Estimation of maximum mass velocity from macroseismic data: A new
method and application to archeoseismological data
, A.M. Korzhenkov
Institute of Earthquake Prediction Theory and Mathematical Geophysics RAS, Moscow, Russia
Institute of Marine Geology and Geophysics, Far East Branch RAS, Yuzhno-Sakhalinsk, Russia
Schmidt Institute of Physics of the Earth RAS, Moscow, Russia
Received 28 January 2018
Accepted 21 June 2018
Available online 15 September 2018
Ancient cities in the Negev desert
PGV estimation from macroseismic data
Earthquake hazard assessment for southern
An important task in seismic hazard assessment is the estimation of intensity and frequency of rare
strong seismic shaking, in particular, the long-term peak ground velocity values (PGVs). A recently
proposed method is suitable for simply estimating PGVs based on the examination of the magnitude of
displacements of rock blocks. The effectiveness of this method is demonstrated by results of studies on
the source zones of two large earthquakes and a vicinity of one strong explosion. In this study, the
method is applied to the examination of archeoseismological data from the ancient Rehovot-ba-Negev
city and other ancient cities from the Negev desert (in Southern Israel) where numerous evidences of
presumable seismic damage were found earlier. The cities and also a sophisticated irrigation system
within the region, which existed in the Negev desert, were abandoned however in the middle of the
seventh century. The abandonment could be caused by a combined effect, from not only the cessation of
the state support from Byzantium as a result of the Arab conquest but also the severe destruction from
the strong earthquake that hit the area at that time. The intensities of the seismic events that hit the
cities were estimated earlier, which are within the range of 8e9. Our estimates indicate that the PGV
values are about 1.5 m/s. Hence, the magnitude of the causative earthquake could be in the range
Mz6.5e7.5, and the location of the epicenter might be at a distance of a few dozens of kilometers from
the ancient Rehovot-ba-Negev city, while the other variants associated with the earthquake seem to be
©2018 Institute of Seismology, China Earthquake Administration, etc. Production and hosting by Elsevier
B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND
The long-term seismic hazard assessment cannot be determined
reliably only from statistical analyses of instrumental data because of
the relatively short time window available for such an approach.
Having this in mind, the paleo- and archeo-seismological studies are
used to validate and correct the seismic hazard estimation based on
instrumental data. Animportanttask in seismic hazard assessment is
the estimation of the intensity and frequency of rare strongest
seismic shaking, in particular, the peak ground velocity (PGV) or peak
ground acceleration (PGA) due to rare large earthquakes. A simple
new method for the evaluation of PGV values from the magnitude of
displacements of rock blocks due to seismic shaking was suggested
in . The applicability of the method was veriﬁed by the exami-
nation of macroseismic effects observed in the source areas of two
large earthquakes and in a vicinity of one explosion that took place in
Tien-Shan region (Kirgizia). The results of this examination provide a
solid basis for the interpretation of rock blocks displacements found
in archeo- and paleoseismic studies. Naturally, the uncertainty in the
results of the examination is larger than that for the analysis of
source areas of recent large earthquakes.
We use the results of archeoseismological study performed in
the ancient Rehovot-ba-Negev city (Rehovot in the Negev, Israel)
*Corresponding author. Institute of Earthquake Prediction Theory and Mathe-
matical Geophysics RAS, Moscow, Russia.
E-mail address: email@example.com (M.V. Rodkin).
Peer review under responsibility of Institute of Seismology, China Earthquake
Production and Hosting by Elsevier on behalf of KeAi
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Geodesy and Geodynamics 10 (2019) 321e330
and in its surroundings [2e9]. The following types of presumably
seismic damage were found and described as follows: tilting and
collapsing of walls, collapse of arches and keystone sliding down-
wards, shifting of fragments of walls, deformation in walls due to
pushing by the adjacent perpendicular wall, opening between
adjacent perpendicular walls, rotation of wall fragments, and ﬁs-
sures in walls and in the wall of the water reservoir. These features
testify for at least two strong earthquakes that occurred in the
ancient town: one in the Byzantine time and the other one in the
Early Arab period . Similar damage effects were found [2e11] in
other ancient cities located in the Negev desert (i.e., Avdat, Haluza,
Mamshit and Shivta).
Using the abovementioned archeoseismic data [2e9] and the
new technique [1,12], we aim to quantify the PGV values connected
with the strong earthquakes that hit the cities in the Negev desert;
we will also try to estimate some possible parameters of these
earthquakes. The results testify to a larger long-term seismic hazard
than previous estimates for the Negev desert where no notable
earthquakes were recorded since 1904.
We use the PGV estimation method (PGVEM) described in .
