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\title{Strong earthquake-prone areas recognition based on the algorithm with a single pure training class. II. Caucasus,}

\author{B. A. Dzeboev$^{1,2}$, A. A. Soloviev$^{3}$,\\ B. V. Dzeranov$^{2}$, J. K. Karapetyan$^{4}$,\\ N. A. Sergeeva$^{1}$}

\affil{1}{Geophysical Center RAS, Moscow,  Russia}
\affil{2}{Geophysical Institute, Affiliate of Vladikavkaz Science Center RAS, Vladikavkaz,  Russia}
\affil{3}{Institute of Earthquake Prediction Theory and Mathematical Geophysics RAS, Moscow,  Russia}
\affil{4}{Institute of Geophysics and Engineering Seismology after A. Nazarov, Gyumri,  Armenia}

\abstract{Strong earthquake-prone areas recognition ($M \geq 6.0$) in the Caucasus is performed by means of the new ``Barrier-3'' pattern recognition algorithm. The obtained result is compared with potentially high seismicity zones recognized previously using the ``Cora-3'' pattern recognition algorithm. It is proposed to define an interpretation of the integral recognition result by the ``Barrier-3'' and ``Cora-3'' algorithms as a fuzzy set of recognition objects in the vicinity of which strong earthquakes may occur in the Caucasus.}


\section{Introduction}

Strong  earthquake-prone  areas  recognition  was  developed  as  a  part  of  mathematical  geophysics  in  the  early  1970s  in  the  works  of  academicians  I.~M.~Gelfand  and  V.~I.~Keilis-Borok
[\itc{Gelfand  et  al.,}  \reflink{Gelf72}{1972},  \reflink{Gelf73}{1973},    \reflink{Gelf74}{1974},  \reflink{Gelf76}{1976}].
This  approach  was  later  named  EPA  (Earthquake-Prone  Areas  recognition)
[\itc{Gvishiani  et  al.,}  \reflink{Gvis88}{1988};
\itc{Kossobokov  and  Soloviev,}  \reflink{Koss18}{2018};
\itc{Soloviev  et  al.,}  \reflink{Solo14}{2014}].
It  is  based  on  the  hypothesis  that  the  epicenters  of  rather  strong  earthquakes  are  confined  to  the  intersections  of  the  morphostructural  lineaments  (morphostructural  nodes)  but  not  to  all  of  them.  A  problem  (EPA  problem),  which  is  solved,  is  to  determine  in  the  region  under  consideration  all  high-seismicity  nodes  where  strong  earthquakes  may  occur.  For  more  than  40  years,  the  EPA  approach  has  been  successfully  used  for  recognition  of  earthquake-prone  areas  in  various  mountain  countries  [\itc{Gvishiani  et  al.,}  \reflink{Gvis88}{1988};
\itc{Soloviev  et  al.,}  \reflink{Solo14}{2014}].
Its  detailed  description,  the  ideas  embodied  in  it  and  the  ways  for  its  development  are  given  in
[\itc{Gvishiani  et  al.,}  \reflink{Gvis88}{1988};
\itc{Kossobokov  and  Soloviev,}  \reflink{Koss18}{2018};
\itc{Soloviev  et  al.,}  \reflink{Solo14}{2014}].

\begin{sloppypar}
Pattern  recognition  algorithms  with  training  ``Cora-3'',  ``Subclasses'',  ``Hamming'',  etc.  are  used  in  the  EPA  approach
[\itc{Gvishiani  et  al.,}  \reflink{Gvis88}{1988}].
They  require  the  a  priori  formation  of  training  samples  of  high-  and  low-seismicity  classes  that  are  used  at  the  learning  stage  of  algorithm  application.  The  most  commonly  used  algorithm  in  EPA  is  \mbox{``Cora-3''}
[\itc{Bongard  et  al.,}  \reflink{Bong66}{1966}].
The  result  of  the  pattern  recognition  in  the  EPA  approach
[\itc{Gvishiani  et  al.,}  \reflink{Gvis88}{1988}]
is  twofold:  (1)  the  rule  of  recognition  and  (2)  the  actual  division  of  objects  (morphostructural  nodes)  into  two  separate  classes  (high  and  low  seismicity  objects).  Actually  the  recognition  rule  contains  a  geological-geophysical  and  geomorphological  description  of  these  classes,  i.e.  criteria  of  high  and  low  seismicity  for  the  considered  region.
\end{sloppypar}

As  shown  in
[\itc{Dzeboev  et  al.,}  \reflink{Dzeb19}{2019};
\itc{Gvishiani  et  al.,}  \reflink{Gvis17a}{2017a}]
the  training  samples  of  the  high  and  low  seismicity  classes  have  different  levels  of  confidence,  but  this  was  ignored  when  a  pattern  recognition  algorithm  is  applied  in  the  EPA  approach.  That  is  a  disadvantage  of  the  approach  and  the  ``Barrier''  algorithm
[\itc{Gvishiani  et  al.,}  \reflink{Gvis17a}{2017a}]
has  been  developed  to  avoid  it.  This  algorithm  requires  only  a  high  seismicity  class  training  sample,  which  is  a  reliable  one.

The  purpose  of  the  ``Barrier''  algorithm  is  to  study  the  characteristics  of  the  ``pure''  training  sample  of  the  high-seismicity  class  and  to  identify  on  this  basis  among  the  whole  set  of  objects  those  that  are  ``similar''  to  objects  from  the  training  sample.  In  the  language  of  set  theory  ``Barrier''  solves  the  problem  of  constructing  in  the  finite  set  of  objects  its  subset,  which  is  extension  of  the  only  one  reliable  training  sample  of  the  high  seismicity  class.

\begin{sloppypar}
Initially,  the  ``Barrier''  algorithm  has  been  successfully  applied  to  recognition  of  strong  (with  $M  \geq  6.0$)  earthquake-prone  areas  in  the  Caucasus
[\itc{Gvishiani  et  al.,}  \reflink{Gvis17a}{2017a}].
Later  the  new  version  ``Barrier-3''
[\itc{Dzeboev  et  al.,}  \reflink{Dzeb19}{2019}]
has  been  developed  on  the  basis  of  the  ``Barrier''  algorithm.  The  modification  consisted  in  the  creation  of  computing  units  that  allow  us  to  estimate  both  the  average  contribution  of  all  geological  and  geophysical  characteristics  and  the  contribution  of  the  three  ``strongest''  characteristics  only.  The  ``Barrier-3''  algorithm  has  been  successfully  used  for  recognition  of  strong  (with  $M  \geq  6.0$)  earthquake-prone  areas  in  the  Altai-Sayans-Cisbaikalia  region
[\itc{Dzeboev  et  al.,}  \reflink{Dzeb19}{2019}].
\end{sloppypar}

This  paper  does  not  describe  the  ``Barrier''  and\linebreak  ``Barrier-3''  algorithms.  The  description  of  the  mathematical  construction  of  the  ``Barrier''  algorithm  in  its  initial  version  is  given  in  the  paper
[\itc{Gvishiani  et  al.,}  \reflink{Gvis17a}{2017a}].
The  description  of  the  computing  units  that  led  to  the  ``Barrier-3''  version  of  the  algorithm  is  given  in  the  paper
[\itc{Dzeboev  et  al.,}  \reflink{Dzeb19}{2019}].

