GeolCarp_Vol70_No6_483

GEOLOGICA CARPATHICA

, DECEMBER 2019, 70, 6, 483–493

doi: 10.2478/geoca-2019-0028

www.geologicacarpathica.com

The relation of the seismicity in the eastern part

of the Ukrainian Carpathians and the distribution

of electrical conductivity in the Earth’s crust

SVETLANA KOVÁČIKOVÁ



, IGOR LOGVINOV

and VIKTOR TARASOV

Institute of Geophysics, Czech Academy of Sciences, Boční II/ 1401, 14131 Praha 4 – 14100, Czech Republic;



svk@ig.cas.cz

Institute of Geophysics, National Academy of Sciences of Ukraine, Palladin av. 32, 03142 Kiev, Ukraine; anna_log@ukr.net

(Manuscript received February 6, 2019; accepted in revised form October 16, 2019)

Abstract: We present results of a study of the peculiarities of the seismicity and electrical conductivity distribution

beneath the Ukrainian Eastern Carpathians. Based on the analysis of seismic data for the years 1999–2016, specific

zones of concentration of earthquake sources related to the principal fault systems and their intersections have been

distinguished. This paper covers two zones, one linked to the contact of the Outer Carpathians and the Carpathian

Foredeep and another one linked to the fault system transverse to the Carpathians strike. Both belts of earthquake sources

concentration correlate well with the geoelectric models of the studied area obtained as a result of 2D and quasi-3D

inversion. Most of the seismic events occur at the intersection of the mentioned seismic zones, at shallower depths, than

the main conductive structures appear, concentrated at their marginal parts. The interrelation of both phenomena suggests

their common explanation by processes occurring in active fault systems: fracturing, shear deformation, migration of

highly mineralized fluids, high porous pressure, accumulation and release of tectonic stress.

Keywords: Ukrainian Carpathians, seismicity, electrical conductivity.

Introduction

The Carpathian region is characterized by increased seismic

activity which is irregularly distributed along the Carpathian

Mts. strike. One of the areas of increased seismicity is the

territory of the Ukrainian Eastern Carpathians (sources —

Kostyuk et al. 1997; European-Mediterranean Seismological

Centre EMSC http://www.emsc-csem.org; Seismological

Bulletins of Ukraine 1999–2016 etc.). Currently, from 3–5 to

20–30 earthquakes with a magnitude of 0.6–0.8 and higher

(reaching 4.2) are instrumentally registered during a year in

the Ukrainian Carpathians; 60–75 % of them in the Transcar-

pathian basin, the rest in the Outer flysch Carpathians and

partly in the Carpathian Foredeep and the adjacent territories

of the East European platform (EEP). For the purposes of this

study, we analysed data from the Seismological Bulletins of

Ukraine for the years 1999–2016 and compiled a summary

catalogue of the Carpathian earthquakes for these years.

Geoelectrically, the Carpathians are characterized by sub-

surface low resistivity sedimentary sequences of the Car-

pathian Foredeep and by the prominent crustal Carpathian

conductivity anomaly CrCA (recently, for example, Twaróg et

al. 2018; Bezák et al. 2019; Červ et al. 2019; Logvinov &

Tarasov 2019). Currently, a database of the magnetotelluric

(MT — natural electromagnetic field) data has been created,

which includes practically 90 % of all results of the MT

research in Ukraine. Using this database and on the basis of

the 2D modelling through a network of 12 profiles, the areal

distribution of geoelectric parameters in the depth interval of

1–16 km for the territory of the Ukrainian Carpathians was

obtained (Logvinov & Tarasov 2019). The quasi-3D thin sheet

inversion made it possible to model the electrical conductivity

distribution in a sheet approximating the upper boundary of

the electrical anomaly source.

Peculiarities in the distribution of earthquakes and increased

conductivity within the Earth attract permanent interest from

researchers. The results of geoelectric studies suggest narrow

interrelation of the revealed conductive structures with fault

tectonics and consequent geothermal and seismic activity in

the whole Carpathians (e.g., Kováč et al. 2002; Toth et al.

2002; Majcin et al. 2014). Following the above mentioned

course, the presented article aims to correlate the seismicity of

the eastern part of the Ukrainian Carpathians with the geoelec-

tric parameters of the Earth’s crust, determined by 2D and 3D

interpretational methods.