This method is based on three assumptions. First, it is known that
the distributions of the impact due to earthquakes (PGV and PGA
values) obey a power law; thus, only the strongest seismic impact is
taken into account, whereas the other much weaker effects are
treated as noise.
Second, it is known that a train of wave motion from a near
earthquake usually contains one greatest amplitude (often repre-
sented by a pair of swings in opposite directions) that far exceeds
the amplitudes of the other parts of the motion. We assume that
this high amplitude is exactly related to the maximum mass ve-
locity (PGV) that makes the rock blocks move into new positions.
Other displacements caused by the seismic motion of signiﬁcantly
lower amplitudes can be treated as noise. Examples of the pairs of
oppositely directed seismic damage effects due to near seismic
events will be given below.
Third, the geometry of a displaced rock block and the rock blocks
that initially surround it play the role of an effective ﬁlter that al-
lows displacements only occur in one particular direction. Strong
seismic impacts in other directions do not cause signiﬁcant dis-
placements of rock blocks due to the geometrical constraints.
From these simplifying assumptions, each seismically induced
displacement of a rock block can be considered as a result of a single
seismic excitation. Other excitations are supposed to be much
weaker and can be treated as noise. Naturally, such simpliﬁed
estimation will involve an error of at least a few dozens of percent.
However, such an error seems admissible, because ﬁnally in most
cases we will use the resulting PGVs on a logarithmic scale. Note
also that the cases of dominant displacements of rock blocks should
be examined only, while the small displacements can be supposed,
with a high probability, to be caused by non-seismic excitations.
This means that only the large PGV values, greater than or equal to
1 m/s, could be detected in most cases. Such large PGV values are
very rare in strong movements caused by earthquakes  because
they seem to be typical for the near source zones of earthquakes
only. The data set containing maximum PGV and PGA values ob-
tained up to 2008, shows only 40 cases in which the PGV values
exceed 1 m/s.
Thus, all we have to do now is to estimate the parameters of this
strongest impact, i.e., the PGV value and its direction. For this sake,
we solve a simpliﬁed mechanical model of energy balance equation
that links the observed displacement of a rock block and the
corresponding value of mass velocity, which is assumed equal to
the PGV value.
The simplest and the most frequently used model of a rockblock
displacement along a horizontal surface with friction is described
by the following energy balance equation:
where, mis the mass of the rock block, Vis its velocity (assumed
equal to PGV), gis the acceleration due to gravity, kis the friction
coefﬁcient, and Lis the amplitude of displacement of the rock block.
The vertical displacements of rock blocks can be easily taken as
incorporated, when they are substantial. More sophisticated
models are used in the cases where the rock blocks drop, move
upward, or are overturned. A description of most such models can
be found in . Any of the models is described by a simple equation
of mechanical energy balance.
Note that the rock block seismogenic displacements can also be
examined in terms of the numerical discrete-element discontin-
uous deformation analysis (DDA) method [10,11,14,15]. We will
touch on a comparison between the two methods in the Discussion
section subsequently. In the next section, we will discuss the results
of the application of our method to the analysis of the rock block
displacements found in the source zones of recent large earth-
quakes and in the vicinity of a strong explosion. Then we will
further analyze the archeo-seismological data.
3. The results from the application of the method to recent
The technique brieﬂy described above was applied to the anal-
ysis of the seismic effects observed in the vicinity of one explosion
and two large earthquakes that occurred in Tien-Shan (Kirgyzia).
Numerous cases of displacement of rock blocks (stones) were
observed in the close vicinity of the explosion that was detonated
on June 11, 1989 in the Uch-Terek area, Kirgizia . The total mass
of the charge located in two parallel closely spaced tunnels was
about 2 kilotons. The rock massif shows an intensive stratiﬁcation,
where the layers are steep, and the azimuththe layers strike is close
to the orientation of the tunnels. A survey of the surface of a ﬂat-
topped mountain adjacent to the tunnels revealed numerous
fresh displacements of stones caused by the explosion. The
photograph of a typical displacement is given in Fig. 1. A total of 69
cases of such displacements were described by A.L. Strom and
analyzed in . The sketch map in Fig. 2 shows the location of the
tunnels and positions of the displaced stones, as well as the am-
plitudes and directions of the displacement. As can be seen from
this ﬁgure, the directions of displacement are determined by both
Fig. 1. The photograph of a typical stone displaced by an explosion. The photograph
was kindly provided by Prof. A.L.Strom.
