![Short-term sequence of the earthquake occurred in the Gulf of Alaska, on 30 November 1987. Graphical procedure to determine the fluctuation range of mainshock magnitude value. that reports the seismic sequence in the earthquake occured in the Gulf of Alaska on 30 November 1987. As can be seen, the mainshock was preceded by a foreshock with a magnitude of 7.0 Mw recorded on l7 November 1987. To calculate the magnitude of the mainshock, the first step is to draw the branched structure [4] with its point of origin located in the foreshock and then locate on higher order seismic branch the point corresponding to 50% (point 3). From foreshock, we draw a horizontal dashed line up to meet the vertical line passing through the mainshock's occurrence time (point 2) and thereafter, we join the point 2 with the intermediate point of the seismic branch (point 3). Finally, from the foreshock we draw its parallel line (solid black lines). The intersection of this half line with the vertical line passing through the time selected for the calculation, provides the value of the minimum expected magnitude. To calculate the maximum value, we join the points 2 and 5 of the seismic branch, then from the intermediate point 3 we draw its parallel line (solid black lines). The intersection of this parallel with the vertical line passing through the time selected for the calculation, provides the value of the maximum expected magnitude.](https://www.researchgate.net/publication/314097313/figure/fig4/AS:668996563116043@1536512618808/Short-term-sequence-of-the-earthquake-occurred-in-the-Gulf-of-Alaska-on-30-November_Q320.jpg)
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Open Journal of Earthquake Research, 2017, 6, 55-71
http://www.scirp.org/journal/ojer
ISSN Online: 2169-9631
ISSN Print: 2169-9623
DOI: 10.4236/ojer.2017.61003 February 27, 2017
How to Identify Foreshocks in Seismic
Sequences to Predict Strong Earthquakes
Giulio Riga1, Paolo Balocchi2
1Geologist, Independent Researcher, Lamezia Terme, Italy
2Geologist, Independent Researcher, Modena, Italy
Abstract
The time analysis of seismic events preceding several strong earthquakes o
c-
curred in recent decades throughout the world, has highlighted some for
e-
shocks’ characteristics, which are
helpful for their discrimination compared to
other types of events. These features can be identified within the seismic s
e-
quence and used as strong events’
precursors. Through the energy release
pattern analysis, which precedes any strong earthquakes, in this study we d
e-
scribe some graphical procedures suitable for distinguishing a foreshock from
an
y other type of earthquake. We have broadly divided foreshocks into two
classes, depending on their position within the energy release pattern, by d
e-
scribing some relationships between the foreshock’s magnitude and the fo
l-
lowing earthquake’s. The results obtained show how the energy release pa
t-
tern of some major earthquakes has distinctive features and repeatability
which it is possible to obtain information from in order to perform sufficien
t-
ly reliable short-term forecasts.
Keywords
Foreshock, Mainshock, Aftershock, Earthquake, Microsequence, Hierarchization
1. Introduction
From the observation of several seismic sequences, we infer that some earth-
quakes are preceded by events of increasing magnitude related to the main
shock, which are called foreshocks [1].
Several studies conducted on seismic sequences show how the seismicity in-
creased significantly before the mainshock. For example, 10 days before the 2009
L’Aquila mainshock occurred, the foreshock sequence was concentrated in the
hanging-wall domain of the normal Paganica fault [2].
The foreshocks are one of the few well-documented precursors to large
How to cite this paper:
Riga, G. and Ba-
locchi
, P. (2017) How to Identify Fore-
shocks in Seismic Sequences to Predict
Strong Earthquakes
.
Open Journal of Earth
-
quake Research
,
6
, 55-71.
https://doi.org/10.4236/ojer.2017.61003
Received:
January 27, 2017
Accepted:
February 24, 2017
Published:
February 27, 2017
Copyright © 201
7 by authors and
Scientific
Research Publishing Inc.
This
work is licensed under the Creative
Commons Attribution International
License (CC BY
4.0).
http://creativecommons.org/licenses/by/4.0/
Open Access
G. Riga, P. Balocchi
56
earthquakes: Therefore, understanding their very nature is crucial for earth-
quake prediction and hazard mitigation. Several studies use foreshock sequences
with (combined with) a statistical and probabilistic approach [2] to predict
earthquakes (retrospectively) [3].
We believe that foreschock are the manifestation of an ongoing energy release
process, with different spatial and temporal scales, which leads to the mainshock.
During its manifestation time, the seismic sequence analysis may be an appro-
priate tool to highlight the various stages of preparing a strong event. Under this
approach we have noticed that an area seismicity before major earthquakes
shows a certain organization [2], according to a repetitive developmental pattern
of “Progressive Earthquakes”-type, [1] consisting of a succession of one or more
foreshocks of various order and one or more mainshocks.
