apparent distances singular source and
spatial uniformity indexes have been smoothed using a
robust filtering. We used a logarithmic scaling of the
distance signal at the filtering. The average levels of the
apparent distances differ for different ways of solving
problem (Figure 3). Logarithmic average (km) is calcu-
lated for 2009-2010 are: ;
lg H3.4
lg H3.7;
lg H3.8;
lg H3.1 ; ;
lg H3.1
lg H3.1;
lg H3.25.
The dynamic range of the signal changes the functions
of distances is one order for a relatively quiet seismic
period of the first two years. Generally more functional
similarity of the apparent distance charts is found for
different pairs of stations of one and the same variant of
estimation. The nature of the behavior functions of the
apparent distances, defined by measurements of fields at
various stations, was found to be significantly different
in the period immediately preceding the explosion of
seismic activity 11 March 2011, and during its highest
The apparent distances calculated for the neighbouring
stations Kanoya-Kakioka (KNY-KAK), Kakioka-Me-
mambetsu (KAK-MBB) revealed the sharp anomalous
reduction of the level in the form of several long deep
local minima of a function during the time interval of
seismic activation, while the estimates, made according
to the distant stations Kanoya-Memambetsu (KNY-MMB)
found no such tendency. An abnormal decrease the ap-
parent distance in the period of seismic activation also
clearly manifested in the energy method calculation
while using measurements of three stations.
4.2. Variations of the Apparent Distance to
the Singular Source Pre-Earthquake on
March 11, 2011 and Related Subsequent
Seismic Activation Zone
11 March 2011 corresponds to 800 monitoring day.
Days are counted from 1 January 2009. Most strongly
the effect of reducing the apparent distances manifested
in the ways of calculation, involving energy assumptions
about the rate of decay of the field (Figure 3(b)). For
energy-geometrical estimation for a pair of stations
(KNY-KAK) abnormal decline apparent distance to the
generalized source is distinctly registered since 776 days,
and reaches the first minimum (52 km) in 794 day moni-
toring (6 days before EQ). Thus, anomalous trend was
found to 24 days before the event. Signal crosses the
level of 1000 km in 784 day, 16 days before the catas-
trophic earthquake. The second deep minimum of the
curve (140 - 150 km) is recorded in 845 - 855 day. Re-
turn to the level of 1000 km occurs in 869 day. The dura-
tion of the anomalous behavior of the function is 85 days.
Еstimation by magnetic fields pair of stations (KAK-
Copyright © 2013 SciRes. OPEN AC CESS
L. F. Moskovskaya / Natural Science 5 (2013) 38-45
Copyright © 2013 SciRes.
Figure 3. The parameters of the singular source and seismic activity. (a) Average indexes field homoge-
neity on the three stations: geometric index 1), energetic index 2), the arithmetic average of the two 3).
Averaged window is 7 days. (b) The distance to the singular source. Version of the estimation and sta-
tions, whose measurements were used to calculate, marked on the right. The results of all variants were
filtered with window 7 days. Graphics consistently shifted relative to the previous on two orders of
magnitude. The vertical lines mark the minima of functions. (с) The time sequence of earthquakes in a
radius of 300 km around the station Kakioka. Vertical lines indicate a pauses of seismic activity. Num-
bers show the duration in days.
MMB) revealed a decline signal since 778 day. The level
of less than 1000 km was traversed in 783 day (17 days
before). The first minimum of H = 262 km is fixed in
791 day (9 days before). The second (global) minimum
apparent distance is detected on 844 day, another mini-
mum H = 240 km on 858 day. Crossing the level of 1000
km occurs in 864 day. The duration of the anomalous
behavior of the functions of the apparent distance is 81
Activization of seismic activity zone manifested in the
perturbation fields, indices homogeneity fall to zero in
some intervals (Figure 3(a)).
Reduction of the apparent distance of the generalized
source, the most violent manifestation of the effect in the
estimates, including the energy component signals, no
effect when processing data pair remote observatories
(KNY-MMB)—all this suggests that the reason for this
behaviour change assessments is the local electromag-
netic heterogeneity. It is concentrated in the vicinity of
the central observatory Kakioka and increases in connec-
tion with the activation of the seismic zone.
When energy method of distances definition simulta-
neously by the fields of the three stations is used, esti-
mates are functionally more sustainable. Anomalous re-
duction of the apparent distances H < 1000 km kept most
long—108 days: on the interval 784 - 891 days. A de-
crease is recorded 16 days before. Three minimum stand
out: H(802) = 331 km, H(822) = 672 km, H(886) = 615
km. It should be noted that in this version of the estima-
tion a large number of points was excluded because of an
incompatibility of a system of equations. The decision
became possible only for 517 data points from 1002.
Thus, we indirectly registered geoelectric processes
related tectonic activity. This effect was found for geo-
physical fields accompanying the tectonic processes of
transformation and the release of huge energies. This re-
sult prompted us to analyze the field of seismicity in the
vicinity of the magnetic observatories on the time inter-
val magnetic monitoring since 2009.
L. F. Moskovskaya / Natural Science 5 (2013) 38-45 43
4.3. Correlation of Variations of the
Apparent Distance to the Singular
Source with the Rhythm of Seismic
Activation of the Geological Structure
Visual analysis of the number of seismic events of
medium and high energy during the time has
shown, that in the vicinity of the station Kakioka clearly
manifested by the rhythmic nature of tectonic processes.
Time intervals of seismic activation interspersed with
pauses. The nature of dynamics of seismic events is
saved when you increase the area under consideration of
the radius of 300 to 500 km. For stations Kanoya and
Memambetsu was not revealed such a pulsation. Se-
quence of seismic events within a radius of 300 km
around the observatory Kakioka is shown in Figure 3(c).