M.V. Rodkin, A.M. Korzhenkov / Geodesy and Geodynamics 10 (2019) 321e330322
the location of the charge and the layering of the rock massif. In a
number of cases, the opposite directions of the displacement take
place at the same site. No signiﬁcant correlation between the stone
sizes and the displacement amplitudes can be found. It is worth
mentioning that the analysis was not performed in a systematical
manner, so that a larger part of the displaced stones could be
Because there are very limited PGVs in excess of 1 m/c in the
strong motion data set, the data on explosions  are also used to
obtain a nomogram that links the PGV value to the energy and the
distance from the causative seismic event . From this nomogram,
the mass of the charge is estimated as 1.7 kilotons, which is not far
from the actual value (2 kilotons).
Large rock block displacements are found in the vicinities of two
recent large earthquakes. The Kemin earthquake (January 3, 1911,
Mw¼7.9) took place in a nearly north-south compressive stress
ﬁeld, where thrust deformations prevail in its source zone. The
northern wing of the seismic fault is upthrown . Even though
the Kemin earthquake occurred more than 100 years ago, the fault
scarp and other surface seismic deformations are quite visible along
the fault zone.
The fault scarp is almost uninterrupted in the part of the source
zone. We have found 19 cases of possible seismogenic displace-
ments of rock blocks on the northern upthrown side of the thrust,
and 8 displacements on the southern downthrown side of the fault.
Using the model of the rock block displacement as described
above, we have estimated the peak mass velocity PGV values and
the directions of the seismic excitation for all the detected rock
block displacements . We used the relationship as denoted in
Equation (1) for the PGV estimation in most cases. Fig. 3 shows the
location of the fault scarp segments, the measurement points, the
azimuth, and the PGV estimates. The PGV estimates for the Kemin
earthquake source zone range in most cases from 1 to 1.5 m/s.
Fig. 3 shows that displacements are mainly perpendicular to the
strike of the seismic scarp, which is consistent with the thrusting
character of the movement on the fault. The direction of the inertial
force on the northern side of the thrust coincides with the move-
ments that characterize a slower onset of motion and a sharp
stoppage. In this case, the inertial force is oriented southward along
the thrust motion. The direction of the seismic effect on the
southern side of the fault is generally opposite to that found on the
northern side (see Fig. 3). The simple linear structure of the scarp is
broken in a few localities where series of separated segments
replace it. The directions of rock block displacements are more
volatile in such areas (see Fig. 3).
The PGV estimates for the case of Kemin earthquake are
somewhat lower than the PGV values obtained in most other cases
[1,12,20]. Presumably, this is because the Kemin earthquake
occurred in January and a thick snow layer hampered the move-
ment of the rock blocks. We have found support for this assumption
by investigating the correlation between the PGV estimates and the
volume of the shifted rock blocks. Obviously, a snow sheet hampers
the movement of smaller stones to a greater degree, which results
in the correlation. The correlation coefﬁcients are similar for the
northern (upthrown) and the southern (downthrown) sides of the
fault, but the displacements (and velocities) are higher at the
northern side with a thinner snow layer. The correlation is esti-
mated under a 95% conﬁdence level.
Higher PGVs (up to 4.5 m/s, with the mean value of 1.6 m/s)
were found in the source zone of the Susamyr earthquake (August
19, 1992, Ms¼7.3, Tien-Shan, Kirgyzia). A histogram of the rock
block displacements found in the source zone of this earthquake is
shown in Fig. 4, which reveals two systems of predominant
displacement azimuths, i.e., the 175
orientations agree with the structure of the causative seismic fault.
The western segment of the surface ruptures is in the zone of the
northwest Susamyr fault, while the eastern segment is in the zone
of the Aramsuy thrust fault . Strong motions take place mostly
along these faults, and the two predominant displacement orien-
, correspond to these segments of
the causative fault. Note that each of these two systems is
composed of two oppositely directed sides.
Some other evidences provided in [20,22,23] also demonstrate
the effectiveness of our method in the analysis of data from the
source zones of large earthquakes.
Similar effects are also typical for the damage to buildings
caused by large earthquakes. An example of such damage is given in
the photograph (Fig. 5) of the epicentral area of the Izmit earth-
quake (Turkey, 1999, Mw¼7.6). The seismic rupture caused by this
earthquake reached the ground surface. It was a dextral strike-slip
fault. Most of the buildings located near the fault collapsed. As
shown in Fig. 5, the direction of the seismic excitation is well
consistent with the direction of the displacement along the seismic
fault, while the opposite directions agree with the different sides of
the fault. An example of the excitation directions differing by 180
at adjacent points on the same side of the fault is also noticeable
(the buildings # 3 and 4 in Fig. 5).
The patterns described above will be taken into account in the
examination of the archeo-seismological data subsequently.