The analysis performed suggests that the space-time occurrence of foreshocks,
ranges from a few hours up to years before the mainshock, and from a few kilo-
meters to thousands of kilometers from mainshock. It is in fact believed that fo-
reshocks may also occur in areas relatively far from the mainshocks and be part
of an external energy release process, which influences the area by triggering the
main event [4].
For a better understanding of foreshocks temporal organization during the
energy release phase, we propose some simple graphical and numeric procedures
that can be used for the preliminary forecast of a major event.
2. Foreshocks’ Characteristics
Foreshock sequences are the most obvious precursor to large earthquakes:
therefore, understanding their origin and relation to mainshocks is crucial for
earthquake prediction and hazard mitigation. Previous studies conducted on
immediate foreshocks in California suggest that these events may be part of a
mainshock rupture nucleation process, because estimated Coulomb stress
changes from foreshocks are too small to produce stress triggering and observed
foreshock areas scale with mainshock magnitude, are consistent with nucleation
instead of earthquake-to-earthquake triggering [2] [5] [6]
Foreshocks occur close to the mainshock and most likely are part of the nuc-
leation process [7]. They may be both physical and tectonic. Most short- and
impending-term foreshocks that occur close to major shocks are considered as
physical. In general, foreshocks occurring around the epicentral area can be con-
sidered as tectonic precursors, as they result from occasional plates’ shifting or
blocks shifting along the fault plane that will break [8]. They most frequently
occur in areas featuring moderately heterogeneous rocks [9] and in the presence
of a moderate pre-stress and rupture stress [10].
Foreshocks’ magnitude values and position during the energy realease phase
allow the implementation of useful models for predicting a strong earthquake.
However, it is necessary to know the features that distinguish them from other
earthquakes. Through the graphical analysis of the seismic sequence, it is possi-
ble to highlight the foreshocks’ characteristics and their grouping in various or-
G. Riga, P. Balocchi
57
ders, based on magnitude and period.
Defined as the “foreshocks’ height”, magnitude represents the distance, in
terms of energy, between a minimum and the subsequent maximum, while pe-
riod is the time or the number of shocks between a foreshock and the next.
Depending on the period or the number of shocks between a foreshock and
the next within the seismic sequence, it is possible to identify foreshocks of dif-
ferent magnitude orders. First order foreshocks characterize short-medium term
time windows, while those of second order usually occur immediately before the
mainshock and exactly in the same area where the mainshock occurs.
The time elapsing between the last second order foreshock and the mainshock
may vary but it typically consists of few days, while those of first order may
happen in different times and areas.
Based on foreshocks magnitude values and temporal position, which charac-
terize the energy release phase, we obtain the following “Progressive Earth-
quakes”-type developmental patterns [1]:
a) From one or more first order or short to medium-term foreshocks and
mainshock (Figure 1(a));
b) From one second order or impending-term foreshock and mainshock
(Figure 1(b));
c) From one or more first order or short to medium-term foreshocks, one
second order or impending-term foreshock and mainshock (Figure 1(c));
d) From one or more various orders foreshocks and from multiple mainshocks
(Figure 1(d)).
By observing the graphs shown in Figure 1, we understand how each earth-
quake is followed by a energy accumulation (red segment) and by an energy re-
Figure 1. Schematic representation of Progressive Earthquakes patterns [1]. The green
and red lines respectively show the energy release and accumulation phases. The green
star indicates the foreshock, the yellow star the aftershock, while the red star shows the
mainshock.
Foreshocks
Mainshock
Foreshock
Mainshock
Foreshocks
Mainshock
1st Order
Foreshocks
Mainshocks
(a) (b)
(c) (d)
Aftershocks Aftershocks
Aftershocks Aftershocks
2nd Order
2nd Order
1st Order 1st Order 2nd Order
G. Riga, P. Balocchi
58
lease phase (green segment) triggered by small magnitude shocks. Major events,
complementing the “Progressive Earthquakes” pattern, in turn trigger a long-
term energy accumulation phase that consists of two or more energetic after-
shocks.
Figure 2 and Figure 3 show the magnitude values trend and different order
foreshocks position in relation to the monthly long-term seismic sequence’s
mainshock in Japan and to the short-term one preceding the earthquake oc-
curred in L’Aquila on 6 April 2009.