Investigated area, geoelectric

and seismological data

The Carpathian region in Ukraine is traditionally subdivided

into the Carpathian Foredeep, the Transcarpathian Depression

and the Carpathians themselves (Fig. 1), the major part of

which is here occupied by the nappes of the Outer flysch

Carpathians (Glushko & Kruglov 1986). The Prealpine base-

ment of the Ukrainian Carpathians is represented by the EEP

complexes with the oldest represented by the Preriphean crys-

talline rocks (Archean-to-early Proterozoic with geological

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ages more than 1650 Ma) followed by the Neoproterozoic

formed during the Baikalian tectonic processes (around

850 Ma). The territory is intersected by a complicated net-

work of faults parallel to the orogene axis and related to indi-

vidual thrust zones as well as transversal faults (Verkhovtsev

2006; Zayats 2013).

Geoelectric investigations

As an input for performing the 2D and quasi-3D geoelectric

modelling, the experimental MT (both electric and magnetic

components of the recorded natural electromagnetic field) and

magnetovariational data (MV, only magnetic components)

from the Ukrainian Carpathians in the period range 1–6400 s

(Gordienko et al. 2011; Logvinov 2015 and sources therein)

and the results from the international profile PREPAN (Adám

et al. 1997) have been used (Fig. 2a).

For the 2D modelling performed using the REBOCC

inversion algorithm (Siripunvaraporn & Egbert 2000), experi-

mental MT sites over the area were projected on eleven profile

lines (plus profile PREPAN). Geoelectric parameters of the

subsurface layers were used as a priori information in the star-

ting interpretational model. Sedimentary layers play a signi-

ficant role in calculating the models of the electrical resistivity

Fig. 2. a — Locations of MT field observation sites and profiles of the 2D inversion (Logvinov & Tarasov 2019); GII — along the II

interna-

tional Geotraverse and SG-I-67 — MT profiles discussed further; dashed lines: thin — boundaries of the principal units of the Ukrainian

Carpathians (zones

CF, C, TC — see Fig. 1), thick — the EEP boundary

;

b — scheme of the Preriphean crystalline basement; c — scheme of

the Baikalian basement (Zayats 2013); 1 — main faults intersecting the surface of the crystalline basement (see Fig. 1), RRD — Rava-Russian-

Davydenko fault (SW boundary of the Preriphean platform); 2 — contour lines of the Preriphean basement (in km): a — reliable,

b — expected; 4 — contour lines of the Baikalian basement surface (in km).

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(ρ) of the Earth’s crust. In the Ukrainian Carpathians region,

the Baikalian basement is overlain by Meso-Cenozoic sedi-

ments. Generally, according to the scheme on Figure 2c, the

thickness of sedimentary rocks in the Carpathian Foredeep

and the folded flysch Carpathians does not exceed 8 km

(Zayats 2013). According to the logging data and the direct

current methods, the rocks composing the flysch Car pathians

are characterized by strongly varying values of ρ. For the Ceno-

zoic rocks, the resistivity values are generally 10–50 ohmm.

The resistivity of the Mesozoic and Paleozoic rocks varies

from 15–30 ohmm to 100 or more ohmm. Mesozoic to Ceno-

zoic deposits of the Carpathian foredeep are charac terized by

ρ values varying from 3–5 ohmm to 10–30 ohmm, whereas

the resistivity of Paleozoic rocks varies from 30–60 ohmm to

100–150 ohmm. Details of the 2D modelling along the pro-

files were described in Logvinov & Tarasov (2018, 2019).

Root mean square deviation rms in the inversion varied

between 1.65 and 2.8.

Currently available geological and geophysical information

is obviously presented in the form of horizontal and vertical

sections. In this work, horizontal sections at various depths are

presented (Fig. 3a–e). For joint presentation of the 2D model-

ling results a three-dimensional matrix was constructed. At each

modelling profile, the spatial coordinates of the modelling

cells were defined and a three-dimensional matrix was built

(variables are: X — longitude, Y — latitude, Z — depth,

ρ — electrical resistivity). With respect to the scale of the

profiles network and the horizontal step of modelling on

the profiles, the initial matrix for the construction of models of

geo electric parameters was transformed into a matrix with the

horizontal cell size 6 km × 6 km. The electrical resistivity (ρ)

within the interval of 100–1000 ohmm was assumed as the

normal resistivity value. At this normal resistivity background,

plots with ρ less than 40 ohmm are shown, giving more than

90 % of contribution to the low resistivity objects (Rokityansky

1982). High resistivity structures may also be geologically

interesting and features with ρ exceeding 1000 ohmm are also

shown in the figures. The densest network of modelling pro-

files is located in the eastern part of the Ukrainian Carpathians,

bounded from the west by an international geotraverse GII

(Fig. 2, Kruglov & Gursky 2007). Therefore, the most condi-

tioned results from this area are used as the resistivity distribu-

tion in the Earth’s crust in the following.