4. Application to archeseismicity
4.1. Historical background
The Rehovot-ba-Negev city (Ruheiba in Arabic) was founded by
the Nabateans at the end of the 1st century B.C. . It is located in
the northern Negev, about 280 m above the sea level, about one
hundred kilometers from the Dead Sea transform. During the
Nabatean, Roman and Byzantine times, it was one of the largest
settlements in the Negev area, ranking among other signiﬁcant
cities such as Avdat, Haluza, Mamshit, Nizana, Saadon, and Shivta
(Fig. 6). These were well-developed settlements located along the
caravan roads that connected the Arabian Peninsula, Petra and the
harbor of Gaza. The ancient citizens built their houses of local hewn
stones, and the roofs were made of stone beams that were sup-
ported on arches. The region was well developed agriculturally.
Remnants of ancient agriculture rainwater collection systems,
Fig. 2. A sketch map showing the location of the charge in the galleries (red), and the
directions and magnitudes of the mass velocities. The distances along the axes are
given in meters in the local coordinate system. The scale of velocity values and the
direction of rock foliation are also shown.
M.V. Rodkin, A.M. Korzhenkov / Geodesy and Geodynamics 10 (2019) 321e330 323
water channels, terraced ﬁelds, and many hundreds of ancient
farmhouses were found there. The irrigation systems gathered
water from the area, which were supposed to be able to increase
the precipitation up to ﬁve times. Thus, the recent average rate of
80 mm rainfall per year, which is apparently not sufﬁcient for
agriculture, was believed to be expanded by those irrigation sys-
tems to about 400 mm that provided quite suitable conditions for
the agriculture at that time. Other authors [25,26] emphasized the
geopolitical aspect and attributed the existing agricultural systems
to the policy of the Byzantine Empire to stabilize the frontier re-
gions by encouraging agricultural settlements. State-sponsored
subsidies made it possible for these systems to survive during un-
avoidable drought years.
Today Rehovot-ba-Negev is a vast space of elongated heaps of
building stones which cover the ground all around the city. At its
maximum, the city covered an area of about 10
ha . The
number of citizens at the Byzantine time is estimated at about 5
thousands. A plan of the city settlement was presented in .
Three churches, a monastery, a caravansary, a bathhouse, and an
open water reservoir were recognized among the ruins of Rehovot
The desert cities revealed the expansion of the Byzantine society
and economy In the 6th century AD . Classical rich basilica style
churches functioned in each of the desert towns. The wealth of the
area was evident in these churches, which had wall facings and
furniture of marble imported from Anatolia, rich mosaics, and
vaults of large wooden beams imported from the Mediterranean.
Meanwhile, Rehovot and also most of the other cities were
abandoned in the fourth decade of the seventh century. This period
coincides with the Arab conquest of Palestine (634e640 AD).
However, the main military actions during the Arab conquest took
place to the north of the Dead Sea, so the war probably hardly
affected the Negev desert cities. Tsafrir et al.  did not ﬁnd any
Arab potteries in the eighth century or later than that time. This
means that the Arab inﬂuence was subordinate there in the seventh
century and after that. Only some minor activities continued here
after the seventh century. Thus, some rooms of the church only
shows signs of human activity long time after that, i.e., during the
Turkish period . In addition, the cistern at the atrium only re-
veals signs that it had been cleaned during the last years of the
period when the place was under the Turkish rule.
Subsequently we will discuss the possible reasons for the
cessation of the use of the sophisticated agriculture system in the
Negev desert and the probability of a long-term seismic hazard in
77.35 77.37 77.39 77.41 77.43 77.4577.45
Fig. 3. The fault scarp segments and corresponding estimates for the Kemin earthquake. Black and green points and line segments correspond to the observation points on the
upthrown north and downthrown south wings of the fault, respectively. The black solid lines indicate direction and magnitude of displacements, and the red broken lines show the
segments of the seismic escarp. The scale of PGV estimations is denoted at the left corner.
Fig. 4. The distribution of azimuths of the rock block displacements in the source zone
of the Susamyr earthquake, which shows two pairs of preferential directions with two
sides differing by 180marked as “A”and “B”.
M.V. Rodkin, A.M. Korzhenkov / Geodesy and Geodynamics 10 (2019) 321e330324
4.2. Types of deformation in buildings: identiﬁcation of earthquake-
Historians and archaeologists usually explain the extinction and
abandonment of ancient cities by hostile invasions, the arrival of
epidemics, political reasons, but very rarely by ecological crises or
natural disasters. However, seismic damage is a factor taken into
account by different authors [5,6,29e33].