By observing the graph of the Japanese seismic sequence we can notice two
“Progressive Earthquakes”-type patterns consisting of two first-order foreshocks
and one mainshock, in which the temporal distance between the second fore-
shock and the mainshock is greater compared to that between the first and the
second foreshock, while the magnitude values decrease.
In the graph showing the seismic sequence of L’Aquila, we see that the energy
release pattern consists of three first order foreshocks, two second order fore-
shocks and one mainshock. The three first-order foreshocks show an “addi-
tive/constant” model (green line) in which the foreshocks’ magnitude values
show a proportionality relationships as the number of seismic events increases,
while the second order foreshocks and the mainshock, show a multiplica-
tive/amplified model (red line) where the magnitude values between the fore-
shocks and mainshock amplify as the number of seismic events raises. This am-
plified effect is due to the short-term occurrence between foreshocks and the
mainshock, which usually lasts just a few days.
Figure 4(a) and Figure 4(b) show the relationship between the foreshock
magnitude and the number of days elapsed since the mainshock, processed using
earthquakes in the “Progressive Earthquakes”-type energy release pattern con-
Figure 2. Earthquake in Japan on 3 March 2011. Green stars show mid-term foreshocks
(first order) while red stars indicate the mainshocks. The vertical axis shows the magni-
tude values, while the horizontal axis displays the progressive number of months record-
ed in the period analyzed.
0100 200 300 400 500
Progressive number of months
2
4
6
8
10
Magnitude
9.0 Mw
8.3 Mw
7.8 Mw
7.8 Ms
7.7 Ms
6.7 M
25/09/2003
11/03/2011
08/05/1974
12/06/197826/05/198328/12/1994
6.8 Mw
24/03/2001
Data Range: 01/01/73 to 11/03/11
Latitude: 42N - 30N
Longitude: 145E - 130E
Depth Range: 1-50 km
Magnitude Range: 2.5-10.0
Catalog used: PDE-USGS
"Progressive earthquakes"- type
"Progressive earthquakes"- type
G. Riga, P. Balocchi
59
Figure 3. Earthquake in L’Aquila on 6 April 2009. Green stars show short-term fore-
shocks (first order), green squares indicate impending-term foreshocks (second order),
while red show the mainshock. The vertical axis shows the magnitude values, while the ho-
rizontal axis displays the progressive number of events recorded in the period analyzed.
Figure 4. Relationship between foreshock magnitude (y-axis) and the number of days
elapsed between foreshock and mainshock (x-axis): (a) related to the whole world; (b) re-
lated to Italy.
cerning 128 earthquakes occurred in various areas of the world and in Italy.
Figure 5(a) shows the relationship between the distance between the fore-
shock epicenter and the mainshock’s and the number of days elapsed between
foreshock and mainshock, while Figure 5(b) shows the relationship between the
foreshock magnitude and the distance between the foreshock and mainshock
epicenters.
The graphs and Table 1 display the following significant trends related to fo-
reshocks frequency rate and characteristics:
1) Many earthquakes occur less than thirty days after the last foreshock, but quite
020 40 60 80 100
10 30 50 70 90
Progressive number of events
2
3
4
5
6
Magnitude
4.1 ML
3.6 ML
22/02/2009
17/03/2009
3.2 ML
30/03/2009
06/04/2009
5.9 ML
05/05/2009
3.9 ML
30/03/2009
3.0 ML
Data Range: 17/02/09 to 06/04/09
Latitude: 41.5N - 43.3N
Longitude: 12.5E - 14.2E
Depth Range: 1-50 km
Magnitude Range: 2.0-10.0
Catalog used: ISIDE-INGV
"Progressive earthquakes"- type
0400 800 1200 1600
Number of days
3
4
5
6
3.5
4.5
5.5
Magnitude
01000 2000 3000
Number of days
3
4
5
6
7
8
Magnitude
N = 128 N = 15
a)b)
G. Riga, P. Balocchi
60
a number of foreshocks occurs twenty-four hours before the mainshock;
2) The frequency rate of foreshocks occurring within a radius of 50 km and over
thirty days, decreases as distance and time increase;
3) Closer events in time and space, show higher magnitude;
4) Magnitude values decrease as distance and number of days increase.
The results obtained show that in some seismic sequences, the “Progressive
Earthquakes”-type energy release phase tend to develop near the epicenter of the
main shock.
Figure 5. (a) Relationship between the number of days elapsed between foreshock and
mainshock (x-axis) and the distance between the foreshock and mainshock epicenters
(y-axis); (b) the relationship between the distance between the foreshock and mainshock
epicenters (x-axis) and the magnitude of the foreshock (y-axis).
Table 1. Correlations between foreshocks and earthquakes.
