






CONTENTS 


4.3.1. 
Introduction. 
4.3.2. 
Theoretical model
analysis. 
4.3.3. 
Statistical validation
test of the methodology. 
4.3.4. 
Explanation of the
achieved accuracy. 
4.3.5. 
Examples
of the application of the methodology on real EQs. 
4.3.5.a. 
Skyros, Greece, 26th
July 2001, Ms = 6.1 R. 
4.3.5.b. 
Northridge EQ,
California, USA, 17/1/1994, M = 6.7 R. 
4.3.5.c. 
Parkfield EQ,
California, USA, 28/9/2004, Mw = 6.0 R. 
4.3.6. 
The “BIG ONE”
earthquake, expected, in California. 
4.3.6.1. 
Los Angeles area. 
4.3.6.2. 
Southern California
area. 
4.3.6.3. 
San Francisco area. 
4.3.6.4. 
Northern California
area. 
4.3.7. 
Some different
seismological applications of the “Lithospheric Seismic Energy Flow
Model (LSEFM)”. 
4.3.7.1. 
Accelerated seismic
energy release and deformation. 


Zakynthos EQ example. 


Seismogenic area (A) example. 
4.3.7.2. 
The “Seismic potential
map”. Its application example in Greece. 

A. The data. 

B. Application of the
method – examples. 

C.
Discussion – Conclusions. 





4.3. Magnitude
determination.
4.3.1. Introduction.
There is a limited number of studies, which refer to the magnitude,
in the Earthquake Prediction literature. The past seismic history
(statistically treated) plus the dimensions of the studied, tectonic
features of a seismogenic area provided some vague clues for the
probable magnitude of the imminent strong EQ.
A physical model that will account for the determination of the
prediction parameters of a strong EQ, is missing, in a way, from the
seismological community.
The starting point of this topic is that different earthquake
prediction parameters, most probably, require a different physical
model which will be applied for its determination. Moreover, these
physical models should not contradict but comply with each other.
For the case of magnitude determination the “Lithospheric Seismic
Energy Flow Model”, which is introduced in section (2.5.1), is used.
This model is based on the balance of the absorbed and released
energy, in the lirhospheric seismogenic area, where an earthquake
will occur in the future.
The rate of seismic energy release, as a function of an inverse
power of the time, remaining to the main, seismic event, has been
proposed and applied to backanalyses of several foreshock main
sequences by Varnes (1987a, b).
In these papers, Varnes analyses the accelerating, precursory
seismic activity in terms of seismic moment release. A simple, in
time (t), empirical power law failure function was postulated (Bufe
and Varnes, 1993) that related the parameters of the remaining time
(tct) to the occurrence of the imminent, strong EQ and its
corresponding magnitude (M) to the seismic moment release (the term
accumulated Benioff strain is often used). Main (1995) studied the
earthquakes from the point of view of a critical phenomenon.
In the same area of Statistical Physics (Main, 1996), Bowman et al.
(1998) showed that the cumulative, seismic strain release increases,
as a power law time to failure, before the final event. Papazachos
et al. (2000) used the same methodology to study the Benioff strain
rate release of the Aegean area. Moreover, an estimate for the
timing of an imminent strong EQ was achieved with an accuracy of +/
1.5 years, by using the same methodology for EQs of the Aegean area
(Papazachos et al. 2001). The time to failure model was used, as a
technique, in which a failure function is fitted to a time series of
accumulated Benioff strain, by Di Giovambattista and Tyupkin (2001),
in order to analyze the relation of the timetofailure model to the
hypothesis of fractal structure of seismicity. This method was
applied on laboratory rock samples fracturing and real strong EQs of
Kamchatka and Italy, as well.
In the early papers, that deal with the “Benioff strain 
accelerated deformation – critical point” method, the studied seismogenic area was related to a circle of an optimum radius R and,
lately, to an elliptical area (Papazachos et al. 2001).
The common feature, of all these papers, is the absence of a
physical model that accounts for the wellknown time to failure
equation which is used very often. This equation is an empirical one
and derives from the Statistical Physics, applied to other fields of
applied science. Moreover, no tectonic information is taken into
account, as far as it concerns the under study seismogenic area.
In this section, two main, new features are presented, for the
understanding of the methodology. The first one is a postulated
physical model that justifies the accelerated energy release method,
while the second one is the deep lithospheric fracture zones (Thanassoulas,
1998) where strong EQs are generated and constrain the extent of the seismogenic area to be studied.
4.3.2. Theoretical model analysis.