\enlargethispage{.2pc}

 \begin{sloppypar}
 This  study  is  devoted  to  application  of  the  ``Barrier-3''  algorithm  for  the  identification  of  earthquake-prone  areas  for  $M  \geq  6.0$  in  the  Caucasus.  The  difference  from  the  research  described  in
  [\itc{Gvishiani  et  al.,}  \reflink{Gvis17a}{2017a}]
  is  not  only  in  the  use  of  ``Barrier-3''  but  also  in  the  set  of  geological-geophysical  and  geomorphological  characteristics  that  are  describing  recognition  objects.  The  entire  set  of  available  geological-geophysical  and  geomorphological  characteristics  was  used  in
  [\itc{Gvishiani  et  al.,}  \reflink{Gvis17a}{2017a}].
  In  our  work  a  preliminary  test  of  the  informativity  of  the  characteristics  in  the  context  of  the  separation  of  recognition  objects  into  high  and  low  seismicity  classes  has  been  performed  following  to
  [\itc{Soloviev  et  al.,}  \reflink{Solo16}{2016}].
  The  recognition  result  by  the  ``Barrier-3''  algorithm  is  compared  with  the  result  obtained  by  ``Cora-3''
  [\itc{Soloviev  et  al.,}  \reflink{Solo16}{2016}].
  \end{sloppypar}

\section{Caucasus  Region}

The  Caucasus  is  a  part  of  the  Alpine-Himalayan  folded  belt  located  between  the  Black  and  Caspian  seas.  It  is  a  complex  system  of  alpine  folded  structures  with  the  latest  active  tectonic  movements.  The  modern  structure,  geodynamics,  and  seismicity  of  the  Caucasus  region  are  determined  by  submeridional  contraction  associated  with  the  continuing  convergence  of  the  African-Arabian  and  Eurasian  plates  of  the  lithosphere
[\itc{Rogozhin  et  al.,}  \reflink{Rogo00}{2000}].

A  number  of  longitudinal  zones  are  distinguished  in  the  tectonic  structure  of  the  Caucasus:  the  zone  of  the  Ciscaucasia  foredeeps,  the  meganticlinorium  of  the  Greater  Caucasus,  the  zone  of  the  Transcaucasian  median  massifs  and  internal  (intermountain)  basins,  the  meganticlinorium  of  the  Lesser  Caucasus  and  the  Middle-Araks  internal  (intermountain)  trough.  Transverse  zonality  is  expressed  in  the  presence  of  a  submeridional  zone  of  the  Transcaucasian  transverse  uplift,  crossing  all  longitudinal  zones,  and  steps  parallel  to  this  zone  and  decreasing  to  the  west  and  east  of  it
[\itc{Khain  and  Limonov,}  \reflink{Khai04}{2004};
\itc{Milanovsky,}  \reflink{Mila96}{1996}].


\subsubsection{Ciscaucasia}  occupies  a  vast  territory  that  is  based  on  the  Scythian  epihercynian  plate.  In  the  southern  part  of  Ciscaucasia  there  are  two  foredeeps  --  Indolo-Kuban  and  Tersk-Caspian,  separated  by  the  Mineralovodsk  saddle.  These  foredeeps  are  filled  with  Cenozoic  sediments,  the  thickness  of  the  sedimentary  cover  reaches  12~km,  and  the  foundation  is  composed  of  Baikal  massifs  and  Paleozoic  folded  systems.  In  the  axial  zone  of  the  Tersko-Caspian  foredeep,  two  large  anticlines  Tersk  and  Sunzhensk  stand  out.  Mineralovodsk  saddle  lies  on  the  axis  of  the  Transcaucasian  transverse  uplift
[\itc{Milanovsky,}\linebreak  \reflink{Mila96}{1996}].
The  Tersk-Caspian  foredeep  is  characterized  by  significant  seismicity  with  shallow  foci  of  earthquakes  (2--10~km).

\begin{sloppypar}
\subsubsection{The  Greater  Caucasus}  is  an  external  alpine  meganticlinorium  extending  in  the  northwest-southeast  direction  from  Taman  almost  to  Baku.  The  length  of  the  Greater  Caucasus  is  1300~km  with  a  width  of  up  to  150~km
[\itc{Khain  and  Limonov,}  \reflink{Khai04}{2004}].
In  the  main  ridge  heights  reach  4--5~km,  the  highest  point  is  the  Elbrus  volcano  (5642~m).
\end{sloppypar}

The  arch-block  structure  of  the  Greater  Caucasus  is  characterized  by  the  asymmetric  structure  with  sharply  defined  axial  uplift.  The  core,  a  wide  northern  limb  relatively  simple  constructed,  crumpled  into  large  folds  and  complicated  by  transverse  uplifts,  and  a  narrower  and  more  complex  constructed  southern  limb  that  is  characterized  by  compressed  folds  with  a  tendency  to  thrust  and  overturn  to  the  south  are  distinguished
[\itc{Milanovsky,}  \reflink{Mila96}{1996}].
The  asymmetry  of  the  Greater  Caucasus  is  also  associated  with  the  presence  of  a  very  narrow  and  steep  zone  of  the  southern  slope.  This  slope  limited  on  the  side  of  intermountain  troughs  by  the  currently  active  thrust  belt,  and  on  the  Black  Sea  side  by  the  fault  zone.  Along  this  zone,  seismic  activity  is  noted.  The  northern  slope  is  smoother  and  it  is  also  limited  by  the  zone  of  deep  faults  very  active  in  contemporary  times,  which  is  manifested  in  increased  seismicity
[\itc{Rogozhin  et  al.,}  \reflink{Rogo00}{2000}].

The  Greater  Caucasus  has  a  pronounced  transverse  zonality.  Meganticlinorium  is  divided  by  submeridional  faults  into  three  large  transverse  segments  --  Northwest,  Central  and  Southeast.  The  Central  segment  occupies  the  highest  position,  and  the  other  two  stepwise  submergence  from  it  to  the  sides  of  the  Azov-Black  Sea  and  Caspian  depressions
[\itc{Khain  and  Limonov,}  \reflink{Khai04}{2004};
\itc{Milanovsky,}  \reflink{Mila68}{1968}].
Transverse  disturbances  in  the  structure  of  the  Greater  Caucasus,  as  a  rule,  are  high-amplitu\-de  faults,  often  having  a  shear  component
[\itc{Rogozhin  et  al.,}  \reflink{Rogo00}{2000}].

In  the  Central  Caucasus,  there  is  a  distinct  axial  uplift  composed  of  dislocated  and  highly  metamorphosed  rocks  of  the  Proterozoic  and  Lower  Paleozoic.  This  segment  lies  in  the  strip  of  the  Transcaucasian  transverse  uplift.

The  northwestern  segment,  separated  from  the  Central  by  the  system  of  Pshekh-Adler  transverse  deep  faults  is  narrower  and  less  elevated  than  the  Central.  It  passes  into  the  Taman-Kerch  transverse  immersion  zone  with  long-term  mud  volcanism.

The  southeastern  segment  is  separated  from  the  Central  by  Transcaucasian  deep  fault,  characterized  by  rapid  submergence  in  the  east  of  the  structures  and  the  axial  zone  of  meganticlinorium.  The  segment  goes  into  the  Absheron  zone  of  transverse  immersion,  which  is  similar  in  many  respects  to  Taman-Kerch.  Mud  volcanoes  are  also  widespread  here
[\itc{Milanovsky,}  \reflink{Mila68}{1968};
\itc{Milanovsky  and  Khain,}  \reflink{Mila63}{1963}].