No Earthquake
Foreshock Mainshock Time
(days)
Distance
(km)
Date M Date M
1 Colfiorito - Italy 26/09/1997 5.6 ML 26/09/1997 5.8 ML 1 1.24
2 L’Aquila - Italy 05/04/2009 3.9 Mw 06/04/2009 6.1 Mw 1 1.90
3 Emilia - Italy 19/05/2012 4.0 Mw 20/05/2012 5.8 Mw 1 2.14
4 Central Italy 26/10/2016 5.9 Mw 30/10/2016 6.5 Mw 4 8.70
5 Vanuatu 09/07/1980 6.9 Mw 17/07/1980 8.0 Mw 8 20.8
6 Vanuatu 28/11/1985 7.2 Ms 28/11/1985 7.6 Ms 1 8.53
7 Vanuatu 16/11/1985 6.8 Ms 21/12/1985 7.6 Ms 5 31.2
8 Afghanistan 05/03/1990 6.0 Ms 25/03/1990 6.3 Ms 10 15.1
9 Japan 09/03/2011 7.3 Mw 11/03/2011 9.0 Mw 2 44.3
10 Japan 18/07/1992 5.8 Mw 18/07/1992 6.9 Mw 1 6.96
11 Nicaragua 10/08/1992 5.7 Mw 02/09/1992 7.7 Mw 23 3.95
12 Gulf of Alaska 17/11/1987 7.0 ML 30/11/1987 7.9 Mw 13 29.5
13 Filippine 17/05/1992 7.1 Mw 17/05/1992 7.3 Mw 1 13.1
14 Colombia 17/10/1992 6.7 Ms 18/10/1992 7.3 Ms 1 26.3
15 Denali-Alaska 23/10/2002 6.7 Mw 03/11/2002 7.9 Mw 11 23.3
16 Grecia 01/02/2014 5.0 Mb 03/02/2014 6.1 Mw 2 14.0
01000 2000 3000
Number of days
0
200
400
600
800
1000
Distance (km)
N = 128
0200 400 600 800 1000
Distance (km)
3
4
5
6
7
8
Magnitude
N = 128
(a) (b)
G. Riga, P. Balocchi
61
3. Foreshocks-Identifying Method
3.1. Use of Trendlines
Today it is believed that a foreshock is physically indistinguishable from any
other earthquake, until a subsequent mainshock classifies it as such [11] [12]
[13].
The methodology proposed to identify foreshocks is based on identifying the
dynamic trendline that characterize the development of the energy accumulation
and release phases [1].
As we can infer from Figure 6, to highlight the energy accumulation and re-
lease phases multiple points of relative maximum both in the case of increasing
(points 1, 2, 3) and decreasing (points 4, 5, 6) magnitude values, have been
joined with a straight line.
As their numerical value varies over time, these straight lines are called dy-
namic trendlines. Trendlines clearly show the direction the magnitude values are
moving in both in the impending and long-term and until the trend remains
unchanged.
A seismic events’s trend is considered unchanged as long as there are no clear
signs of reversal, such as the trendline break. In fact, the crossing of the energy
accumulation trendline (transition point) marks the beginning of an energy re-
lease phase that can be of “Flash earthquakes-” or “Progressive Earstquakes-”
type [1]. The first is characterised by one or more mainshocks, the second by an
initial foreshock followed by a first magnitude values’ fall, which means that the
magnitudo values are returning close or under the energy accumulation phase’s
trendline. Subsequently, the magnitude values begin to raise again up to form a
second foreshock from which it is possible to obtain the direction of the energy
release phase’s trendline.
Besides showing the ongoing trend, it seems that the trendlines momentarily
prevent the magnitude values from raising and, in some cases, they allow know-
ing in advance certain levels of magnitude that will be achieved in the future. In
fact, the Figure 6 shows also how the knowledge of the magnitude levels
achieved in points 1 and 2 allows calculating in advance the magnitude value of
point 3 in the energy accumulation phase or of point 6 in the energy release
phase after points 4 and 5 have formed.
The trendline drawn from points 6 (first order foreshock) and 7 (aftershock)
allows identifying the second order foreshocks 8 and 9.
An earthquake in the “Progressive Earthquakes”-type energy release pattern
cannot be identified as foreshock or mainshock until a subsequent energetic af-
tershock is formed. In the absence of an energetic aftershock, the foreshock or
mainshock is identified as provisional.
Figure 7 reports the seismic sequence of the Denali earthquake (Alaska) oc-
curred on 3 November 2002.