The rocky desert Negev, Southern Israel, provides an excellent
platform for archeoseismological research. During the Roman and
Byzantine periods some cities were built there (Fig. 6) using so-
phisticated building methods. The cities ﬂourished between the
2nd and the beginning of the 7th centuries, and were then aban-
doned by the middle of the 7th century. The ruins of the cities are
well preserved, as the terrain were later inhabited only by rare
nomads, and the remaining stone walls and ruins were little
damaged under the dry climate. Archeoseismological studies at the
ancient building complexes of the Negev revealed some evidences
of their severe damages caused by strong earthquakes [2e11 ] . The
few well-excavated buildings at Rehovot provide quite persuasive
examples of such seismic damages. After describing this damages,
we will parameterize the causative seismic events in more details.
Different kinds of seismic damages were found in Rehovot and
its surrounding areas, see Refs. [2e9] for more details. Some of
them are used in our study for quantitative parameterization of the
seismic excitation. The types of presumable seismic damages were
found and described as follows.
Tilted and collapsed walls. Tilt and following collapse of walls
are typical features of damages due to earthquakes. Naturally, tilts
and collapses of walls could also be caused by military activities and
by long period of natural weathering and denudation. However,
only the seismic effect could produce systematic wall tilts and
collapses toward a certain direction [2,3,7,8]. At Rehovot an evident
systematic character in the failure of the walls was found: the walls
that generally trend ~140
fell toward ~50
, and walls that trend
collapsed towards ~140
. Similar preferred orientations of
seismic effects have already been described above in section 3for
the cases of large earthquakes and an explosion. A typical example
of the tilting and collapse of walls is presented in Fig. 7.
Shifting of wall fragments is found to be rather abundant as
well. A typical example of a 15-cm eastward shift of two stones
found in the excavated quarter of the Rehovot city, is presented in
Rotations of wall fragments is also a common phenomenon
due to large recent and ancient earthquakes [6,12]. The pulling out
of foundation stones accompanied by their rotation indicates dy-
namic hitting in the process of violent horizontal oscillations of the
whole wall. Seismic ground motion is the mechanism that can
cause such rotation. The multiple cases of rotation and their
directional systematics support the seismogenic character of this
kind of damage [2e9]. An example of such rotation at the eastern
wall of the Northern Church in Rehovot is presented in Fig. 9. Here
one stone in the upper preserved row of the wall has been rotated
clockwise. Stones located above this level are overturned.
The recurrence of large seismic events is supported by ex-
amples of repairs of walls. Sloping support walls were found in
Rehovot in the North and South Churches and in a number of pri-
vate buildings [8,24]. Revetment walls are cemented by grey mortar
consisting of chalk and ashes, but its main support is gravity. The
revetment is laid on a loess layer, but its foundation is situated
higher than that of the original walls. This indicates a considerable
time delay between the construction of walls and their repair. In
most cases the revetment walls were 1.80 m high and 90 cm wide at
An example of repair can be well seen at the NE corner of the
Northern Church in Rehovot (Fig. 10). The cut through the wall is
clearly visible where the wall was destroyed. The signs of stones
falling northwards from the original wall can be seen. The
encircling revetment wall is still of good quality nowadays,
which demonstrates that it was probably built before the decay
of the Byzantine Empire. However, later another seismic led to
the destruction of the revetment wall. The same signs can also
Fig. 5. A photograph showing an example of the damage to buildings caused by the Izmit earthquake (Turkey,1999, Mw¼7.6). The photograph was kindly provided by Prof. Erhan
Altunel. The white dashed line shows the seismic rupture, and the white arrows denote the direction of the motion (the dextral strike-slip movement). The grey arrows indicate the
collapse direction of the buildings, according to .
M.V. Rodkin, A.M. Korzhenkov / Geodesy and Geodynamics 10 (2019) 321e330 325
be observed in Rehovot at the central southern jamb of the
Northern Church. Similar cases of wall repair were found in
other Negev desert cities, e.g., in the Avdat, Mamshit and Shivta
Columns supported by walls. Columns in ancient and modern
buildings cause re-distribution of the static load in the building,
and also serve as art decoration. Therefore, when a column sup-
ported by a wall is found, it means that the column was severely
damaged and a supporting wall became necessary. Such an
example is described in Ref. . Another example of later adjust-
ment of a damaged building was noted at the Staircase Tower. At its
northeastern corner, there was a large (75 80 cm) window .
Originally, it was used for letting in light and air, but later it was
used as an entrance from the atrium, because long blocks used as
steps were found on both sides of the window. As one can imagine,
the “normal”entrance was damaged by an earthquake and could
not be used, so people began to use the better-preserved window as
an entrance instead. In Ref.  it is written that the support walls
are typical for the Northern Church which was severely damaged
by a strong earthquake that had occurred before 505 AD. Note that a
few severe earthquakes hit the region in 447, 498, and 502 AD.
Another strong earthquake occurred during the 7th century AD.