\subsubsection{Transcaucasia}  is  an  intermountain  zone  located  between  the  structures  of  the  Greater  and  Lesser  Caucasus.  The  Kakheti-Lechkhumi  deep  fault  separates  the  meganticlinorium  of  the  Greater  Caucasus  from  this  zone,  where  the  Rioni  and  Kura  intermountain  troughs  made  up  of  a  thick  rock  mass,  (3--8~km)  of  Pliocene-Quaternary  orogenic  formations  and  separated  by  the  Dzirula  ledge  are  distinguished.  In  this  ledge,  the  ancient  Baikal  and  Palaeozoic  basements  are  exposed.  The  troughs  are  expanding  and  deepening  to  the  west  and  east  pass  into  the  Black  Sea  and  South  Caspian  deep-sea  basins
[\itc{Milanovsky,}  \reflink{Mila68}{1968};
\itc{Milanovsky  and  Khain,}  \reflink{Mila63}{1963}].
The  intermountain  troughs  are  characterized  by  a  complex  modern  structure,  the  presence  of  young  folding  and  young  shear  disturbances
[\itc{Rogozhin  et  al.,}  \reflink{Rogo00}{2000}].

\subsubsection{The  Lesser  Caucasus}  is  an  internal  meganticlinorium  of  the  alpine  region.  This  is  a  complex  system  of  ridges,  volcanic  uplands,  and  plateaus.  The  length  of  the  Lesser  Caucasus  is  about  600~km,  the  height  of  the  peaks  is  up  to  four  kilometers,  the  highest  peak  is  Mount  Aragats  (4090~m).  In  plain  view,  the  Lesser  Caucasus  is  represented  by  a  wide  (150--200  km)  arc  convex  to  the  north  with  inflection  to  the  south  of  the  Dzirula  ledge,  i.e.  in  the  zone  of  the  Transcaucasian  transverse  uplift.  According  to  tectonic  structure,  the  Lesser  Caucasus  differs  from  the  meganticlinorium  of  the  Greater  Caucasus  by  the  absence  of  a  main  axial  ridge,  several  anticlinoria  and  synclinoria  with  a  relatively  simple  folded  structure  stand  out
[\itc{Milanovsky,}  \reflink{Mila68}{1968}].
This  meganticlinorium  is  characterized  by  echelon-like  uplifts  substituting  each  other  with  an  upward  amplitude  of  up  to  3.5~km,  although  on  average  they  are  smaller.  In  the  Lesser  Caucasus,  the  latest  movements  are  most  evident  in  the  western  and  northwestern  parts,  within  Lake  Sevan  and  to  the  west.  This  area  is  characterized  by  increased  seismicity
[\itc{Rogozhin  et  al.,}  \reflink{Rogo00}{2000}].

The  meganticlinorium  of  the  Lesser  Caucasus  is  boun\-ded  from  the  south  by  a  narrow  Middle-Araks  intermountain  trough.  The  foundation  of  the  basin  is  submerged  to  a  depth  of  5~km,  the  cover  is  composed  of  Eocene-Neogene  molasses  with  interbeds  of  young  lavas.

The  modern  appearance  of  the  Caucasus  was  formed  at  the  latest  (late  orogenic)  stage  of  tectonic  development,  covering  a  period  of  about  the  last  10  million  years.  This  period  is  characterized  by  a  significant  intensification  of  tectonic  movements  and  volcanic  activity.  At  this  stage,  due  to  the  increasing  role  of  upward  movements,  powerful  mountain  structures  (meganticlinoria)  arose.  The  deepening  and  expansion  of  foredeeps  and  intermountain  depressions  took  place.  Regions  that  have  experienced  stable  recent  uplifts  include  two  large  longitudinal  zones  --  the  structures  of  the  Greater  and  Lesser  Caucasus.  The  stable  submergences  include  the  Azov  and  Black  Sea  Depressions  in  the  west  and  the  South  Caspian  Depression  and  the  western  part  of  the  Middle  Caspian  in  the  east.  Significant  changes  in  the  direction  of  vertical  tectonic  movements  occurred  in  the  rest  of  the  Caucasus;  in  some  cases,  the  sign  of  movements  changed  several  times.  The  folding  processes  took  place  in  the  zones  of  marginal  and  intermountain  depressions  and  some  parts  of  the  Greater  and  Lesser  Caucasus.  The  uplift  was  accompanied  by  active  movements  in  the  zones  of  deep  faults  and  a  significant  outburst  of  volcanism  mainly  in  the  zone  of  the  Transcaucasian  transverse  fault  and  its  ruptures
[\itc{Milanovsky,}  \reflink{Mila77}{1977}].

At  the  present  stage,  the  tectonic  development  of  the  Caucasus  continues.  The  lifting  of  the  Greater  and  Lesser  Caucasus,  the  submergence  of  troughs,  the  growth  of  folds  and  the  movement  along  deep  faults  continue,  as  evidenced  by  the  significant  scope  of  modern  movements  and  the  significant  seismicity  of  the  Caucasus.

Repeated  leveling  in  the  Caucasus  allowed  us  to  establish  not  only  the  direction  but  also  the  rates  of  tectonic  movements.  In  the  Greater  and  Lesser  Caucasus,  the  rate  of  uplift  is  up  to  10~mm/year  or  more  and  the  subsidence  rate  (in  the  troughs)  up  to  6~mm/year,  but  the  nature  of  the  velocity  distribution  is  different.  Platform  areas  are  generally  more  stable  --  average  velocities  rarely  exceed  2~mm/year
[\itc{GUGK,}  \reflink{GUGK86}{1986};
\itc{Zakharov,}  \reflink{Zakh06}{2006}].

In  general,  the  Caucasus  mountain  structures  are  characterized  by  an  increase  in  the  intensity  and  contrast  of  modern  vertical  movements  from  west  to  east.  Movement  speeds,  reaching  0--2~mm/year  in  the  Western  Caucasus,  increase  in  the  axial  zone  of  the  Central  Caucasus  to  10--13~mm/year.  From  west  to  east,  towards  the  activated  areas,  the  gradients  of  modern  vertical  movements,  intensity,  density,  frequency  and  depth  of  earthquakes  also  increase
[\itc{Lilienberg  and  Shirinov,}  \reflink{Lili77}{1977}].

\begin{sloppypar}
For  the  central  sector  of  the  Greater  Caucasus  meganticlinorium,  there  is  a  difference  in  the  direction  of  modern  horizontal  surface  movements  according  to  measurements  by  satellite  geodesy  (GPS)
[\itc{Prilepin  et  al.,}  \reflink{Pril97}{1997}].
Given  the  general  tendency  for  the  measurement  points  to  move  northward  in  Transcaucasia  and  on  the  northern  slope  of  the  mountain-folding  structure  of  the  Greater  Caucasus,  there  are  several  places  on  the  southern  slope  where  movements  to  the  south  are  recorded
[\itc{Rogozhin  et  al.,}  \reflink{Rogo15}{2015}].
\end{sloppypar}

The  results  of  geodynamic  research  in  the  Caucasus  region  using  GPS  technology  in  1991--1994  showed  the  existence  of  rapid  horizontal  movement  of  the  Miskhan-Zangezur  middle  massif  of  the  Lesser  Caucasus  relative  to  the  motionless  North-Caucasian  marginal  massif  to  the  north.  It  was  also  established  that  the  displacement  rates  of  the  mobile  system  of  the  Lesser  Caucasus  relative  to  the  North  Caucasus  marginal  massif  decrease  from  south  to  north  and  from  east  to  west,  which  can  be  interpreted  as  an  uneven  horizontal  reduction  of  the  mountainous  region  in  the  various  parts  of  Caucasus
[\itc{Rogozhin  et  al.,}  \reflink{Rogo00}{2000}].