It is well known that the stress, built up, in a focal area, is a
very slow process which follows closely the motion of the lithospheric plates. It takes a long period of time (many years) to
reach the point when an earthquake will occur because of the rock
fracturing.
In normal conditions, the stored energy is discharged through the
normal (background) small magnitude seismicity of the area. When a
strong earthquake is in preparation, this normal seismicity is
decreased, for a certain time period, and therefore, the detected
seismic “quiescence” was used as a precursory indicator.
The latter is presented in the following figure (4.3.2.1). The
cumulative number of seismic events, plotted, against time, deviates
from the form of a linear function and resumes its normal one after
the occurrence of the expected EQ.
Fig. 4.3.2.1. Example of a seismic quiescence
precursor.
Although this methodology gave successful results, with the way it
treated the seismological data, it does not answer the question of
the magnitude, neither the time of occurrence and it still remains
in the domain of statistical methods. On the other hand, in terms of
Physics, the same phenomenon can be studied from the energy transfer
and balance point of view of the regional seismogenic area.
An open, physical system, that constantly absorbs energy, remains
in a dynamic equilibrium when the inflow energy is equal to
outflow energy, otherwise that physical system, should “explode”,
at a certain moment, releasing the excessive, stored energy, in a
short time.
In the case of seismicity, the open physical system, in question,
is the regional area of the lithosphere where the EQ will occur.
Practically, the lithosphere is at a state of critical dynamic
equilibrium, or it is teetering on the edge of instability, with no
critical length scale (Bak, Tang and Wiesenfeld 1988; Bak 1996) as
far as it concerns inflow and outflow of strain energy. The
following figure (4.3.2.2) shows the postulated “energy  flow
model” in such a condition.
Fig. 4.3.2.2. Energy – flow model of the
lithosphere and cumulative energy outflow (Ec), as a
function of time.
Theoretically, following this working physical model, the
cumulative energy release in a seismogenic area, during a normal,
seismic period, should be a linear function (equation 2.5.1.8) of
time, due to energy conservation law of Physics. This is
demonstrated in the lower right part of the figure (4.3.2.2).
The cumulative energy (Ec) release function vs. time (t), for a
specific, seismogenic area, can be determined by converting the
magnitude of each, recorded, EQ in the past, into energy, using any
suitable formula that exists in the seismological literature. In the
present work was used the following empirical formula (Tselentis,
1997):
LogE = 11.8 + 1.5Ms
(4.3.2.1)
Where:
E is the energy, calculated, in ergs.
Ms is the magnitude of each EQ, in Richter scale.
By applying this procedure to all EQs that occurred during the
period of study, the cumulative energy Ec can be calculated and
therefore, the graph Ec = f(t) can be constructed.
As an example for the results, expected, over a seismogenic but of
normal energy release period, the following figure (4.3.2.3) is
presented. In a 20 years period of time that preceded the
1997/11/18, Ms 6.6R EQ in Greece, two distinct, normal energy
release periods can be identified. The first one spans from 1 to 43,
while the second spans from 67 to 205, in time scale (months). In
these two periods the cumulative energy outflow, due to normal
seismicity, is that of the form of a linear function in time.
Fig. 4.3.2.3. Cumulative energy outflow graph vs.
time, for the seismogenic area of the EQ, on 18/11/1997
(Ms=6.6R) in Greece. Time period: 1977 – 1997.
Although this is the normal condition of the lithosphere, due to
certain, mostly frictional, mechanical reasons, the seismogenic
area, at a specific time, “locks”. At this state the normal
seismicity decreases and therefore the energy outflow decreases. As
an immediate result, the inflow energy is stored in the seismogenic
area. This stored excessive energy will be released in the future as
an EQ of corresponding magnitude, at the time, when the seismogenic
area “unlocks” during rock rupture. This is demonstrated in the
following figure (4.3.2.4).
Fig. 4.3.2.4. Theoretical cumulative energy
outflow “lock” model.
In figure (4.3.2.4), the two black arrows indicate the start and
the end of the “lock period”. At the end of the “lock period”, the
imminent EQ takes place. Its magnitude is calculated by the two
energy levels E1, 2 using formula (4.3.2.1). After the expected EQ
has occurred, the seismogenic region resumes its normal energy
release rate, based on seismicity of small EQs.
A more general case is the one, in which the seismogenic area is
always in critical strain conditions (mechanically locked) and