The resulting resistivity distribution for the first 4 km

(Fig. 3a) is in good agreement with the geoelectrical characte-

ristics of sedimentary rocks described above. An interesting

feature of the obtained distributions of ρ is the presence of

an arc-shaped area in the central part bounded by a contour

line of 100 ohmm. At the south-west, it appears at the intersec-

tion of geographic coordinates 23°E and 48°N, a locality in the

Transcarpathian depression. Further, the structure crosses the

flysch Carpathians and in the area with coordinates of about

23.5°E and 48.5°N, its strike is close to the Precarpathian

fault’s stretching. In the described depth interval, three ano-

malous objects (ρ less than 10 ohmm) are allocated in the area.

Beneath 5 km, only local high conductivity (or low resistivity)

objects remain on the horizontal sections in the same areas as

in the shallower depths. The highest conductivity values are

observed in the central object at a depth of 5 km (with coordi-

nates of its centre approximately 24.3°E and 48.7°N). Beneath

the 8 km depth, the central conductive structure splits onto

three separate high conductivity objects traced down to 16 km.

Comparison of the described conductivity distribution with

the fault tectonics allows us to associate individual conductive

structures with faults of the Carpathians stretching and trans-

verse (with respect to the Carpathians) faults. Such feature

is quite clearly traced down to the depth of about 8 km.

Another feature of this area is the presence of a high-resistivity

structure located to the south of the central conductive

structure. In a volumetric presentation, its position suggests

encompas sing of the high-resistivity block by the conductive

structure. In depth, this block disappears beneath the Baikalian

basement surface (Fig. 2c). The central and eastern structures

(limited by contour line ρ = 40 ohmm) can be traced through

the whole depth interval presented in Figure 3, but their cen-

tres migrate, as they approach the Earth’s surface. Rapid

change of the anomalous object’s position occurs in the depth

interval of 8–10 km. This depth interval separates the conduc-

tive objects into two floors also by the conductivity value.

The largest conductivity is observed at a depth of 16 km and

deeper, which indicates the location of their roots in the crys-

talline basement rocks (Fig. 2b).

The obtained 2D models were used as a priori layered 1D

structure and the source depth for the quasi-3D geoelectric

modelling based on the thin sheet theory applicable at quite

long periods (the range of hundreds to thousands seconds)

when, in a quasi-static approach, the electromagnetic wave-

length exceeds the thickness of the upper crustal layers

(Schmucker 1970; Vasseur & Weidelt 1977). The upper boun-

dary of the electrical anomaly source is then approximated by

a horizontally inhomogeneous sheet buried in a layered Earth.

In this case, the electrical conductivity (reverse of the resisti-

vity) is replaced by the integrated conductance S (Siemens)

distribution over the sheet and the vertical changes of the con-

ductivity are neglected. In the procedure, only magnetic com-

ponents of electromagnetic records (induction arrows) were

used. The method is sensitive mainly to the horizontal conduc-

tivity gradients which makes it suitable especially for tracing

regional crustal conductors that may mark significant tectonic

boundaries and structures. Details of the technique were pre-

sented in Kováčiková et al. (2005). The thin sheet applied in

the inversion was located in a layered medium at the depth of

8 km approximating the upper boundary of the Carpathian

conductivity anomaly. Its source is presumably located in the

depth interval of about 10–20 km although to the east, it

approaches the surface reaching about 8 or less km in Ukraine

(Logvinov 2015). Choice of the modelling parameters and

results was presented in Kováčiková et al. (2016). The model

consisted of 46 × 46 cells; the cell size was 10 km × 10 km with

respect to the used period range (400 s – 6400 s). Starting with

the normal conductance in the thin sheet (1000 S), the inver-

sion was performed up to 15 iterations and finished reaching

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Geophysics NAS Ukraine, Simferopol. It listed data on 949