The  nature  of  modern  movements  in  the  Caucasus  region  largely  determines  its  seismic  activity  and  the  location  of  the  strongest  earthquake  sources.  The  greatest  concentration  of  earthquake  epicenters  and  their  maximum  intensity  correspond  to  the  conjugation  areas  of  the  latest  structures  with  movements  of  various  signs  (uplifts  and  subsidences).  The  epicenters  of  earthquakes  are  confined  to  the  boundaries  of  the  uplift  and  relative  subsidence  regions  (foothills,  intermountain  and  foothill  troughs)  which  have  both  a  general  Caucasian  and  a  meridional  direction.  The  Transcaucasian  transverse  uplift  is  a  zone  of  increased  seismic  activity.  Within  this  uplift  the  main  strong  earthquakes  of  the  Caucasus  are  concentrated.

\section{Earthquake-Prone  Areas  in  the  Caucasus,  $M \geq $ 6.0}

Morphostructural  nodes  or  intersections  of  morphostructural  lineaments
[\itc{Gvishiani  et  al.,}  \reflink{Gvis88}{1988}]
are  considered  as  recognition  objects  in  the  application  of  the  ``Barrier-3''  algorithm,  as  well  as  in  the  framework  of  the  EPA  approach.  They  are  determined  as  a  result  of  the  morphostructural  zoning
[\itc{Alekseevskaya  et  al.,}  \reflink{Alek77}{1977};
\itc{Ranzman,}  \reflink{Ranz79}{1979}].

In  papers
[\itc{Gvishiani  et  al.,}  \reflink{Gvis86}{1986},  \reflink{Gvis87b}{1987b};
\itc{Soloviev  et  al.,}  \reflink{Solo13}{2013},  \reflink{Solo16}{2016}],
a  scheme  of  the  morphostructural  leneaments  has  been  constructed  for  the  Caucasus.  The  scheme  highlights  237  intersections  of  the  morphostructural  lineaments
(\figref{1}).                      %  (Fig.  1).
An  analysis  of  the  positions  of  earthquake  epicenters  with  $M  \geq  6.0$
(\tabref{1})                    %  (Tab.  1)
versus  to  the  intersections  of  morphostructural  lineaments  was  performed  in  the  paper
[\itc{Soloviev  et  al.,}  \reflink{Solo13}{2013},  \reflink{Solo16}{2016}].
The  analysis  shows  that  the  epicenters  of  earthquakes  with  $M  \geq  6.0$  are  located  in  the  vicinities  of  lineament  intersections  of  the  Caucasus.

\begin{sidewaysfigure}                      % Fig 1
\figurewidth{145mm}
\setimage{}{}{155mm}{}{2019es000691-f01}
\fcaplabel{Scheme  of  morphostructural  zoning  (thick  lines  --  lineaments  of  the  I  rank,
medium  --  II  rank,
thin  --  III  rank,
solid  lines  --  longitudinal  lineaments,
dashed  --  transverse  lineaments
[\itc{Soloviev  et  al.,}  \reflink{Solo13}{2013}]),
earthquake-prone  zones  with
$M  \geq  6.0$  (empty  ellipses  with  blue  borders  --  zones  recognized  by  the  ``Barrier-3''  algorithm,  white  ellipses  --  ``Cora-3'',
white  ellipses  with  blue  borders  --  both  algorithms)  and  the  epicenters  of  crustal  earthquakes  with
$M  \geq  6.0$ occurred  in  the  Caucasus  (\tabref{1} and  \tabref{3})
before  1900  (brown  circles),  in  1900--1992  (red  circles),
and  after  1992  (green  circles).}\vspace*{.5pc}
\end{sidewaysfigure}



Applying  the  ``Barrier-3''  algorithm  we  use  as  a  training  sample  of  the  high  seismicity  class  the  same  16  intersections,  which  were  used  in  the  paper
[\itc{Soloviev  et  al.,}  \reflink{Solo16}{2016}]
for  the  ``Cora-3''  algorithm.  In  the  25-km  vicinities  of  these  intersections,  the  crustal  earthquake  epicenters  with  $M  \geq  6.0$  are  known  for  the  period  1900--1992
(\tabref{1}                      %  (Tab.  1
and  the  red  circles  in
\figref{1}).                      %  Fig.  1).
The  intersections  of  lineaments  in  the  vicinities  of  which  the  earthquake  epicenters  with  $5.5  \leq  M  <  6.0$  since  1900  or  the  earthquake  epicenters  with  $M  \geq  6.0$  that  occurred  before  1900  are  known
(\tabref{1}                    %  (Tab.  1
and  the  brown  circles  on
\figref{1})                      %  Fig.  1)
were  not  included  in  the  training  samples  for  the  ``Cora-3''  algorithm
[\itc{Soloviev  et  al.,}  \reflink{Solo16}{2016}].
There  are  150  such  intersections.  The  remaining  71  intersections  formed  the  training  sample  of  the  low  seismicity  class  for  the  ``Cora-3''  algorithm
[\itc{Soloviev  et  al.,}  \reflink{Solo16}{2016}].