It turned out that the reduction in the extent or another,
apparent distances to the effective current source pre-
cedes almost all the launches of a series of earthquakes.
Reduction accompanied by a decrease field homogeneity
(Figure 3(a)). Vertical lines are plotted on the local
minima in figure. The most powerful seismic shocks
(M> ), occurring within the series, also may be pre-
ceded by the apparent distance reduction (interval 6-7,
The results of mathematical modeling can be genera-
lized to the two main assertions. Estimation of the ap-
parent distance to the singular generalized current source,
which can be matched to the anomalous magnetic field,
was obtained. The apparent distance greatly changes in
time. And these variations are associated with geody-
namic processes in the region.
5.1. The Apparent distance to the
Generalized Source
The question arises: what is the sense to invest in the
distance to the generalized source? For understanding, let
remind the main sources of magnetic variations of the
planetary origin. Variations of the currents flowing in the
environments of the Earth are the cause of the variations
of the magnetic field. Carriers of current systems are
spatially separated.
For low and mid-latitudes they are: a circular electric
current trapped particles in the radiation belts (height
R, —radius of the Earth km),
ionospheric currents (100 to 1000 km), the most inten-
sive at altitudes between 100 and 400 km, Sq variation
and equatorial electrojet, currents in plasma [20], the
currents in the lithosphere. Interaction of the magneto-
sphere with the solar wind causes variations in the ring
current, accompanied by variations of the magnetic field,
which in turn induce electric currents in the downstream
areas of increased conductivity.
A set of continuously existing coordinated currents
distributed in environment is normal or background.
Depth (or height) of penetration and density of the nor-
mal currents in the shells may vary with time. Currents
of the lithosphere and ionosphere will considerably in-
fluence the result of the estimations, as the distance from
the observatories to them much less. Generalized current
source is the mathematically equivalent solution (in
terms of creating the anomalous magnetic field in points
observations) to the system of currents, distributed on a
set of spatially separated physical carrier. Effective dis-
tance reflects a measure of the intensity of the electro-
magnetic excitation of the environment.
5.2. Variations of the Apparent Distance to
the Generalized Current Source
Local space-time electromagnetic variations, associ-
ated with geodynamic processes, are imposed on the en-
ergy main carrier signal. The share of these processes in
the aggregate result of the calculation is significant due
to the proximity of sources of anomalies to the points of
registration of the magnetic field.
Model of the singular source registers phenomenon.
The real reasons can be varied. We can speak about pas-
sive variations are associated with variations of the inte-
gral parameters of the environment, and active – caused
by existence of current systems. Variations of pressure,
humidity, temperature, structural changes or rock de-
struction are reflect in the geoelectric characteristics of
the geological section [6,8,11]. Active sources of electric
current, generated under pressure in the course of rock
failure, may also be the causes of electromagnetic
anomalies [9,10]. Perturbations of atmosphere and iono-
sphere are associated with seismic activation of the
earth's crust [12,14]. Change column resistance over an
area of seismic preparation leads to a change in the
ionospheric potential. Variations of atmospheric electric-
ity cause variations of ionospheric parameters: electron
and ion concentrations, electron and ion temperature,
ionic composition, scale heights of the ionospheric lay-
Thus, the model of an effective singular source of cur-
rent works as a detector and the amplifier response func-
tion on the electromagnetic processes in the environ-
ments of the earth and caused by tectonic movements of
the earth’s crust.
The paper presents a simple model of the joint inter-
pretation of synchronous measurements of the magnetic
field observatories in Japan. Anomalous magnetic field
in spaced points is transformed in function of the dis-
Copyright © 2013 SciRes. OPEN AC CESS
L. F. Moskovskaya / Natural Science 5 (2013) 38-45
tance to the singular source. Space-time local anomalies
are superimposed on the background level of the carrier
signal, which is determined by the global processes of
electromagnetic dynamics of shells of the Earth. The
cause of local variations may be associated with elec-
tromagnetic phenomena accompanying the geodynamic
processes in the lithosphere-atmosphere-ionosphere.
Important characteristics of the anomalous phenome-
non are the spatial and temporal scale of variations. The
anomalous behavior of the apparent distance to the gen-
eralized source in the energy methods of calculation
manifested not less than two weeks before the catastro-
phic earthquake. Changes curves were recorded during
the three months. Regular declining of the apparent dis-
tances and decrease field homogeneity, coinciding with
the lull seismic activity time intervals, can be interpreted
as the emergence in these periods, and an additional per-
turbation of the magnetic field. This effect is registered
synchronously at all stations, and has a spatial dimension
not less than the size of the entire structure. In turn ab-
normal manifestations, which are caused by activization
zones 11 March 2011, localized in the vicinity of the
station Kakioka, in the measurements of the remote sta-
tions are manifested weaker.
The main result of the study is the fact that, according
to the measurements of the magnetic field of three ob-
servatories in Japan for 2009-2011, the regular variations
of the apparent distances to the effective singular source,
associated with the rhythm of the geodynamic processes
in the vicinity of the station Kakioka, were recorded.
Most strongly the apparent distance decrease manifested
in connection with the activation of seismicity of the
region, including the catastrophic earthquake on March
11, 2011 with the magnitude M = 9.1.
Singular generalized source diagnoses measure elec-
tromagnetic heterogeneity of lithosphere and the iono-
sphere in the vicinity of the magnetic observatories. The
system of three observatories proved itself as a kind of
magnetic locator electromagnetic phenomena associated
with seismic activity in the vicinity of the observatory
I must express my deep appreciation to the scientific communities of
the supporting scientific sites, for the opportunity to use data of mag-
netic observatories Japan and Seismic catalogue California. And thank
Professor Yu. A. Kopytenko for constructive discussion of the results.
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