earthquakes occur randomly in time, due to mainly frictional,
mechanical reasons. This is demonstrated in the following figure
(4.3.2.4a).
Fig. 4.3.2.4a. Stepwise cumulative, seismic
energy release sketch presentation. The dashed line
indicates the corresponding, normal, cumulative energy
outflow under stable conditions. Stepwise, solid black
line represents the “always locked” mode of the
lithosphere cumulative energy outflow.
In such cases, the normal cumulative energy release time function
is defined by the cumulative energy levels which were achieved at
the time the earthquakes occurred. Therefore, this function is
represented by the straight line (in least squares sense) that is
defined by the cumulative energy steps.
What is important, in this physical model, is the fact that,
theoretically, during the lock period, the stored energy should
equal the energy that could be released, due to the corresponding
total EQs that didn’t take place during the quiescence time period
(energy conservation law of Physics).
The practical outcome of this is that, it is possible to calculate
the magnitude of the imminent EQ by knowing:
a. The normal energy release rate of a seismogenic
area.
This is calculated from the past seismic history of the seismogenic
area.
b. The time of start of the lock period.
This is determined from the graph Ec = f(t), where (Ec) is the
cumulative energy of the seismogenic region, released, during the
past period. This time is characterized by sudden decrease of the
gradient (dEc/dt) of the Ec = f(t).
c. The time of occurrence of the imminent EQ.
The latter can be estimated, by other methods, very accurately (see
section 4.1 and Thanassoulas et al., 2001)
It is obvious, from the graph Ec(t), that the longest the lock
period is, the largest the magnitude of the EQ will be.
The application of this methodology has some prerequisites in order to be
fulfilled.
The first one is a long, in time, seismic data history. This is
required so that the normal outflow energy rate, of the specific
regional area, can be estimated, as correctly as it can be.
From this graph can be determined the start of the lock period, too.
The second prerequisite is the knowledge of the “end” of the “lock
period”. This is, generally, achieved by other methods (Thanassoulas
et al. 2001) and presented in section (4.1). The monitoring of the
change of various, other, physical parameters can signify the end of
the “lock” period by the presence of their anomalous values. In this
case, it is assumed that it was identified within an accuracy of +/
1 month. Therefore, during the period of study, the Ec (cumulative
energy) is determined at 1 month’s sample time intervals.
The postulated methodology was applied, retrospectively, on a
specific strong EQ in Greece, as an example. This EQ, having a
magnitude of Ms = 6.6R, occurred in Greece on 1997/11/18, Lat. =
37.260, Lon. = 20.490.
In the following figure (4.3.2.5) is presented the cumulative
energy (Ec) which was calculated for a spatial window 1.60x1.60
centered at the epicentral area and for the period from 1964 to
1997.
Fig. 4.3.2.5. Demonstration of a real case
“locked” period. Sudden steps indicate the time of
occurrence of EQs (abrupt energy release, Ecx1E18=ergs).
The (Ec) was calculated for a total period of 34 years, before its
occurrence, with sampling interval of one month. Two major (Ec)
increase steps, plus some smaller ones, characterize the graph. The
step, located, on the right end of the graph, is the one that
corresponds to the seismic event, its magnitude is to be,
retrospectively, predicted. Major steps indicate large amounts of
energy release (strong EQs), while smaller steps indicate the
occurrence of seismic events of minor importance.
Consequently, taking into account short periods of time, for the
seismic data history of the area under study, only small magnitude
EQs can be estimated. On the other hand, taking into account long
periods of time, it is possible to identify long, corresponding
“lock” periods and therefore, large magnitudes can be calculated. In
the present case, the rate of cumulative energy release was
calculated by using the (Ec) levels, immediately, after the two
strong events (67, 151 time axis of graph). The two cumulative
energy levels, just after these two major, seismic events (1969,
1976), indicate the expected Ec(t) value under continuous normal
seismic energy release (Fig. 4.3.2.6).
Fig. 4.3.2.6. Normal, outflow energy
(Ecx1E18=ergs) release rate (solid line) determination
for the period 1964 1997.
The previous graph shows that prior to each strong EQ, a long
“lock” period preceded it. The last “lock” period started on time
151, although seismic events, of minor importance, had occurred on
229 and 367 times. The latter, released some energy, but not enough,