This could be the same earthquake that destroyed Avdat [2,35]. This
earthquake could also drive the inhabitants out of Rehovot, which
occurred soon after (or slightly before) of the Arab conquest.
In Refs. [5,8] it was emphasized that the degree of the damage in
all cities studied in the Negev desert (Avdat, Haluza, Mamshit,
Rehovot and Shivta) is similar. To produce such deformation, a local
seismic intensity of I >8 was needed. In Ref.  it was suggested
that at least some of causative large earthquakes took place on local
faults that traversed the Negev rather than in the more remote
Dead Sea Transform zone. In the latter case, the degree of
Fig. 6. The ancient caravan routes, dry water streams, and cities in the Negev desert.
M.V. Rodkin, A.M. Korzhenkov / Geodesy and Geodynamics 10 (2019) 321e330326
deformation had to decay rapidly from Mamshit in the east to
Rehovot in the west. However, such tendency was not found.
We further use the archeoseismological data described above to
carry out a preliminary quantitative parameterization of the caus-
4.3. A preliminary quantitative parametrization of seismic events
Only a minor part of the territory of the Rehovot city was
excavated, and in very few cases the information needed for the
application of our new method [1,12] is available. It can also be
suggested that few displacements of maximum amplitude were
described. No statistics information is available for the veriﬁcation.
Therefore, the estimates of seismic excitation amplitudes presented
below will be described with only some preliminary results.
The minimum tilt of a wall that is enough to cause it to collapse
has to satisfy the condition that the projection of the center of
gravity of the inclined wall locates outside its base (Fig. 11). This
model is used routinely to describe the falling of columns, and it
also seems to be suitable for describing the case of segments of
walls when they can be treated as a single block. The typical sizes of
the walls of principal buildings (such as churches) appears to meet
the following relationship: the height H¼5 m and the thickness
L¼1 m. The parameters of the walls of typical residential houses
appears to satisfy the following condition: the height H¼2.5 m and
the thickness L¼0.5 m. In both cases, we have the same value of
the critical inclination angle
that causes the collapse of a wall:
From (2) we obtain the value of
that ranges from 11
both typical residential houses and for defensive and church walls
(Figs. 7 and 10). Because of the severe damage to all walls, one can
suppose that the earthquake-induced tilt angle of the walls as:
, or greater.
However, a wall is not a rigid body. While the inclination angle
of a wall increases and approaches the critical value, a destruction
of the upper part of the wall is possible (see the grey part in Fig. 11b
for an example of the wall). When the upper part of the wall is
destructed, the lower part will be able to bear greater tilt angles. It
turns out that the tilt of the walls can exceed 12
, and this tilt can
become larger gradually with respect to the time due to relaxation.
As a matter of fact, the observed tilt angles of the lower parts of the
walls (including the example in Fig. 4 and other cases) reach up to
One can obtain an approximate estimate of the peak ground
velocity (PGV) in a seismic wave that is able to cause an
inclination of a wall. The potential energy increase U of a wall block
(with the mass m) can be estimated from the following equation
(see also Fig. 11)
Fig. 7. A tilt of 18and collapse of a wall westward at the SW corner of the western
yard of the Northern Church in Rehovot. The opening between the two perpendicular
walls is shown by the two-way arrow, and the through-going ﬁssure (joint) cuts three
adjacent stones in succession (shown by the three one-way arrows), cited from .
Fig. 8. A horizontal 15-cm eastward shift of the upper part of an arch column in the
excavated quarter of Rehovot-ba-Negev.
Fig. 9. Clockwise rotation of a stone in the eastern wall of the Northern Church in
M.V. Rodkin, A.M. Korzhenkov / Geodesy and Geodynamics 10 (2019) 321e330 327
From the law of energy conservation the increase in potential
energy should be equal to the kinetic energy Еof the seismic wave
From Equations (3) and (4) we obtain the PGVs for the cases of
typical residential houses and principal buildings, respectively:
where the PGV value is estimated as 0.7e1.0 m/s in our study.
In other cases for the sub-horizontal shift of a segment of a wall
(Fig. 8), the equation of energy balance (2) can be applied
where kis the friction coefﬁcient and Lthe sub-horizontal shift
value. The friction coefﬁcient k ranges from 0.8 to 1.0, and the sub-
horizontal shift Lfor the example as shown in Fig. 8 equals 15 cm.
The amplitudes of the displacement 10e15 cm appear to be typical
for other cases as well. Hence, we can get an approximate estimate
for the PGV as: V¼1.2 e1.7 m/s.
This PGV estimate is quite close to that obtained by Equation (5),
which suggests that the obtained estimates are at a conﬁdent level.