The earthquake was preceded by three first order foreshocks (green stars) and
by a second order foreshock (green square). As can be seen, the trendline drawn
from points 1 and 2 shows a hypothetical medium—long term trend and allows
G. Riga, P. Balocchi
62
estimating point 3’s magnitude (next minimum), while the intersection of the
straight line passing through points 3 and 4 with the vertical line passing
through the mainshock occurence point (point 5), provides the dynamic main-
shock’s magnitude value. Alternatively, where the seismic sequence includes
multiple first order foreshocks, the dynamic mainshock’s magnitude value is
provided by the linear interpolation between them (dashed green line).
Figure 6. Short-term sequence of L’Aquila earthquake on 6 April 2009 (red star). The
yellow stars indicate the strongest aftershocks in the energy accumulation phase, the
green stars indicate the first order foreshocks, while the green square shows the second
order foreshocks. The solid black circle indicates in the transition point from the energy
accumulation to energy release phase.
Figure 7. Long-term sequence of Denali earthquake (Alaska) on 3 November 2002 (red
star). The yellow stars indicate the strongest aftershocks in the energy accumulation
phase, the green stars indicate the first order foreshocks, while the green square shows the
second order foreshocks. The solid black circle indicates in the transition point from
energy accumulation to energy release phase.
0 100 200 300
Progressive number of events
2
3
4
5
6
7
Magnitude
Transition point
Energy accumulation trend line
Release of energy trend line
1
234
5
6
10
78
9
0400 800 1200
200 600 1000 1400
Progressive number of events
2
4
6
8
Magnitude
7.9 Mw
6.2 Mw
5.5 Mw
5.2 Mw
5
07/01/90
30/12/81
06/10/85
03/11/02
23/10/02
1
2
4
Transition point
6.7 Mw
Energy accumulation trend line
Release of energy trend line
Release of energy trend line
Data Range: 01/22/73 to 04/11/02
Latitude: 66N - 62N
Longitude: 141W - 150W
Depth Range: 1-50 km
Magnitude Range: 2.0-10.0
Catalog used: PDE-USGS
3
G. Riga, P. Balocchi
63
3.2. Seismic Sequence Hierarchization
The use of a hierarchization process in the seismic sequence analysis, allows lo-
cating foreshocks and mainshock during the energy release phase. More accurate
data on the foreshocks formation can be obtained from the seismic grid of the
energy accumulation and release phases (Figure 8) representing the cyclic pat-
tern of reference that includes cycles of different duration.
Obtained through the hierarchization process, the graph [4], highlights how
during the energy release phase, only the energy release seismic branches of dif-
ferent order (1r, 2r, 3r, 4r) convey to the foreshocks (nodes F1, F2, F3) or main-
shock (node M), while in the energy accumulation phase, both the energy accu-
mulation (3a) and release (2r, 1r) seismic branches convey to the aftershock
(nodes A1, A2, A3) of a previous event,
The extension of the first higher order seismic branch of the branched struc-
ture (branch 3a) up to the point of calculation allows identifying the transition
point (full black circle) and the various orders foreshocks of the energy release
phase. We can note how the various orders foreshocks and the mainshock are
positioned above the dashed red line that represents the descending trendline
drawn from the higher order seismic branch.
In some seismic sequences, it is apparent how a longer period after the last
first order foreshock corresponds to a greater magnitude of the subsequent fo-
reshock or mainshock.
3.3. Index Simplified Force (ISF)
ISF is an simple and very sensitive short-term oscillator, which can be used to
monitor the strength and the developmental state of a seismic sequence and to
detect the foreshocks as well as the energy accumulation phase’s trend.
ISF uses two types of seismic data: the magnitude values and the number of
events recorded during the day. The greater is the variation of the magnitude
Figure 8. Seismic sequence of the L’Aquila earthquake on 6 April 2009.
0100 200 300
Progressive number of events
2
3
4
5
6
Magnitude
6.1 Mw
Trend line
F1
F2
F3
F4
F5
4r 3r
1r
1r
1r
1r
2r
2r
06/04/09
A1
A2 A3
M
3a
3a
2r
2r 1r 1r
2r
2r
3r
2a
2a
2a
G. Riga, P. Balocchi
64
values and/or of the number of events, the greater the strength of the sequence.
Therefore, whenever you have a daily increase of the magnitude value due to the
occurrence of a foreshock or mainshock or a number of seismic events or of
both, a peak is formed on the graph, followed by a gradual reduction in the am-
plitude of the ISF oscillation over time.