to modify drastically the last identified “lock” period. In other
words, the seismogenic area was only partially, discharged. It can
be said that, the area under study was “locked” finally on time 151
(1976) and from that time on, it accumulated energy which was
released through the 1997 strong EQ.
In the following figure (4.3.2.7) is demonstrated the determination
of the magnitude.
Fig. 4.3.2.7. Calculation, of the expected
magnitude, assuming that the origin time of the imminent
EQ is known. (E1) and (E2) lines indicate the initial
and final cumulative energy levels. The solid line
indicates the assumed cumulative energy outflowrate,
in time, function.
The E2 level is determined from the intersection of a vertical line
on the predicted time of the expected EQ and the normal outflow
energy release rate function.
Following this procedure, the calculated magnitude for the EQ on
1997/11/18 (Ms = 6.6R) was determined as Ms = 6.5R
The magnitude Ms which is calculated by this methodology deviates
for only .1 R from what was determined (Ms = 6.6R) by the Geodynamic
Institute of Athens.
EQ: 18th, Nov. 1997 GEIN of Athens determination : Ms = 6.6R
Energyflow model application :
Ms = 6.5R
The same procedure was applied, retrospectively, for the
determination of the studied by Mizoue et al. (1978) magnitude of
EQs on Kii Peninsula, Central Japan. In this work the cumulative
earthquake energy release of the under study area is presented in
the following figure (4.3.2.7a).
Fig. 4.3.2.7a. Cumulative energy earthquake
energy release graph (after Mizoue et al. 1978). Energy
levels E1, E2 resulted in a Mc=4.77, while E3, E4
resulted in a Mc=4.34 for the corresponding EQs. The
dashed and solid lines represent the corresponding
energy release rates for both cases.
The dashed line indicates the energy flow rate for the EQ on Aug.
07, 1977, M=4.7R, while the solid line indicates the energy flow
rate for the EQ on Jan 16, 1977, M=4.3. The short, solid horizontal
lines (E1, 2, 3, 4) indicate the minimum and maximum, cumulative
energy levels which are taken into account for the calculation of
the corresponding magnitude. In the case of the EQ on Jan 16, 1977,
M=4.3R, the corresponding magnitude from fig. (4.3.2.7a), is
calculated as M=4.34R, while for the EQ on Aug. 07, 1977, M=4.7, is
M=4.77R.
In both cases, the error in the magnitude calculation is less than
0.1R, too.
4.3.3. Statistical validation test of the
methodology.
A statistical test was applied to a larger data set (1972  2001
for EQs of Ms>=6.4R) so that the validity of the method could be
verified. The data set was obtained by downloading the data file of
Greek seismicity, for the period of time from 1964 to 2001,
available online, by the Geodynamic Institute of Athens (URL
address in references).
In this analysis were adopted the following parameters for the
application of the postulated method:
a. Time span: The data file of the Geodynamic Institute
of Athens extends (on line) back to 1964. Consequently, the seismic
data were processed up to 1972 so that a minimum of 8 years past,
seismic history would be available for the determination of the
normal, cumulative energy outflow rate for the subsequent strong
seismic events to be studied.
b. Spatial window: It was selected as a 1.60x1.60
window, over the epicentral area to be studied, so that should be
taken into account only the narrow, epicentral area, seismic
history.
c. Magnitude threshold: This was selected as 6.4R so
that only significantly large seismic events would be studied.
In the following Table 1 the 18 EQs, which were studied, are
listed, ranking in magnitude scale. The first column indicates the
year, month, day, hour, and the minute (yyyymmddhhmm format) when
each event took place. The second column indicates the corresponding
Latitude, the third column indicates the corresponding Longitude and
the last one indicates its Magnitude in Ms (Ms=ML+.5).
TABLE  1
Date – time 
Lat. 
Lon. 
Ms 
197904150619 
42.00 
19.00 
7.3 
198308061543 
40.08 
24.81 
7.1 
198201181927 
39.90 
24.50 
6.9 
198102242053 
38.14 
23.00 
6.8 
198112191410 
39.20 
25.30 
6.8 
198301171241 
37.97 
20.25 
6.7 
197205042140 
35.30 
23.60 
6.6 
199505130847 
40.18 
21.71 
6.6 
199607200000 
36.11 
27.52 
6.6 
199711181307 
37.26 
20.49 
6.6 
197806202003 
40.80 
23.30 
6.5 
198007090211 
39.20 
22.90 
6.5 
198112271739 
38.90 
24.90 
6.5 
197709112319 
35.00 
23.10 
6.4 
198102250235 
38.20 
23.00 
6.4 
198307051201 
40.27 
27.13 
6.4 
198406211043 
35.36 
23.31 
6.4 
199409011612 
41.15 
21.26 
6.4 
For
each one of these EQs, the corresponding magnitude was determined,
following the postulated methodology. The results are presented in
the following table (2).
TABLE  2
Observed Determined
Date–time 
Magnitude 
Magnitude 
dM 
197904150619 
7.3 
7.25 
 0.05 