\begin{table}       %  Table  1
\tablewidth{115mm}
\ftablabel{Earthquakes  with  $M  \geq  6.0$  in  the  Caucasus
[\itc{Kondorskaya  et  al.,}  \reflink{Kond82}{1982};
\itc{Shebalin  and  Tatevosian,}  \reflink{Sheb97}{1997};
\itc{Godzikovskaya,} \reflink{Godz99}{1999}]}
\vspace{5pt}
\tiny
\begin{tabular}
{@{}l@{\hspace{15pt}}
c@{\hspace{12pt}}
c@{\hspace{12pt}}
c@{\hspace{12pt}}
c@{\hspace{12pt}}
c@{\hspace{12pt}}
c@{\hspace{12pt}}
c@{\hspace{12pt}}
c@{\hspace{12pt}}
c@{}}
\hline
\\  [-7pt]
\numero  &  Date  &  $\varphi$,  \deg  &  $\lambda$,  \deg  &  $M$  &  \numero  &  Date  &  $\varphi$,  \deg  &  $\lambda$,  \deg  &  $M$  \\
    [7pt]    \hline      \\  [-4pt]
1.&  427                &40.5  &  46.5  &  6.5  &  31.  &  11.06.1859  &  40.7  &  48.5  &  6.1  \\
2.&  21.07.735    &39.5  &  45.4  &  7.0  &  32.  &  24.05.1861  &  40.0  &  46.6  &  6.6  \\
3.&  742                &42.4  &  44.9  &  6.4  &  33.  &  19.12.1862  &  39.7  &  47.9  &  6.0  \\
4.&  27.12.893    &40.0  &  44.6  &  6.4  &  34.  &  30.12.1863  &  38.2  &  48.6  &  6.1  \\
5.&  23.04.1088  &41.4  &  43.2  &  6.0  &  35.  &  23.07.1867  &  40.0  &  47.0  &  6.3  \\
6.&  1122              &40.3  &  46.3  &  6.1  &  36.  &  25.02.1868  &  41.0  &  43.0  &  6.2  \\
7.&  28.11.1132  &40.5  &  43.5  &  6.0  &  37.  &  18.03.1868  &  40.2  &  46.8  &  6.3  \\
8.&  30.09.1139  &40.3  &  46.2  &  7.7  &  38.  &  28.01.1872  &  40.6  &  48.7  &  6.0  \\
9.&  07.1192        &40.7  &  48.6  &  6.1  &  39.  &  01.11.1875  &  39.8  &  41.1  &  6.1  \\
10.&10.1235        &40.4  &  47.0  &  6.3  &  40.  &  26.06.1889  &  42.5  &  48.0  &  6.1  \\
11.&17.04.1283  &41.6  &  43.3  &  6.8  &  41.  &  22.09.1896  &  41.6  &  45.0  &  6.3  \\
12.&1308              &39.4  &  46.2  &  6.1  &  42.  &  31.12.1899  &  41.55&  43.6  &  6.3  \\
13.&1350              &42.9  &  43.1  &  6.5  &  43.  &  13.02.1902  &  40.7  &  48.5  &  6.9  \\
14.&29.11.1406  &39.7  &  46.5  &  7.0  &  44.  &  21.10.1905  &  43.3  &  41.7  &  6.4  \\
15.&  1605            &40.5  &  43.3  &  6.1  &  45.  &  12.10.1912  &  41.5  &  44.2  &  6.3  \\
16.&  1622            &38.5  &  46.2  &  6.2  &  46.  &  20.02.1920  &  41.9  &  44.0  &  6.2  \\
17.&  1660            &40.0  &  41.3  &  6.5  &  47.  &  19.02.1924  &  39.4  &  48.6  &  6.6  \\
18.&14.01.1668  &41.0  &  48.0  &  7.8  &  48.  &  27.04.1931  &  39.4  &  46.1  &  6.2  \\
19.&11.01.1671  &41.5  &  48.7  &  6.2  &  49.  &  01.05.1935  &  40.6  &  43.7  &  6.2  \\
20.&04.06.1679  &40.2  &  44.7  &  6.4  &  50.  &  07.05.1940  &  41.7  &  43.8  &  6.0  \\
21.&  1688            &40.3  &  41.5  &  6.5  &  51.  &  29.06.1948  &  41.9  &  46.8  &  6.1  \\
22.&08.07.1718  &40.3  &  41.5  &  6.5  &  52.  &  16.07.1963  &  43.2  &  41.7  &  6.4  \\
23.&05.08.1742  &42.1  &  45.6  &  6.8  &  53.  &  14.05.1970  &  43.0  &  47.09&  6.6  \\
24.&10.1779        &40.3  &  41.5  &  6.5  &  54.  &  28.07.1976  &  43.17&  45.6  &  6.2  \\
25.&20.10.1827  &40.7  &  44.9  &  6.5  &  55.  &  30.10.1983  &  40.35&  42.18&  6.8  \\
26.&09.03.1830  &43.1  &  46.7  &  6.8  &  56.  &  07.12.1988  &  40.86&  44.17&  6.9  \\
27.&09.04.1851  &40.0  &  47.3  &  6.1  &  57.  &  29.04.1991  &  42.45&  43.67&  7.0  \\
28.&24.07.1852  &39.9  &  41.3  &  6.0  &  58.  &  15.06.1991  &  42.46&  44.01&  6.1  \\
29.&21.01.1859  &40.0  &  41.7  &  6.0  &  59.  &  23.10.1992  &  42.59&  45.1  &  6.5  \\
30.&02.06.1859  &40.0  &  41.3  &  6.4  &          &                        &            &            &    \\
[4pt]  \hline
\end{tabular}
\end{table}




\begin{sidewaystable}     %% Table  2
\tablewidth{155mm}
\ftablabel{The  Initial  List  of  Geological-Geophysical  and  Geomorphological  Characteristics  of  Recognition  Objects  in  the  Caucasus}
\vspace{5pt}
\scriptsize
\begin{tabular}
{@{}l@{\hspace{12pt}}
c@{}
c@{}}
\hline
\multicolumn{2}{c|}{} &    \\  [-4pt]
\multicolumn{2}{c|}{ Characteristics} & Algorithm  \\
    [4pt]    \hline  &  &    \\  [-4pt]
Maximum  height                                   &  $H_{\max}$ & ``Barrier-3'', ``Cora-3'' \\
Minimum  height                                   &  $H_{\min}$ & ``Barrier-3'', ``Cora-3'' \\
The  range  of  heights                           &  $dH  =  H_{\max}-  H_{\min}$ & ``Barrier-3'', ``Cora-3'' \\
Height  gradient                                  &  $dH/l$  & \\
The  combination  of  relief  types               &  Top & ``Barrier-3'', ``Cora-3'' \\
The  area  of  Quaternary  sediments              &  $Q$ & ``Barrier-3'', ``Cora-3'' \\
The  highest  rank  of  lineament                 &  HR  & ``Barrier-3'' \\
The  number  of  lineaments  at the  intersection &  NL  & ``Cora-3'' \\
The  distance  to  the  nearest  intersection     &  $R_{\mathrm{int}}$  & ``Barrier-3'' \\
Number  of  lineaments  in  the  neighborhood  &  &  \\
of  the  intersection  &  NLC    & ``Barrier-3'', ``Cora-3'' \\
The  distance  to  the  nearest  lineament  of  rank  I &R1  & ``Barrier-3'' \\
The  distance  to  the  nearest  lineament  of  rank  II &R2 & ``Barrier-3'', ``Cora-3'' \\
The  maximum  value  of  the  Bouguer  anomaly           &$B_{\max}$  & ``Cora-3'' \\
The  minimum  value  of  the  Bouguer  anomaly           &$B_{\min}$  & ``Cora-3'' \\
The  range  of  the  Bouguer  anomaly  values            &$dB  =  B_{\max}-  B_{\min}$ & ``Barrier-3'', ``Cora-3'' \\
The  maximum  value  of  magnetic  anomaly               &$MO_{\max}$  & ``Cora-3'' \\
The  minimum  value  of  magnetic  anomaly               &$HO_{\min}$  & ``Cora-3'' \\
The  range  of  the  magnetic  anomaly  values    &$MO_{\mathrm{dif}} = MO_{\max}- MO_{\min}$  & ``Cora-3'' \\
[4pt]  \hline
\end{tabular}
\end{sidewaystable}