events limited by coordinates 21–26.8°E and 47.5–50°N

(Fig.1b) their source times, epicentre coordinates, focal

depths, magnitudes M

(horizontal component magnitude)

and M

(earthquake duration magnitude) and classification

according to the K-class system (Rautian et al. 2007). Five

zones of concentration of earthquake epicentres can be distin-

guished within the Ukrainian Carpathians region. They are

related to: the Transcarpathian Depression (Z1); Precarpathian

fault (Z2); a belt stretching approximately from 22,5°E and

48°N to 24°E and 50°N (Z3); another belt stretching from

23°E and 47.8°N to 26°E and 50°N (Z4); an area limited

by the longitudes 26–26.8°N and latitudes 48–49°N (Z5).

Of course, the selection of the zones is relative and conven-

tional and further research will help to make more reliable

conclusions. Characteristics of the Transcarpathian earthquakes

are described in many studies (e.g., Malytskyy 2006; Gnyp

2009; Lozynyak et al. 2011; Maksymchuk et al. 2011;

Nazarevych et al. 2016). The zones Z3 and Z5 practically do

not fall into the area of geoelectric parameters obtained by the

2D modelling. Therefore, in this paper we consider characte-

ristics of earthquakes concentrated along the Precarpathian

fault and in the belt Z4. The area of the most conditioned geo-

electric 2D modelling results is located east of the Geotraverse

II line (GII in Fig. 2, Zverev & Kosminskaya 1980). According

to the above mentioned database of the Ukrainian Carpathians

earthquakes for the years 1999–2016, in the area of the most

conditioned 2D modelling results, the earthquake epicentre

coordinates were defined at 280 points, 273 of them belonging

to the energy class K

(Rautian et al. 2007). At 243 points, not

only the depth intervals but, specifically, the focal depths (with

average δh varying for individual years from 1.62 to 0.3) have

been defined since the year 2000. The magnitude M

(hori-

zontal component magnitude) was defined for the periods

1999–2003 and 2013–2016 (a total of 107 earthquakes), and

the magnitude M

(earthquake duration magnitude) — for 232

earthquakes since the year 2002.

In Figure 4, the epicentres and depths of earthquake hypo-

centres, typical for the Z2 and Z4 zones and the position of

the main fault zones are presented. The zone Z2 is linked to

the contact of the flysch Carpathians and the Carpathian

Foredeep and is characterized by a change of the earthquake

hypocentre depths along its strike. The zone Z4 is located

between the Tyachev–Nadvornyansk–Monastyrets (TNM)

and Khust–Korets (KHK) fault zones along its whole length.

The normal value of hypocentres depth varies within the inter-

val of 2–4 km. At the same time, two nodes can be seen, where

the hypocentres are observed in the depth interval of 2–16 km.

One of the nodes (with approximate size 60 × 60 km) is located

at the intersection of the Transcarpathian fault (TCR) and

TNM (zone “n1” in Fig. 4a), the second one (with approxi-

mate size 50 × 20 km) — at the intersection of the Uzhok fault

(UGK), the Precarpathian fault (PCR) and TNM (zone “n2” in

Fig. 4a and detail in Fig. 4b). From the analysis of the epicen-

tres distribution presented in Figure 4a, another zone of earth-

quake concentration associated with the KHK fault can be

identified — at the KHK line between its intersections with

TCR and PCR (“z” in Fig. 4a).

The normal value of the hypocentre depths in this zone

corresponds to the depth of about 6 km, which as deeper than

in surrounding areas. Regionally, it should be noted that the

zone Z4 divides the territory of the flysch Carpathians into

eastern and western parts. In the eastern part, the number of

earthquakes is significantly lower than in the western part and

the hypocentre depth exceeds 6 km. As was mentioned above,

the M

magnitude was defined for the half number of earth-

quakes compared with the M

magnitude. Therefore, in order

to characterize the distribution of the zones of earthquake epi-

centre concentration Z2 and Z4, the magnitude M

was used.

Both zones were divided into cells with a size of 30 × 30 km

(Fig. 5a), in which the magnitudes (Fig. 5b) were defined, with

the Z2 cell No. 5 completely coinciding with the Z4 cell No. 6.