198308061543 
7.1 
7.06 
 0.04 

198201181927 
6.9 
 
 
198102242053 
6.8 
6.71 
+0.09 
198112191410 
6.8 
 
 
198301171241 
6.7 
6.73 
+0.03 
197205042140 
6.6 
6.40 
 0.20 

199505130847 
6.6 
6.15 
 0.45 

199607200000 
6.6 
6.51 
 0.09 

199711181307 
6.6 
6.59 
 0.01 

197806202003 
6.5 
6.35 
 0.15 

198007090211 
6.5 
6.51 
+0.01 
198112271739 
6.5 
6.49 
 0.01 

197709112319 
6.4 
6.30 
 0.10 

198102250235 
6.4 
6.34 
 0.06 

198307051201 
6.4 
6.31 
 0.09 

198406211043 
6.4 
6.56 
+0.16 
199409011612 
6.4 
6.29 
 0.11 

From a total of 18 strong EQs, for the 16 of them, it was possible
to calculate the expected magnitude with a very high accuracy. This
corresponds to an 89% success rate in magnitude calculation. For two
of them the methodology failed. In the discussion, an explanation on
this will be given. Further statistical processing of the dM values
results in:
dM Mean = .067R
and
dM S.Dev = 0.13R
For the 11 out of the 16 EQs, for which the magnitude determination
was possible, the dM value is less than 0.1R, corresponding to a
73.33%. One only extreme value of –0.45 was calculated and the rest
4 of them were calculated with a dM value, ranging between 0.1R and
0.2R.
4.3.4. Explanation of the achieved accuracy.
The accuracy, in the calculation of the magnitude for a pending,
future earthquake, is surprisingly large. Whenever this methodology
was discussed with seismologists, it was difficult for them to
accept such a small deviation from the magnitudes, calculated, by
traditional, statistical, seismological methods. It must be pointed
out, too, that the predicted, seismological magnitudes deviate at
least +/ 0.5 R from the real ones.
Let us assume that a seismological group calculates magnitudes of
seismic events. The calculated magnitudes are affected by the error
tendency of the group, due to various causes. The introduced errors
on the magnitude calculations are represented by a “white noise”,
superimposed, on the real magnitude values, since it is a random
process.
This process is presented in the following figure (4.3.4.1).
Fig. 4.3.4.1. The dependence of introduced
errors (black dots), by a seismological group, in the
calculation of the real magnitude value (solid
horizontal line) of a seismic event is presented in
sketchdrawing.
The real magnitude value, of each calculated seismic event, will
correspond with the one indicated by the determined, straight line,
in a least square sense, through all the individual calculations
made by the same, seismological group.
If these “noisy” seismic magnitudes are used to calculate the
cumulative, seismic energy release, then the following graph of
figure (4.3.4.2) results. The black part of the graph corresponds to
the past seismic events. In the case a future seismic event takes
place, the stored, cumulative, seismic energy that will be released
and which corresponds to that time of the seismic event, will be
located in the extrapolated (red) part of the past (black) graph.
This is presented in the following figure (4.3.4.2).
Fig. 4.3.4.2. Sketch presentation of the
cumulative energy that corresponds to the past (black)
and future (red), seismic events.
Consequently, in case of a future earthquake (red dot) of which the
time of occurrence is already known by other means, the stored,
cumulative energy that corresponds to its time of occurrence, can be
found by extrapolating the cumulative energy black graph of figure
(4.3.4.2), in time. Therefore, working backwards for the calculation
of its magnitude, inevitably, its magnitude will deviate at most, as
indicates the “white noise”, which was introduced by the
seismological group which made the calculations. Even better, the
deviation will be less, since it will be located on the real value
magnitude graph which is calculated in the least squares sense. The
latter is presented in the following figure (4.3.4.3).
Fig. 4.3.4.3. Correlation of the magnitude of a
future, seismic event (red dot) in relation to
magnitudes (black dots), calculated, by seismological
methods and the errors involved in this seismological
procedure.
In conclusion, the achievement of better accuracies (in the
majority less than +/ 0.1 R) in predicted magnitudes, compared with
the calculated ones (+/ 0.5 R at best) by statistical seismological
methods, should not be considered as a surprising fact.
Actually, what can be said in simple words, about this technique is
that, past seismicity constructs the cumulative energy graph in a
leastsquare sense and this very same graph is exactly used to
calculate, backwards, the exact magnitude of the future, seismic
event.
4.3.5. Examples of the application of the methodology
on real EQs.
The “Lithospheric Seismic Energy Flow Model” methodology was tested
“a posteriori” against known past strong earthquakes, whose seismic
parameters of location, time of occurrence and seismological
magnitude are already known. The following earthquakes were selected
as typical examples:
a. Skyros, Greece, 26/7/2001, Ms = 6.1 R.
b. Northridge EQ, California, USA, 17/1/1994, M = 6.7
R.
c. Parkfield EQ, California, USA, 28/9/2004, Mw = 6.0
R.
The last two examples were chosen to make it clear that, the
methodology is undependable on place and seismology research group,
provided that a regular, earthquake catalog is available, concerning
the past seismicity of the under study area.
4.3.5.a. Skyros, Greece, 26th July 2001, Ms = 6.1 R.
The postulated methodology was applied to Skyros EQ. A few days
before the occurrence of Skyros EQ, electrical precursory signals
were recorded by the (VOL) monitoring site.
The location of Skyros azimuthal direction resulted as the source of
their origin after detailed processing of these signals (Thanassoulas