Due to the effect of the values fluctuations above the zero line, ISF has the ap-
pearance of a seismogram where, values above zero indicate the energy release
phases, while negative values indicate the energy accumulation phases. ISF’s
high values are associated with an increase in the number of earthquakes and/or
high magnitude values. Positive and increasing index values show an energy re-
lease phase that is being strengthened, while positive and decreasing values show
an energy accumulation phase. Values close to zero show that none of the two
phases is ongoing and both anticipate a trend reversal.
Figure 9 shows an example of a seismic sequence structured for ISF calcula-
tion. The graph is built taking into account the following conditions:
a) If the magnitude value increases compared with the previous day, it means
that an energy release phase is ongoing (green segment) ;
b) If the value decreases, it means that there is an energy accumulation phase
ongoing (red segment);
c) If the value is equal, we have the same phase as the day before.
From the graph we can infer how, as the events progress, the magnitude val-
ues are not random but follow a trend according to increasing trends up to the
process reversal. We can notice also growing trend phases, characterized by in-
creasing maximum and minimum, and decreasing trend phases characterized by
decreasing maximum and minimum.
Figure 9. Seismic sequence structured for IFS calculation.
0 20 40 60
Progressive number of days
2
3
4
5
6
7
Magnitude
Red : magnitude falling
Green: magnitude rising
G. Riga, P. Balocchi
65
The analysis of many seismic sequences revealed the existence of three main
types of trends that can be identified in advance: (a) the main trend (lasting a
few years); (b) the intermediate trend (lasting several months); (c) the minor
trend (lasting a few weeks). It is therefore evident that there is not only one type
of trend but different trends (one inside another) according to the observation
time horizon.
To calculate the ISF, we simply identify the value of the daily maximum mag-
nitude and multiply it by the number of daily shocks, attributing a positive or
negative value depending on whether the value of the maximum magnitude of
the day considered is greater (green segment) or smaller compared to that of the
previous day (red segment). In the case where the maximum magnitude value of
the day considered is equal to the previous day’s, the previous day ISF sign is at-
tached to ISF.
max events
ISF M N=±⋅
(1)
Figure 10 and Figure 11 show the ISF obtained from seismic sequences re-
lated to central Italy in 2016 and Japan in 2011.
The ISF graph related to central Italy (Figure 10) from 16 to 23 August 2016
shows low values, then a first peak due to the occurrence on 24 August (green
star) of the first order foreshock whose magnitude was 6.0 Mw.
Later, after a brief energy accumulation phase highlighted by a progressive
decrease of ISF values, we observe a second peak in correspondence of the
second order foreshock (green star) on 26 October whose magnitude was 5.9
Mw. The positive peak is followed by a negative minimum which corresponds to
the triggering point of the energy release phase (red triangle) that ends on 30
October with the mainshock whose magnitude is 6.5 Mw, which is indicated on
the graph by a positive ISF peak. The epicenter of the second order foreshock on
Figure 10. Seismic sequence force index in central Italy (2016).
0 40 80 120 16020 60 100 140
Progressive number of days
-1000
0
1000
2000
-500
500
1500
Index simplified force
6.0 Mw
24/08/16
5.9 Mw
26/10/16
6.5 Mw
30/10/16
Foreshock Mainshock
CENTRAL ITALY EARTHQUAKE
1st Order
2nd Order
Data Range: 24/08/16 to 05/01/17
Latitude: 42.4N - 43.2N
Longitude: 12.9E - 13.6E
Depth Range: 1-50 km
Magnitude Range: 2.0-10.0
Catalog used: ISIDe-INGV
Trigger point
Tp
G. Riga, P. Balocchi
66
Table 2. Succession of earthquakes in the “Progressive Earthquakes”-type pattern (Cen-
tral Italy earthquake) between 24 August and 30 October 2016.
No Earthquake
Date
Magnitude Identification Order Time
(days)
Distance
(km)
1 24/08/2016 6.0 MW Foreshock 1st Order - -
2 26/10/2016 5.9 Mw Foreshock 2st Order 64 24.98
3 30/10/2016 6.5 Mw Mainshock -- 4 8.70
Table 3. Succession of earthquakes in “Progressive Earthquakes”-type pattern (Central
Italy earthquake) between 16 and 30 October 2016.