\tabref{2}                    %  Tab.  2
shows  the  initial  list  of  geological  and  geophysical  characteristics  that  are  used  for  describing  the  recognition  objects  in  the  Caucasus.  According  to  the  results  of  evaluating  the  informativity  of  characteristics
[\itc{Soloviev  et  al.,}  \reflink{Solo16}{2016}]
it  has  been  decided  in  the  case  of  one  training  class
[\itc{Dzeboev  et  al.,}  \reflink{Dzeb19}{2019}]
to  use  11  characteristics  (\tabref{2})                    %  Tab.  2)
when  the  ``Barrier-3''  algorithm  is  applied.  According  to  the  results  of  evaluating  the  informativity  of  characteristics  for  two  training  classes,  14  characteristics  (\tabref{2})                    %  Tab.  2)
were  used  in  recognition  by  the  ``Cora-3''  algorithm
[\itc{Soloviev  et  al.,}  \reflink{Solo16}{2016}].
Note  that  8  characteristics
(\tabref{2})                    %  (Tab.  2)
were  used  in  recognition  by  the  both  algorithms.  They  are:  maximum  ($H_{\max}$),  minimum  ($H_{\min}$)  heights  and  their  difference  ($dH  =  H_{\max}-  H_{\min}$),  combination  of  relief  types  (Top),  area  of  Quaternary  sediments  ($Q$),  number  of  lineaments  in  the  vicinity  of  the  intersection  (NLC),  distance  to  the  closest  lineament  of  rank  II  (R2)  and  the  difference  between  maximum  and  minimum  of  the  Bouguer  anomaly  (dB).  To  reproduce  the  result  and  enhance  its  reliability,  the  values  of  the  characteristics  of  recognition  objects
(\tabref{2})                    %  (Tab.  2)
are  calculated  by  means  of  an  intelligent  GIS
[\itc{Nikolov  et  al.,}  \reflink{Niko15}{2015};
\itc{Soloviev  et  al.,}  \reflink{Solo18a}{2018a}],
developed  at  the  Geophysical  Center  of  the  Russian  Academy  of  Sciences.  This  facilitates  reproducing  the  result  and  enhancing  its  reliability.

Circles  with  a  radius  of  25  km  with  centers  in  relevant  intersections  of  lineaments  were  taken  in  the  capacity  of  vicinities  of  the  recognition  objects  inside  which  the  values  of  geological  and  geophysical  characteristics  are  calculated.  This  radius  corresponds  to  the  magnitude  threshold  (6.0)  of  strong  earthquakes  for  which  potential  areas  of  their  occurrence  are  determined
[\itc{Gvishiani  et  al.,}  \reflink{Gvis17a}{2017a};
\itc{Soloviev  et  al.,}  \reflink{Solo13}{2013},  \reflink{Solo16}{2016}].

Empty  ellipses  with  blue  borders  show  in
\figref{1}                      %  Fig.  1
the  result  of  earthquake-prone  areas  recognition  obtained  in  the  Caucasus  for  $M  \geq  6.0$  by  means  of  the  ``Barrier-3''  algorithm.  According  to  the  result  of  recognition,  108  out  of  237  considered  recognition  objects  were  assigned  to  the  high  seismicity  class.  It  means  that  when  the  ``Barrier-3''  algorithm  is  used  for  recognition  within  framework  of  the  EPA  approach
[\itc{Gvishiani  et  al.,}  \reflink{Gvis88}{1988}],
the  set  of  ellipses  in
\figref{1}                      %  Fig.  1
(circles  with  a  radius  of  25  km  with  the  centers  in  the  corresponding  108  intersections  of  lineaments)  shows  the  earthquake-prone  areas  for  $M  \geq  6.0$  in  the  Caucasus.  It  should  be  noted  that  in  addition  to  the  16  objects  from  the  training  sample,  92  intersections  of  221  are  declared  as  high  seismicity.

\begin{sidewaysfigure}                      % Fig 2
\figurewidth{140mm}
\setimage{}{}{155mm}{}{2019es000691-f02}
\fcaplabel{Recognition  of  high-seismicity  zones
($M  \geq  6.0$)
in  the  Caucasus  using  the  ``Barrier-3''  algorithm:  a)  the  average  contribution  11  geological  and  geophysical  characteristics  used  in  recognition;  b)  the  contribution  of  the  characteristics,  expressed  through  their  hit  in  the  triples  of  the  ``strongest''  characteristics.}
\end{sidewaysfigure}

\figref{2}                      %  Fig.  2
presents  histograms  that  show  the  contribution  of  11  geological  and  geophysical  characteristics
(\tabref{2})                    %  (Tab.  2)
in  the  result  of  recognition  by  the  ``Barrier-3''  the  objects,  which  belong  to  high  seismicity  class.
\figref{2}a                      %  Fig.  2a
shows  for  each  characteristic  its  contribution  in  the  recognition  result  that  is  the  number  of  objects  recognized  as  high  seismicity,  which  are  close  according  to  this  characteristic  (in  the  sense  of  proximity  embedded  in  the  algorithm)  to  any  object  from  the  training  sample  of  the  high  seismicity  class.  The  numbers  given  in
\figref{2}a                      %  Fig.  2a
have  been  preliminarily  divided  by  the  number  of  objects  in  the  training  sample  (16  in  our  case).  The  contribution  of  characteristics  is  described  also  as  follows.  For  each  characteristic  the  numbers  of  objects  from  the  high  seismicity  class,  which  are  close  according  to  this  characteristic  to  each  object  from  the  training  sample,  are  calculated.  Using  these  numbers  we  determine  for  each  object  from  the  training  sample  the  three  ``strongest''  characteristics  according  to  which  the  largest  numbers  of  high  seismic  objects  are  close  to  this  object  from  the  training  sample.
\figref{2}b                      %  Fig.  2b
shows  the  numbers  of  objects  from  the  training  sample,  for  which  the  characteristics  fall  in  the  triple  ``strongest''.  A  detailed  description  of  the  calculation  of  the  contribution  of  the  characteristics  is  given  in  the  paper  [\itc{Dzeboev  et  al.,}  \reflink{Dzeb19}{2019}].


It  follows  from
\figref{2}                      %  Fig.  2
that  the  greatest  contribution  to  the  formation  of  the  high-seismicity  class  of  objects  by  the  ``Barrier-3''  algorithm  is  made  by  the  characteristics,  which  are  responsible  for  the  relief  height  ($H_{\max}$  and  $H_{\min}$),  the  area  of  the  Quaternary  sediments  ($Q$),  the  highest  rank  of  the  lineament  (HR),  the  number  of  lineaments  in  the  neighborhood  (NLC),  as  well  as  the  distance  to  the  nearest  lineaments  of  the  I  (R1)  and  II  (R2)  ranks.  The  neighborhoods  of  the  intersections  of  lineaments  in  the  Caucasus,  recognized  by  the  ``Barrier-3''  algorithm  as  high  seismicity  for  $M  \geq  6.0$  are  characterized  against  the  background  of  the  whole  set  of  recognition  objects  by  large  values  of  maximum  and  minimum  heights  ($H_{\max}\geq  2500$~m  and  $H_{\min}  \geq  600$~m),  not  a  large  area  of  quaternary  sediments  ($Q  \leq  30$\%),
they  are  formed  by  three  or  more  lineaments  of  the  II  or  III  ranks
(NLC  $\geq  3$,  HR  =  2  or  HR  =  3,  R2  $\leq  30$~km)  and  are  located  at  relatively  insignificant  distances  from  the  I  rank  lineament  ($0  <  {\mathrm  R1}  \leq  50$~km).  These  signs  are  naturally  interpreted  as  criteria  for  high  seismicity  in  the  Caucasus.  From
\figref{2}                      %  Fig.  2
we  can  see  that  the  height  range  and  combination  of  relief  types  also  contribute  to  the  formation  of  the  recognition  result.