et al. 2001). Moreover, suddenly the seismic activity increased on
Skyros regional area (EQ on 21st July, Ms = 5.1R took place),
indicating thus, in an indirect way, the regional area that was
activated seismically and consequently generated the emitted and
recorded, electrical signals.
Starting with this hint, the postulated methodology was applied to
a window of 1.60x1.60, centered, on the epicentral area of the 5.1R
EQ on 21st July, in an attempt to predict the magnitude of the
expected EQ. The timing of Skyros EQ was calculated by other
methodology (Thanassoulas et al. 2001a, b). Therefore, it was a
simple task to detect the presence of any seismic “lock” state of
the regional seismogenic area of Skyros, by studying the past
seismicity of this area, and if any, to calculate the magnitude of
the oncoming EQ. The period considered for the past seismic history
of the area spans from 1988 to July 22nd, 2001.
At a first approach, a magnitude of M = 6.1R was calculated. This
value was based on the last “lock” period, detected, in the regional
area of Skyros. The calculated magnitude equals Ms = 6.1R and fits
the value, provided, by the Greek Seismological Observatory in
Patras. This is shown in the following figure (4.3.5.a.1).
Fig. 4.3.5.a.1. Magnitude determination is shown, for
the last lock period.
The normal energy outflow rate at Skyros area, is indicated by the
slope of the trend (solid line) that starts just after the first
seismic event on the left side of the graph. In the next figure
(4.3.5.a.2) is considered a longer “lock” period. The calculated
magnitude equals Ms = 6.3R and fits the value provided by the Greek
Seismic Observatory in Thessaloniki.
Fig. 4.3.5.a.2. Magnitude determination, when a
longer lock period is considered.
Nevertheless, no matter what the actual, real magnitude of this EQ
is, both solutions presented herein, are in very good agreement to
the magnitude, calculated, by most seismological observatories.
4.3.5.b. Northridge EQ, California, USA, 17/1/1994, M
= 6.7 R
The validity of the LSEFM methodology was tested, on the strong EQ
of Northridge 17th January 1994 (M=6.7R, lat = 34.21, long =
118.54), too. In the following figure (4.3.5.b.1) the epicentral
area of Northridge EQ is presented by a blue circle.
Fig. 4.3.5.b.1. Location map of Northridge EQ
(blue circle) and the Los Angeles city (map after USGS).
Following the methodology of the "LSEFM", the cumulative, seismic
energy release graph was constructed for the period 1932 to 2004.
The sampling interval is (1) month. That is each Y value of this
graph represents the total, seismic energy, released, over a month.
The cumulative, seismic energy release was studied over a
rectangular area around Los Angeles and is indicated by the
coordinates:
Upper left: 34.75/119.25 Upper right: 34.75/117.25,
Lower left: 33.25/119.25 Lower right: 33.25/117.25.
The calculated, cumulative energy release graph is presented in
figure (4.3.5.b.2).
Fig. 4.3.5.b.2. Cumulative, seismic energy
release, for the period 1932  2004, calculated, for the
regional area of Northridge EQ.
The abrupt steps of the graph indicate the occurrence of strong EQs
(in the past), in the studied frame.
From left to right the following three EQs are shown:
a. 1933, March 11th, Lat. = 33.64 Long. = 117.97
Magnitude = 6.4R
b. 1970, February 9th, Lat. = 34.42 Long. = 118.37
Magnitude = 6.6R
c. 1994, January 17th, Lat. = 34.21 Long. = 118.54
Magnitude = 6.7R
What is obvious, from the previous figure (4.3.5.b.2), is the fact
that the regional area of Northridge  Los Angeles remains in a
"locked" state, for very long periods, acquiring seismic energy,
through any suitable, physical, seismological mechanism, no matter
what it is.
The accumulated, seismic energy is released, mainly, through strong
EQs. Energy release through smallsize seismicity does not modify,
significantly, the appearance of the graph. The LSEFM method
indicates indirectly, the "normal, cumulative energy release
timefunction", under unlocked conditions. Therefore, the next to
come strong EQ magnitude can be calculated by taking into account
the seismic history of the area under study. This is presented in
the following figure (4.3.5.b.3).
Fig. 4.3.5.b.3. Calculation of magnitude of
Northridge EQ is shown, by using the "LSEFM"
methodology.
The seismological methods determined a magnitude for the EQ in
Northridge of M = 6.7 R. The lithospheric, seismic energy flow
model, which was applied to the regional area of Los Angeles,
calculated its magnitude as M = 6.45 R. The normal, seismic energy
flow rate is indicated by the two peaks of energy release,
generated, from the two earlier, strong seismic events (1933, 1970).
The difference in magnitude, between the two methods, is only dM =
.29 R, not too bad at all. It must be pointed out, too, that the
epicentral area and the timing of the EQ in Northridge, which were
used in this test, were known in advance (a posteriori study).
4.3.5.c. Parkfield EQ, California, USA, 28th
September 2004, Mw = 6.0 R.
The LSEFM method was applied to the regional area of Parkfield, in
an attempt to calculate the magnitude of the earthquake on September
28th, 2004, Mw=6.0R. The details are as follows:
The adopted, seismogenic area is the one presented in the following
figure (4.3.5.c.1).
Fig. 4.3.5.c.1. Location – geological map of the
earthquake in Parkfield (red circle) and used seismic,
energy release frame location map (map after USGS).
The coordinates of the used frame are:
Upper left: 36.6 / 121.1 Upper right: 36.6 / 119.5
Lower left: 35.0 / 121.1 Lower right: 35.0 / 119.5
The calculated cumulative seismic energy release graph vs. time is
shown in the following figure (4.3.5.c.2).
Fig. 4.3.5.c.2. Calculated cumulative seismic