No Earthquake
Date
Magnitude Identification Order Time
(days)
Distance
(km)
1 16/10/2016 4.0 Mw Foreshock 1st Order - -
2 26/10/2016 5.4 Mw Foreshock 1st Order 10 15.2
3 26/10/2016 5.9 Mw Foreshock 1st Order <1 3.23
1 29/10/2016 4.1 Mw Foreshock 2st Order 3 11.24
2 30/10/2016 6.5 Mw Mainshock -- 1 8.70
0100 200 300 400 500
Progressive number of events
2
3
4
5
6
7
Magnitude
Foreshock
Mainshock Aftershock Warning signs
SEISMIC SEQUENCE
CENTRAL ITALY EARTHQUAKE
Date Range: 19/09/16 to 30/10/16
Latitude : 43.4 - 42.4N
Longitude : 13.6 - 12.7E
Depth Range: 1-50 km
Magnitude Range:2.5-10.0
Catalog used : ISIDE(INGV)
6.5 Mw
30/10/16
5.9 Mw
26/10/16
4.0 Mw
16/10/16
5.4 Mw
26/10/16
4.1 Mw
29/10/16
Figure 11. Seismic sequence and succession of earthquakes in “Progressive Earth-
quakes”-type pattern (Central Italy earthquake) between 16 and 30 October 2016.
26 October was located approximately 8.70 km from the main shock epicenter. The
energy accumulation phase that is triggered after the mainshock is represented by a
progressive and slow decrease in the oscillations amplitude of the ISF values.
Table 2 displays the short-term “Progressive Earthquakes”-type earthquakes
in the energy release phase in central Italy, the occurrence time and the distance
between them, while Table 3 and Figure 11 shows the impending-term pattern
of the strongest earthquakes recorded in Central Italy between 16 and 30 Octo-
G. Riga, P. Balocchi
67
Figure 12. Seismic sequence force indicator of Japan earthquakes in 2011.
Table 4. Succession “Progressive Earthquakes”-type pattern earthquakes (Japan earth-
quake).
No Earthquake
Date
Magnitude Identification Order Time
(days)
Distance
(km)
1 09/03/2011 7.3 MW Foreshock 1st Order - -
2 11/03/2011 9.0 Mw Mainshock --- 2 44.3
ber 2016, the occurrence time and the distance between them.
Figure 12 shows the ISF seismic sequence in Japan during the time window
from 2 January to 31 December 2011. Up to 8 March 2011, the graph shows an
initial portion of cyclical fluctuations of small amplitude, followed, on 9 March,
by a first peak due to the occurrence of the foreshock with a magnitude of 7.3
Mw (green star) associated with an increase in the number of recorded events
and shortly afterwards by a further ISF increase due to main shock with a mag-
nitude of 9.0 Mw (red star) occurred on the same day. A third peak of greater
amplitude is formed following the aftershock occurrence on 13 March whose
magnitude was 6.6 Mw (yellow star) associated with a strong increase in the
number of daily events recorded. After the 13 March earthquake, the ISF index
value decrease over time and, at the end of December, they reach values similar
to pre-foreshock’s on 9 March 2011.
Table 4 reports the “Progressive Earthquakes”-type pattern earthquakes in the
energy release phase of the Japan earthquake.
3.4. Mainshock Magnitude Calculation
3.4.1. Graphical Method
A quick method for estimating the mainshock magnitude is shown in Figure 13
0 100 200 300 400
Progressive number of days
-800
-400
0
400
800
Index simplified force
9.0 Mw
11/03/11
Data Range: 02/01/11 to 31/12/11
Latitude: 42N - 30N
Longitude: 145E - 130E
Depth Range: 1-50 km
Magnitude Range: 2.5-10.0
Catalog used: NIED
Foreshock Mainshock
7.3 Mw
09/03/11
Aftershock
6.6 Mw
13/03/11
Tp
Trigger point
G. Riga, P. Balocchi
68
Figure 13. Short-term sequence of the earthquake occurred in the Gulf of Alaska, on 30
November 1987. Graphical procedure to determine the fluctuation range of mainshock
magnitude value.
that reports the seismic sequence in the earthquake occured in the Gulf of Alaska
on 30 November 1987.
As can be seen, the mainshock was preceded by a foreshock with a magnitude
of 7.0 Mw recorded on l7 November 1987. To calculate the magnitude of the
mainshock, the first step is to draw the branched structure [4] with its point of
origin located in the foreshock and then locate on higher order seismic branch
the point corresponding to 50% (point 3). From foreshock, we draw a horizontal
dashed line up to meet the vertical line passing through the mainshock’s occur-
rence time (point 2) and thereafter, we join the point 2 with the intermediate
point of the seismic branch (point 3). Finally, from the foreshock we draw its
parallel line (solid black lines). The intersection of this half line with the vertical
line passing through the time selected for the calculation, provides the value of
the minimum expected magnitude. To calculate the maximum value, we join the
points 2 and 5 of the seismic branch, then from the intermediate point 3 we
draw its parallel line (solid black lines). The intersection of this parallel with the
vertical line passing through the time selected for the calculation, provides the
value of the maximum expected magnitude.