Then we evaluate the parameters of the earthquake that could
cause such 0.7e1.5 m/s PGV values. The Modiﬁed Mercalli (MM)
scale, the European Macroseismic Scale (EMS-98), and most other
scales do not take into account the terms of objectively quantiﬁable
measurements such as the shaking amplitude, frequency, peak
ground velocity (PGV), or peak ground acceleration (PGA). It is
noted however, that the maximum PGV and PGA values (especially
the PGV) for the same intensity I tend to increase as the amount of
data on strong motions increase [36,37]. According to the new
macroseismic scale of provided by F. Aptikaev (Table 1) the PGV
values obtained in our study are corresponding to the seismic in-
tensity Iranges from 8.5 to 9.5 [36,37]. Some earlier studies in
Refs. [5,8] indicated that the intensity values Iranges from 8 to 9.
One should also keep in mind that the variation range of the
possible PGA and PGV values corresponding to the same intensity I
is supposed to be at very high level [36,37], and these independent
estimates can be considered as close to each other.
Some preliminary variants of the possible pairs of parameters
that characterize the causative large earthquake (e.g., the magni-
tude and the distance from the Rehovot city) could be determined
using the nomogram from . According to this nomogram,
PGV ¼1e2 m/s could be generated by a shallow local earthquake
with the magnitude Mz6.0, or by an earthquake with the
magnitude Mz6.5e7.5 located at a distance of a few dozen kilo-
meters from the site. In the case that a causative large earthquake
occurs within the Dead Sea transform zone at a distance of about
one hundred kilometers, the magnitude of the event should be as
high as Mz8.5e9.0. Since this magnitude estimate is quite large,
our results support the suggestion in Refs. [5,8] that large local
earthquakes can occur in the Negev desert.
Here we discuss two issues. The ﬁrst one is about the signiﬁcant
discrepancy between different estimates of earthquake hazard for
the Negev desert area, and the second one is the comparison be-
tween our PGVEM method and the numerical discrete element
discontinuous deformation analysis (DDA) method [10,11,14,15].
No notable earthquakes have been recorded in the Negev desert
area since 1904. There were no indication of the existence of active
faults in the area. The area is believed to have suffered only from
distant earthquakes occurring in the Dead Sea transform zone. The
Fig. 10. Continuation of the revetment wall (the ﬁeld station 7) of the Northern
Fig. 11. A sketch map showing the destruction of an ideal rigid wall (a), and of a more
realistic wall composed of blocks of stones separated by joints (b).
The typical peak ground velocities (PGVs) and peak ground accelerations (PGAs) at
different intensities (I).
I5 5.5 6 6.5 7 7.5 8 8.5 9 9.5
PGV (cm/s) 1.3 2.2 3.8 6.5 11 19 33 57 98 170
) 17.5 28 44 70 110 175 280 440 700 1100
M.V. Rodkin, A.M. Korzhenkov / Geodesy and Geodynamics 10 (2019) 321e330328
known seismic damage in the Avdat and Mamshit cities [10,11] are
believed to be caused by the Dead Sea transform zone earthquakes.
However, similar cases of earthquake-induced damage were found
in other Negev cities including Rehovot, but no tendency of a
decreasing amplitude of damage with respect to increasing dis-
tance from the Dead Sea transform zone was found [2e9]. In the
model of the lithospheric dynamics and seismicity for the Near East
 several major fault zones are indicated in this region, indi-
cating that some other active seismic zones may exist in the region,
apart from the Dead Sea transform. A recent geological research has
revealed the existence of a strike-slip fault, i.e., the “Saadon fault”
next to the site of Saadon, and also close to Rehovot. The length of
the surface part of the fault is somewhat below 1.0 km and its
vertical displacement is 2e3m.
Our results additionally support the assumption that large
earthquakes can occur in the Negev desert region, in addition to the
Dead Sea area. To further address this issue we suggest that more
detailed studies to be carried out in the future.
As to the methodological comparison issue, we have used the
PGVEM method based on the energy balance equations. This
approach can be considered as an alternative to the numerical
discrete element discontinuous deformation analysis (DDA)
method [10,11,14,15]. The DDA method is based upon the study of
the kinematics of individual blocks as a function of seismic loading,
gravity, and friction along the block interfaces. The displacement
and deformation of discrete blocks are treated in the DDA method
as the accumulation of short-time steps. At each time step, after
examining the motion equation one takes into account the loading
conditions, the material properties of each block and properties of
the contact between adjacent blocks. Then the relevant motion
equations are solved. The DDA method estimates the peak ground
acceleration (PGA). It should be pointed out that the numerical
error will increase along with an increasing time step, so this
method requires a small time step. However, when using a small
time step, the convergence of the results will be only achieved after
a long period of calculation, which may be a problem when solving
a multi-block system, even with super computers .