The Transcarpathian node of earthquake concentration is

charac terized by the cells 2 and 3. The node at the intersection

of the UGK, PCR and TNM can be characterized by the distri-

bution of the M

magnitude in the cells 5 and 6. Although at

this time, it is difficult to provide a serious correlation, as in

the vicinity of the second node, the earthquake parameter esti-

mation is complicated by the absence of the required quality

network of seismic stations (a list of the Carpathian seismic

stations is given, for example, in Verbitsky et al 2013). A sig-

nificant difference of the folded Carpathians earthquake

parameters west of Z4 from the eastern part is also evident in

the distribution of released seismic energy. A fast decrease of

earthquake parameters during transition from the flysch

Carpathians to the Carpathian Foredeep can be visible in zone

Z4 (difference between sections 1–6 and 7–12). In zone Z2 we

can see decrease of folded Carpathians earthquake parameters

west and east of Z4 (Z2 sections 1–5 and 6–8).

Discussion

With respect to the earthquake distribution in depth, hori-

zontal sections reflecting the main peculiarities in distribution

of both parameters were selected for comparison of geoelec-

tric and seismological data (Fig. 6). The difference between

the models resulting from the 2D and 3D geoelectric model-

ling methods can be explained by more smooth distribution of

magnetic responses applied in the quasi-3D modelling.

A slice representing a depth interval of 4–6 km (Fig. 6b)

demonstrates a regional change in conductivity anomalies:

above the depth of 4 km, a good conductivity of the rocks of

the Carpathian Foredeep in the south-east is visible, disap-

pearing at a greater depth. At depths between 2 and 7 km,

the number of seismic events is about 100, whereas at greater

depths their number rapidly decreases to 14–15 within the

depth intervals of 7–9 km and 9–11 km, 6 events within the

depth interval of 11–13 km and 4 earthquakes within the depth

interval of 13–17 km. In a depth interval of 2–11 km, most

of the hypocentres are located outside the contours of the

most conductive parts of the anomalous structures (less than

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10 ohmm). The belt of earthquake epicentre locations within

the Z4 zone correlates well with the conductive structure

strike, and the decrease of the earthquake numbers with depth

is accompanied by a decrease in the number of local con-

ductive structures as well as decrease of their integrated

conductivity.

Correlation of the conductivity distribution with the number

of earthquakes is clearly visible in the thin sheet modelling

results (Fig. 6h, i). Above the sheet located at a depth of 8 km,

93 seismic events within the depth interval of 5–7 km are

observed, and only 17 earthquakes are observed within the

depth interval of 7–9 km. According to the thin-sheet model-

ling results, it can be also seen, that earthquakes occur mostly

in the marginal parts of the conductive structures.

As was mentioned above, the sedimentary cover of the

Ukrainian Carpathians is represented by the Meso- to Cenozoic

rocks of variable thickness, lithology, and level of dia-,

cata- and metagenetic stages of transformation of the carbon-

bea ring material. Paleozoic rocks occurring in the Carpathians

are transformed under the high temperature and pressure con-

ditions to a degree that makes their classification as sedimen-

tary rocks doubtful. General knowledge about the changes in

the properties of primary sedimentary formations under the

influence of high pressure and temperature when immersed in

deep sedimentary basins suggests, that during heating, which

corresponds to their deep sections, the late katagenesis can be

reached at the depth of 3.5–7.5 km with the temperatures of

100–200 °C; below the depth of 10 km and with temperature

of 300 °C the rocks transform into metamorphic rocks and

cannot be assumed to belong to sediments (Gordienko et al.

2011).

In Figure 7, geological sections of the upper part of the

Carpathian crust along two profiles bounding the studied area

(Figs. 1, 2) are presented. Profile A–B (practically coinciding

Fig. 4. a — distribution of epicentres (crosses) and depths of hypocentres H (km) of the Ukrainian Carpathians earthquakes for the years

1999–2016 (see introduction); 1 — main faults: TCR, CHR, UGK and TNM (see Fig.1); 2 — faults active during last 3 Ma (see Fig. 3) ; areas

z, n1, n2 bounded by white dashed lines — zones of earthquake concentration; b — detailed seismicity image in the zone of intersection of

the UGK, PCR and TNM fault zones.