3.4.2. Numerical Methods
The empirical relations developed can be used to assess the magnitude of various
order foreshock or “Progressive Earthquakes”-type pattern mainshock by know-
ing the magnitude of the previous foreshock.
The relationships were obtained from the study of M > 3.8 foreshocks rec-
orded by the Italian seismological network NIED network and by the USGS
network between 1970 and 2016.
The average Mainshock Magnitude (MM) value is estimated through the fol-
lowing empirical relationship, obtained from the graphs displayed in Figure 14:
0 100 200 300
Progressive number of events
2
4
6
8
Magnitude
7.0 Mw 7.9 Mw
12
3
4
5
6
F
17/11/87 30/11/87
Data Range: 09/12/84 to 30/11/87
Latitude: 64N - 54N
Longitude: 133W - 153W
Depth Range: 1-50 km
Magnitude Range: 2.0-10.0
Catalog used: PDE-USGS
G. Riga, P. Balocchi
69
Figure 14. Relationship between foreshocks and mainshock: (a) valid for all areas of the
world; (b) valid for Italy.
Relationship valid for all areas of the world with a foreshock magnitude (MF)
in Mw:
1.048 0.695
MF
M = M+
(2)
Relationship valid for the Italian territory with a foreshock magnitude (MF) in
Mw.
1.147 0.610
MF
M = M+
(3)
In the second procedure, the expected earthquake magnitude value is obtained
with a formula empirically derived from a statistical analysis of the magnitude
values of first and second order foreshocks that preceded the mainshocks in dif-
ferent areas of the world.
The equation to calculate the magnitude is as follows:
Relationship valid for all areas of the world with a foreshock magnitude (MF)
in Mw:
( )
3.407 ln 1.318
MF
M= M+⋅
(4)
4. Conclusions
The study of various order foreshocks the “Progressive Earthquake”-type energy
release phase consists of, has provided a different methods of comparison be-
tween foreshocks and big earthquakes, leading to a better understanding of the
phases regulating the preparation process of strong earthquakes.
The results obtained show that in some seismic sequences, the “Progressive
Earthquake”-type energy release phase tends to develop near the main shock ep-
icenter.
In particular, the analysis of the distances in time and space between fore-
shocks and mainshock has highlighted how some foreshocks occur shortly be-
fore the mainshock, within a radius of 50 kilometers from its epicenter. We also
pointed out how the foreshocks frequency rate decreases as the distance from the
mainshock epicenter and time increase, while the magnitude values decrease as
4683 5 7
Magnitude of foreshock (Mw)
4
6
8
10
3
5
7
9
Magnitude of foreshock or mainshock (Mw)
M
M
= 1.048M
F
+ 0.695
N=156
a)
r2=0.828
34567
Magnitude of foreshock (Mw)
4
6
8
3
5
7
9
Magnitude of foreshock or mainshock (Mw)
M
M
= 1.147M
F
+ 0.610
N=32
b)
r
2
=0.849
G. Riga, P. Balocchi
70
the distance and the number of days increase.
The graphical analysis of the seismic sequence has shown how the foreshocks
lie above the trendline that joins decreasing magnitude maximum values that
form during the energy accumulation or above the seismic branch extension
whose order is greater compared to the branched structure.
An in-depth examination of the branched structure showed how during the
energy release phase only the branches seismic energy release of different order
convey to foreshocks or mainshock, while in the energy accumulation phase the
seismic branches of both energy accumulation and release phases convey to af-
tershock.
ISF (Index Simplified Force) can be used to obtain information about the
strength of the seismic sequence in a given moment, to locate the foreshocks and
to monitor the energy accumulation and release phase progress.
Based on the data resulting from the observations of several seismic se-
quences, we obtained some graphical and numeric procedures to determine the
mainshock’s magnitude value using the trendline, the branched structure’s
higher order seismic branch or the foreshock magnitude value.
We believe that the described method shows the foreshock identification limit
during seismic sequences. Actually, as is not always possible to identify the event
that precedes a strong earthquake, one prefers to classify it as provisional fore-
shock. The subsequent evolution of the seismic sequence will provide more in-
formation so that an appropriate foreshocks classification can be implemented.
The aforementioned procedures show how, starting from the analysis of the
“Progressive Earthquakes”-type energy release phase, it is possible to obtain in-
formation to locate the foreshocks and make sufficiently reliable short-term
forecasts. Seismic sequence’s evolution monitoring is essential to identify cor-
rectly the foreshock that precedes strong events.
References
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M
w 6.3) of 6
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