energy release is shown, for the period 1957  2004, for
Parkfield area.
The calculated magnitude of Parkfield earthquake is Ms=5.94R (fig.
4.3.5.c.3), compared with the Mw=6.0R, calculated, by seismological
methods.
Fig. 4.3.5.c.3. Calculation of the magnitude of
the strong EQ, in Parkfield area, that occurred on
September 28th, 2004.
4.3.6. The BIG ONE earthquake, expected, in
California.
Several seismological studies and related observations indicate the
probability of a strong EQ to strike, in future, in the area in
Southern / Northern California. It is speculated, too, that a
magnitude of 8 R could be possible (therefore, it is called as THE
BIG ONE), but it is still unknown, when this event will take place.
It must be pointed out that, an 8R earthquake is almost 33 times
larger, in terms of released energy, than a 7R EQ and 1000 times
larger than a 6R EQ. Therefore, the graph of the seismic, cumulative
energy to be released, before the occurrence of the BIG ONE, must
present a corresponding, high value of change, in the energy flow
rate, before its occurrence.
The possibility of the BIG ONE is investigated, using the LSEFM
method, for both Los Angeles / San Francisco regional areas and
Southern / Northern California, as well.
4.3.6.1. Los Angeles area.
As a working hypothesis, it is assumed, in this case, that the
present seismological energy flow rate status, of the regional area
of Los Angeles, will not change up to year 3000. As a spatial frame,
for the calculation of the cumulative energy flow was used the one
in figure (4.3.5.b.1).
The cumulative energy outflow graph was projected up to the year
3000 and the expected magnitude of the future strong EQ was
calculated for specific years of occurrence. The results are
presented in the following TABLE – 1
TABLE – 1
Y E A R MAGNITUDE
(in Richter)
2010 
6.69 
2020 
6.82 
2030 
6.92 
2040 
6.99 
2050 
7.05 
2100 
7.23 
2200 
7.42 
2300 
7.53 
2400 
7.61 
2500 
7.68 
2600 
7.73 
2700 
7.77 
2800 
7.81 
2900 
7.84 
3000 
7.88 
The year, when the calculation of the magnitude is made, is
indicated in the first column, while in the second one is presented
the calculated magnitude. Assuming that, during this period of time
(almost 1000 years), no significant EQs will occur, which could
release a large amount of seismic energy, then the calculated
magnitudes are correct, according to the methodology that is
followed. The seismological observations, of the previous history of
the under study area, indicate that the latter is rather impossible,
since a repetition period of 3040 years is quite common for the
strong EQs of the above area. Therefore, the calculated magnitudes
have to be less than what was calculated for this period of time. In
such a case, the magnitude of 8 R for the regional area of Los
Angeles is rather unrealistic, even within the next 1000 years.
4.3.6.2. Southern California area.
As a working hypothesis, it is assumed, that the entire Southern
California is the seismogenic area under study. The following
coordinates define the area under consideration:
Upper left: 36.00 / 121.00 Upper right: 36.00 / 114.5
Lower left: 32.75 / 121.00 Lower right: 32.75 / 114.5
and is presented in the following figure (4.3.6.2.1).
Fig. 4.3.6.2.1. Spatial window used, for the study
of the Southern California (map after USGS).
The calculated cumulative energy outflow for this spatial window,
is presented in the following figure (4.3.6.2.2).
Fig. 4.3.6.2.2. Cumulative, seismic energy
release, for the period 1932  2010, calculated, for the
area of Southern California.
The calculated magnitudes for the next 1000 years are presented in
the following TABLE  2.
TABLE – 2
Y E A R MAGNITUDE
(in Richter)
2004 
7.09 
2010 
7.23 
2020 
7.38 
2030 
7.43 
2040 
7.52 
2050 
7.61 
2100 
7.75 
2200 
7.94 
2300 
8.05 
2400 
8.14 
2500 
8.19 
2600 
8.25 
2700 
8.30 
2800 
8.33 
2900 
8.37 
3000 
8.39 
The higher values, observed, (for almost 0.5R), of Table  2
compared with Table – 1, are attributed to the seismicity of the
area, outside the regional area of Los Angeles. In any case,
significant, larger values (M>8R) of magnitude above the one of the
"BIG ONE" are valid, under the present, constant, seismic
conditions, almost after 300 years. In case that normal, strong EQs
(M=67R) occur during this period of time, then the magnitudes of
Table  2 will be slightly decreased and therefore, the time span
for initiating an 8R EQ will increase, accordingly.
4.3.6.3. San Francisco area.
In a similar way, the expected values, for a hypothetical future
strong EQ, for San Francisco frame area and for each specific time
of occurrence up to year 3000, were calculated and are presented in
TABLE  3.
TABLE – 3
Y E A R
MAGNITUDE
(in Richter)
2010 
6.44 
2020 
6.56 
2030 
6.63 
2040 
6.67 
2050 
6.71 
2100 
6.88 
2200 
7.06 
2300 
7.17 
2400 
7.25 
2500 
7.31 
2600 
7.36 
2700 
7.41 
2800 
7.45 
2900 
7.48 
3000 
7.51 
The maximum, expected magnitude for a future, strong EQ is M =
7.51R, theoretically in year 3000.
This result is due to the fact that there is not any large, seismic
energy, stored, in the frame of San Francisco area. This is
indicated, too, by the study of its cumulative seismic energy
release in the past, by using the available file that concerns the
seismicity of the area.
4.3.6.4. Northern California area.
Finally, the possibility for the "BIG ONE" is investigated for the
regional area of Northern California. The used seismic energy
release frame is presented in the following figure (4.3.6.4.1).
Fig. 4.3.6.4.1. Spatial window (seismic energy
release frame) used for the study of the Northern
California (map after USGS).
The corresponding, cumulative, seismic energy release graph is
presented in the following figure (4.3.6.4.2).