\begin{sloppypar}
White  ellipses  in
\figref{1}                      %  Fig.  1
show  the  result  of  earthquake-prone  areas  recognition  obtained  by  means  of  the  ``Cora-3''  algorithm  for  $M  \geq  6.0$  in  the  Caucasus.  This  result  is  published  in  the  paper
[\itc{Soloviev  et  al.,}  \reflink{Solo16}{2016}].
The  total  number  of  objects  assigned  to  the  high  seismicity  class  is  107.  They  include  all  16  objects  from  the  training  sample  of  the  high  seismicity  class,  22  objects  from  a  training  sample  of  a  low  seismicity  class,  and  69  objects  that  were  not  included  in  the  training  samples.  Practically  all  the  intersections  recognized  by  the  ``Cora-3''  algorithm  as  high  seismicity  are  associated  with  lineaments  of  the  I-st  and  \mbox{II-nd}  ranks.  This  suggests  that  high  seismicity  objects  are  located  at  the  boundaries  separating  the  largest  blocks  of  the  Earth's  crust  of  the  Caucasus
[\itc{Soloviev  et  al.,}  \reflink{Solo13}{2013}].
The  total  number  of  objects  assigned  to  the  high  seismicity  class  by  the  ``Barrier-3''  algorithm  is  108  and  all  16  objects  from  the  training  sample  of  the  high  seismicity  class  are  among  them.
\end{sloppypar}

A  comparative  analysis  of  the  recognition  results  by  the  ``Barrier-3''  and  ``Cora-3''  algorithms  has  been  carried  out.  The  numbers  of  objects  that  are  classified  as  high  seismicity  and  as  low  seismicity  by  the  both  algorithms  are  73  and  95  respectively.  The  remaining  69  objects  are  classifiede  as  high  seismicity  by  one  algorithm  only:  35  by  the  ``Barrier-3''  and  34  by  the  ``Cora-3''.

Denote  B  and  C  the  high  seismicity  zones  obtained  by  means  of  ``Barrier-3''  and  ``Cora-3''  algorithms  respectively.
\figref{1}                      %  Fig.  1
shows  these  zones  and  the  differences  in  the  recognition  results  obtained  by  the  two  different  algorithms  are  observed  in  the  western  part  of  the  Central  Caucasus,  on  the  Caspian  Sea  coast,  and  also  in  the  southwest  and  southeast  sectors  of  the  considered  morphostructural  zoning  scheme.

All  17  epicenters  of  earthquakes  with  $M  \geq  6.0$  that  occurred  during  the  period  1900--1992
(\tabref{1}                    %  (Tab.  1
and  the  red  circles  in
\figref{1})                      %  Fig.  1)
and  were  used  for  the  formation  of  the  training  sample  of  the  high  seismicity  class,  are  inside  the  common  part
$D  =  B  \cap  C$  of  the  zones  B  and  C.  Of  the  42  epicenters  of  earthquakes  with  $M  \geq  6.0$  that  occurred  before  1900
(\tabref{1}                    %  (Tab.  1
and  the  brown  circles  on  the
\figref{1}),                      %  Fig.  1),
7  and  8  epicenters  are  outside  the  zones  B  and  C,  respectively.  Half  of  these  epicenters  are  located  at  insignificant  distances  from  the  relevant  zone  and  one  can  explain  their  location  out  of  high  seismicity  zones  by  the  fact  that  the  coordinates  of  the  earthquake  epicenters  that  occurred  before  1900
(\tabref{1})                    %  (Tab.  1)
may  be  incorrect.  Moreover,  only  one  of  the  earthquakes  with  the  epicenters  located  outside  the  zones  B  and  C  has  a  magnitude  exceeding  significantly  6.0  ($M  =  7.8$).  For  all  others  --  $6.0  \leq  M  \leq  6.5$  and  this  means  that  some  of  these  earthquakes  may  not  be  the  subject  of  study  because  of  possible  errors  in  magnitude.

\begin{table}                                    %  Table  3
\tablewidth{115mm}
\ftablabel{Earthquakes  With  $M  \geq  6.0$  in  the  Caucasus  Since  1993}
\vspace{5pt}
\begin{tabular}
{@{}l@{\hspace{20pt}}
c@{\hspace{26pt}}
c@{\hspace{26pt}}
c@{\hspace{26pt}}
c@{}}
\hline
\\  [-7pt]
\numero  &  Date  &  $\varphi$,  \deg  &  $\lambda$,  \deg  &  $M$  \\
    [7pt]    \hline      \\  [-4pt]
1.  &  09.07.1998  &  38.717  &  48.507  &  6.0  \\
2.  &  25.11.2000  &  40.167  &  49.954  &  6.5  \\
3.  &  07.09.2009  &  42.66    &  43.443  &  6.0  \\
[4pt]  \hline
\end{tabular}
\end{table}



After  1992,  3  earthquakes  with  $M  \geq  6.0$  occurred  in  the  studied  region
(\tabref{3}                    %  (Tab.  3
and  the  green  circles  in
\figref{1}).                      %  Fig.  1).
Information  about  these  earthquakes  was  not  used  in  the  formation  of  the  training  samples  for  the  ``Barrier-3''  and  ``Cora-3''  algorithms.  An  analysis  of  the  location  of  their  epicenters  showed  that  two  of  them  are  located  within  zone  D.  It  has  to  be  noted  that  the  hypocenter  of  the  third  earthquake  that  occurred  in  the  Caspian  Sea  near  the  city  of  Baku  outside  the  both  zones  B  and  C  was  according  to  one  data,  located  in  the  crust,  on  others  deeper  --  under  the  crust.  Thus,  perhaps  this  earthquake  is  not  an  object  of  our  study.

Finally  one  can  summarize  that  only  4  (6\%)
out  of  the  62  epicenters  of  earthquakes  with  $M  \geq  6.0$  occurring  since  ancient  times  until  2018  are  outside  the  union  of  the  zones  B  and  C.

An  analysis  of  the  high  seismicity  criteria  in  the  Caucasus  identified  by  the  ``Barrier-3''  algorithm  in  the  present  work  and  the  ``Cora-3''  algorithm  in  the  paper  [\itc{Soloviev  et  al.,}    \reflink{Solo16}{2016}]
shows  their  sufficient  proximity.


\section{Conclusions}

\begin{sloppypar}
Applying  in  the  EPA  approach  the  original  ``Barrier-3''  algorithm  instead  of  the  pattern  recognition  algorithms  (e.g.  ``Cora-3'')  used  before  for  dichotomy  is  an  attempt  to  open  a  new  stage  in  the  development  of  this  approach
[\itc{Gvishiani  et  al.,}  \reflink{Gvis88}{1988}].
According  to  the  paper
[\itc{Gvishiani  and  Gurvich,}  \reflink{Gvis92}{1992}],
the  problem  of  strong  earthquake-prone  areas  recognition  is  a  dynamic
[\itc{Dubois  and  Gvishiani,}  \reflink{Dubo98}{1998}],
  limitary  problem  of  recognition.  As  shown  in  the  paper
  [\itc{Gvishiani  and  Gurvich,}  \reflink{Gvis92}{1992};
  \itc{Gvishiani  and  Dubois,}  \reflink{Gvis02}{2002}],
  in  limitary  problems,  there  is  only  a  single  reliable  (``pure'')  training  class  formed  by  objects  with  which  strong  earthquakes  that  have  already  occurred  are  associated.  Moreover,  as  a  result  of  recognition,  objects  from  the  low  seismicity  training  sample  in  the  desired  limitary  classification  may  end  up  in  a  high-seismicity  class.
  \end{sloppypar}