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with the geotraverse GII) is adopted from the Tectonic map

of Ukraine, 1:1 000 000 (Kruglov & Gursky 2007), profile

SG-1-67 — according to Zayats (2013). The profiles are

aligned along the S-W border of the Borislav-Pokuty nappe

(Fig. 1a). Along both profiles, variations of thickness of for-

mations of various ages in the Carpathians tectonic units

(Krosno zone, Skyba and Borislav-Pokuty nappe) associated

with seismicity within the zones Z2 and Z4 can be seen. Below

the depth of 2–4 km, the information about the geological

structure of these tectonic zones is not clear due to the absence

of boreholes and detailed areal seismic investigations. Accor-

ding to the geological sections, to the S-E of the GII within

the rock strata beneath the Cretaceous deposits, the Paleogene

rocks contribution rises. From the point of view of geoelec-

trics, an important characteristic of the sections is distribution

of well-conductive Neogene sediments of the Sambir nappe

beneath the overlying Cretaceous deposits of the whole Skyba

nappe.

Deeper, metamorphic rocks of either Hercynian (at the profile

SG-1-67) or even older age (Profile A–B) occur. According to

the Preriphean basement scheme (Fig. 2b), the TNM fault is

located within the zone of rapid change in the thickness of

sedimentary rocks above the Baikalian basement, and of the

entire thickness of the Preriphean rocks. To the N-W from the

fault, the gradient of increase of the thickness of deposits is

smaller than to the S-E of it. This conclusion is confirmed also

in the presented sections (Fig. 7). As was mentioned above,

abrupt changes of the geoelectrical parameters can be obser-

ved. The resistivity of structures within the Skyba zone

increases with depth down to the depth of 8 km (Figs. 3, 7),

what confirms a conclusion about the sedimentary character of

deposits of the Prebaikalian tectogenesis.

Distribution of low resistivity structures and location of

seismic events outside the area of anomalous conductivity

suggests possible geological mechanisms. We can suppose

that seismicity is associated with stress occurring at the mar-

gins of the low resistivity structures, which are conditioned by

rocks saturated with fluids. Fluid inflow may occur from both

the Neogene sediments immersed under the Cretaceous ones

and from deeper horizons of the Earth’s crust, what is sug-

gested by the existence of conductive structures at depths

exceeding 10 km. A complex of factors, such as rheological

stratification of the crust, the high-temperature fluids pressure

and differential tectonic stresses, leads to stress accumulation

and brittle deformation at the margins of such areas, while

inside, the stress is redistributed with respect to the equivalent

rheology of the medium and the hydrodynamics of the fluids

(Ellsworth 2013; Nazarevych & Nazarevych 2013). Another,

a more controversial factor that can be responsible for location

of seismic events on the margins of electrically anomalous

objects in the studied area is the possible existence of frag-

mentary zones of partial melting (where elastic energy cannot

be accumulated) related to thermal activation at the intersec-

tion of deep fault systems (Korchin et al 2013; Kováčiková et

Fig. 5. a — Distribution of the earthquake epicentres (crosses), in which the magnitudes MD were defined; b — relation of the magnitudes MD

for Z2 and Z4 and the earthquakes number N; numbers in circles — the cell numbers.

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al. 2016). In this case the seismicity occurs outside zones of

partial melting where elastic energy cannot accumulate.

Conclusion

The analysis of the distribution of low resistivity structures

and seismicity in the Ukrainian Carpathians allows us to make

conclusions about their narrow correlation. In the geoelectric

models, both conductive sediments of the Carpathian Foredeep

and structures corresponding to the crustal CrCA can be dis-

tinguished. Distribution of the conductive structures suggests

their relation to faults parallel to the Carpathians strike as well

as transversal faults (the TNM zone).

Comparison of the 2D and quasi-3D geoelectric models

with earthquakes distribution indicates concentration of most

hypocentres outside the conductive zones and suggests asso-

ciation of both phenomena with fluid migration conditioned

by a complex of factors. Of course, specification of the nature

of the seismicity and geoelectric characteristics of rocks in

the studied area requires further research, nevertheless, the

achieved degree of correlation of the geoelectric data and

the seismicity makes it possible to recommend the use of geo-

electric data in combination with other geological and geo-

physical information in construction of seismic zonation maps.

Acknowledgements: We thank Anton Kushnir and two ano-

nymous reviewers for the detailed review and constructive

comments and suggestions.

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