In mechanics the introduction of energy balance equations can
be frequently used as an alternative to the analysis of motion
equations. In most cases, even though the energy balance approach
results in a less exact description, it is much simpler to implement.
We believe that it applies to our case as well.
In our study the peak ground velocity (PGV) is estimated by the
PGVEM method estimates, whereas the peak ground acceleration
(PGA) is estimated by the DDA method. We compare our estimates
with those obtained using the DDA method. The case of toppled
columns in Susita town located in northern Israel and presumably
destroyed by a strong earthquake is examined. A row of columns
was thrown down in a common direction. The results of the DDA
analysis are taken from . The DDA approach estimates the PGA
as ranging from 0.2 to 0.5 g. Using the regression relation from
Table 1, these PGAs correspond to the intensity I¼7.5e8.5. In our
PGV approach, the minimal velocity required for the column
toppling is estimated as 60 cm/s. From Table 1 we infer that these
PGV values correspond to I¼8.5, very close to the estimate ob-
tained by using the DDA method.
Concerning the problem of city abandonment in the Negev
desert, two factors appear to be necessary to take into account.
First, without the state support during the inevitable drought years,
these cities could not keep ﬂourishing, and this support ceased
after the Arabic conquest. Second, a large earthquake at the
beginning of the seventh century severely damaged the infra-
structure of the cities and the agricultural rainwater collection
systems. Both factors necessitated the rapid population decline and
the city abandonment in the Negev desert.
A new and simple method for an approximate estimation of PGV
values based on the examination of the displacement magnitudes
of rock blocks is proposed. The effectiveness of the method is
demonstrated by results of the studies performed in the focal zones
of two large earthquakes and a vicinity of one strong explosion.
Concerning the role of large earthquakes in the abandonment of
previously prosperous Negev desert cities, it should be noted that
the shock from the large earthquake occurred almost simulta-
neously with the termination of the state support from Byzantium.
The combination of both factors probably brought an end to the
These results provide an additional support to the assumption
that large earthquakes with Mz6.5e7.5 can occur in the Negev
desert area, and also suggest that the region about one hundred
kilometers west to the Dead Sea rift zone is not seismically quiet.
Large earthquakes are possible to occur in the region once in a few
hundred to a few thousand years. We suggest that further studies
ought to be carried out to better address this issue.
The work was carried out at partial ﬁnancial support of ISTC
grant No. G-2153.
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Dr. Mikhail V. Rodkin, born September 11, 1954, Russia.
Chief Scientist of the Institute of Earthquake Prediction
Theory and Mathematical Geophysics Russian Ac. Sci.
Graduated from Physical Department, Moscow State Uni-
versity (1977). Ph.D. in Physics and Mathematics
(Geophysics), Institute of Physics of the Earth, Moscow
(1986). Dr. in Physics and Mathematics (Geophysics),
Institute of Physics of the Earth, Moscow (2003). Author of
9 monographs and more than 250 papers published.
Expert of the Russian Federation in Ecology and Physics,
and expert of the Russian Foundation for Basic Research in
seismology and oil geology. Member of editorial teams of
the Russian journals “Journal of Volcanology and Seis-
mology”,“Priroda”(Nature), “Earth and Universe“.
Engaged in natural hazards statistics, earthquakes regime
and seismic risk, physics of earthquake origin and earth-
quake prognosis, and in the deep ﬂuid regime in connec-
tion with processes of earthquake generation and
formation of hydrocarbon and ore deposits, algorithms of
Korzhenkov, Andrey M., Head of Laboratory, Schmidt's
Institute of Physics of the Earth, Russian Academy of Sci-
ences, the (co)author of more than 300 scientific publica-
tions. He has got his PH.D. majored in Geological and
Mineralogical Sciences, supervised by Prof. Dr. Habil. Oleg
K. Chediya, from Institute of Seismology, in 1988. He has
been awarded Alexander Von Humboldt Foundation
research fellowship from Potsdam University, Germany
during 2000e2002 and letter of commendation from
President of National Academy of Sciences of Kyrgyz Re-
public in 2007. His areas of expertise includes Arche-
oseismology, active tectonics, tectonic geomorphology;
Neotectonics, fault zone structure and geomorphology;
earthquake surface rupture and paleoseismology; fault
zone structure and paleoseismology in the Tian Shan,
Middle East and Caucasus mountains; active deformation
in central Asia; integrated investigation of earthquake
hazards; and Quaternary and Cenozoic Geology.
M.V. Rodkin, A.M. Korzhenkov / Geodesy and Geodynamics 10 (2019) 321e330330