\begin{sloppypar}
The  ``Barrier-3''  algorithm  in  its  idea  and  construction  meets  more  adequately  than  the  dichotomy  the  dynamic  problem  of  earthquake-prone  areas  recognition  [\itc{Gvishiani  et  al.,}  \reflink{Gvis17a}{2017a}].
The  algorithm  requires  the  sole  training  sample  of  the  high-seismicity  class  and  determines  this  class  by  expanding  the  training  sample.
\end{sloppypar}

\begin{sloppypar}
The  ``Barrier-3''  algorithm  has  proven  itself  in  earthquake-prone  areas  recognition  with  a  sole  training  sample  in  the  Caucasus
[\itc{Gvishiani  et  al.,}  \reflink{Gvis17a}{2017a};
and  this  work]
and  the  Altai-Sayan-Baikal  region
[\itc{Dzeboev  et  al.,}  \reflink{Dzeb19}{2019}].
This  fact  strengthens  our  assumptions  that  determining  the  strong  earthquake-prone  areas  by  expanding  their  training  sample  is  adequate  for  solving  the  EPA  problem.  In  contrast  to  the  FCAZ  method  (Formalized  Clustering  And  Zoning)
[\itc{Gvishiani  and  Dzeboev,}  \reflink{Gvis15}{2015};
\itc{Gvishiani  et  al.,}  \reflink{Gvis13}{2013},  \reflink{Gvis16}{2016},  \reflink{Gvis17b}{2017b}]
that  was  also  developed  in  the  Geophysical  Center  of  the  Russian  Academy  of  Sciences  the  use  of  ``Barrier-3''  does  not  change  fundamentally  the  EPA  approach  [\itc{Gvishiani  et  al.,}  \reflink{Gvis17a}{2017a}].
In  this  case,  only  the  recognition  block  with  training  changes.  \mbox{``Barrier-3''}  comes  to  the  place  of  ``Dichotomy  algorithm'',  leaving  the  blocks  of  morphostructural  zoning  and  measurement  of  geological,  geophysical  and  geomorphological  parameters  unchanged.  Thus,  the  authors  assume  that  the  pattern  recognition  block  in  the  classical  EPA  approach  may  vary:  both  ``Dichotomy  algorithm''  and  ``Barrier-3''  may  be  used.  In  the  case  of  good  consistency  of  both  options,  we  can  talk  about  the  high  reliability  of  the  result.
\end{sloppypar}

\begin{sloppypar}
It  should  be  noted  that  the  recognition  results  obtained  independently  by  the  ``Barrier-3''  and  ``Cora-3''  algorithms  are  control  experiments  for  each  other.  Due  to  the  proximity  of  the  results  for  Caucasus,  these  control  experiments  should  be  considered  successful.  This  increases  the  reliability  assessment  of  both  the  result  of  the  EPA  (``Dichotomy  algorithm'')  and  the  EPA  (``Barrier-3'').
\end{sloppypar}

\begin{sloppypar}
Nowadays  in  the  Geophysical  Center  of  the  Russian  Academy  of  Sciences  under  the  guidance  of  Academician  A.  D.  Gvishiani  a  project  for  the  creation  and  evolving  of  a  universal  \mbox{GIS-oriented}  database  is  developing
[\itc{Soloviev  et  al.,}  \reflink{Solo18b}{2018b}].
It  contains  solutions  of  a  problem  of  strong  earthquake-prone  areas  recognition  in  various  regions  of  the  world  that  were  obtained  using  the  EPA (``Dichotomy  algorithm''),  EPA (``Barrier-3'')  and  other  methods
[\itc{Gvishiani  et  al.,}  \reflink{Gvis87a}{1987a},  \reflink{Gvis88}{1988};
\itc{Soloviev  et  al.,}  \reflink{Solo14}{2014}].
Later  this  will  make  it  possible  to  verify  the  universality  of  the  variation  of  the  pattern  recognition  block  for  other  regions,  where  the  EPA  (``Dichotomy  algorithm'')  recognition  was  previously  successfully  performed
[\itc{Soloviev  et  al.,}  \reflink{Solo14}{2014}].
\end{sloppypar}



One  possible  interpretation  of  the  integral  recognition  result  by  the  ``Barrier-3''  and  ``Cora-3''  algorithms,  obtained  in  this  paper,  can  be  its  definition  as  a  fuzzy  set
  $\{  W,  \mu_{B_B,  B_C}  \}$
  of  lineament  intersections,  in  the  neighborhood  of  which  strong  earthquakes  can  occur  in  the  considered  region.  The  corresponding  membership  function  of  such  a  set  would  have  the  following  form:\vspace*{-.5pc}
  \enlargethispage{-1.2ex}

\begin{eqnarray*}
\mu_{B_B,  B_C}  (w)  =
\end{eqnarray*}
\begin{eqnarray*}
\left\{
\begin{array}{ll}
1,  &  w  \in  B_B  \cap  B_C    \\
0.5,  &  w  \in  B_B  \bigtriangleup  B_C \! = \! (B_B \! \cup \! B_C)\backslash  (B_B \! \cap \! B_C)        \\
0,  &  w  \notin  B_B  \cup  B_C    %%%  ???  in
\end{array}
\right.
\end{eqnarray*}
where  $w  \in  W$  are  the  objects  of  recognition,  and  $B_B$,  $B_C$  are  those  of  them,  which  are  recognized  as  high  seismicity  by  the  algorithms  ``Barrier-3''  and  ``Cora-3''  respectively.
\figref{3}                      %  Fig.  3
shows  an  example  of  interpreting  the  results  of  earthquake-prone  areas  recognition  with  $M  \geq  6.0$  in  the  Caucasus  in  the  form  of  a  fuzzy  set.

\begin{sidewaysfigure}                      % Fig 3
\figurewidth{140mm}
\setimage{}{}{155mm}{}{2019es000691-f03}
\fcaplabel{Presentation  of  integral  recognition  results  of  earthquake-prone  areas  recognition  in  the  Caucasus  with
$M  \geq  6.0$
by  the  ``Barrier-3''  and  ``Cora-3''  algorithms  as  a  fuzzy  set  of  neighborhoods  of  lineament  intersections.  Red  color  shows  neighborhoods  of  intersections  with  the  membership  function
$    \mu_{B_B,  B_C}  =1$,
yellow    --  $    \mu_{B_B,  B_C}  =  0.5$,
green  --  $    \mu_{B_B,  B_C}  =  0$.}\vspace*{-.76pc}
\end{sidewaysfigure}

The  development  of  the  ``Barrier-3''  algorithm  can  be  considered  as  a  new  step  in  solving  the  problem  of  strong  earthquake-prone  areas  recognition
[\itc{Gvishiani  et  al.,}    \reflink{Gvis88}{1988}].


\acknowledgments{This  work  was  conducted  in  the  framework  of  budgetary  funding  of  the  Geophysical  Center  of  RAS,  the  Institute  of  Earthquake  Prediction  Theory  and  Mathematical  Geophysics  of  RAS  and  the  Geophysical  Institute  VSC  RAS,  adopted  by  the  Ministry  of  Science  and  Higher  Education  of  the  Russian  Federation.}




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\end{document}