Fig. 4.3.6.4.2. Cumulative, seismic energy
release, for the period 1910  2010, calculated for the
Northern California Area.
Following the same methodology, were calculated, and are presented
in TABLE – 4, the expected magnitude values, for a hypothetical,
future strong EQ, for the Northern California frame area and for
each specific time of occurrence, up to year 3000.
TABLE – 4
Y E A R MAGNITUDE
(in Richter)
2004 
7.71 
2010 
7.73 
2020 
7.79 
2030 
7.83 
2040 
7.88 
2050 
7.91 
2100 
8.04 
2200 
8.20 
2300 
8.30 
2400 
8.38 
2500 
8.43 
2600 
8.48 
2700 
8.53 
2800 
8.56 
2900 
8.60 
3000 
8.63 
Theoretically, for an EQ of 8R magnitude, the required seismic
energy could be accumulated around year 2100. The calculated larger
magnitude values are due to the large extent of the frame area
(Northern California) and therefore, larger seismic energy release
is totally observed vs. time all over the area under study.
In short, the following concluding remarks can be made:
a. From Table  1, it is suggested that a 7.5R EQ could
hit the regional area of Los Angeles in a period of time not earlier
than 300 years, provided that the seismic status does not change at
all. This period can be extended more, because of the seismic
events, which will probably occur within the next 300 years, of
intermediate (67R) magnitude, which will release part of the
seismic energy which is stored in the regional area.
b. From Table  2, it is suggested that a 7.5R EQ could
hit the area of Southern California in a period of time not earlier
than 40 years. This period could be extended more for the same
reasons as for (a).
c. From Table  1, THE BIG ONE takes almost 1000 years
for the accumulation of the required, seismic energy (M = 8R), for
the case of the regional area of Los Angeles. This period of time
could be prolonged more because of the reasons, presented, in
paragraph (a).
d. From Table  2, THE BIG ONE takes almost 300 years
for the accumulation of the required seismic energy (M = 8R) for the
case of the area of Southern California. This period of time could
be prolonged more for the reasons, presented, in paragraph (a).
e. From Table  3. Within the time span up to year 3000
AC, the maximum, expected, EQ magnitude is M = 7.51R for the case of
the area of San Francisco.
f. From Table  4. THE BIG ONE takes almost 100 years
for the accumulation of the required seismic energy (M = 8R) for the
case of the area of Northern California. This period of time could
be prolonged more because of the reasons presented in paragraph (a).
The following two questions are of great interest:
Which is the most probable area, in Southern / Northern California,
to be hit in the future by a strong EQ?
This question can be answered by the construction of the seismic,
potential map (see following presentation) of Southern / Northern
California. This map will present the seismic energy accumulation
spatial distribution. Its maximum values indicate the most dangerous
areas to be hit in the future.
When will a strong EQ (or the BIG ONE) hit?
Strong EQs are preceded very often by precursory, electrical
signals which are generated at the focal area and depend, quite
well, on the tidal waves of the lithosphere. These signals are kind
of shortterm warning that an EQ is initiated and the focal area is
at a state just before collapsing. Therefore, these signals not only
signify the shortterm time window which is needed for the future
strong EQ prediction, but they provide the means for its epicentral
area determination, too.
Finally, what is necessary, for the utilization of an effective
monitoring of an oncoming strong EQ, is the installation of a
network for monitoring the EQ generated, precursory, electrical,
signals, all over the area of Southern / Northern California. An
example of such a network, the installation of which is still in
progress, over Greece, is presented later on.
4.3.7. Some different seismological applications of
the “Lithospheric Seismic Energy Flow Model  LSEFM”.
The LSEFM model, not only provides a solution for the prediction of
the magnitude of a future, strong EQ, but even more, it presents a
physical justification for the “accelerating, seismic energy release
 deformation” and “seismic quiescence”, which is frequently
observed before many strong EQs.
Moreover, starting from this model, it is possible to calculate
maps of the seismic energy which is stored in large seismogenic
areas (seismic potential maps). Therefore, it is possible to use
them as a tool for the intermediate term characterization of seismic
prone areas. An example of such, generated, maps, is presented for
the Greek territory.
Both applications are presented as follows:
4.3.7.1. Accelerated, seismic energy release and
deformation.
The rate of seismic energy release, as a function of an inverse
power of the time remaining to the main seismic event, was proposed
and applied to backanalyses of several foreshock main sequences by
Varnes (1987a, b).
In these papers, Varnes analyses the accelerating precursory,
seismic activity, in terms of seismic moment release. A simple in
time (t), empirical power law failure function was postulated (Bufe
and Varnes, 1993) that relates the parameters of the remaining time
(tct) to the occurrence of the imminent strong EQ and its
corresponding magnitude (M) to the seismic moment release (the term,
accumulated Benioff strain, is often used). Main (1995) studies the
earthquakes from the point of view of a critical phenomenon.
In the same area of Statistical Physics (Main, 1996), Bowman et al.
(1998) showed that the cumulative, seismic strain release increases
as a power law time to failure before the final event. Papazachos et
al. (2000) used the same methodology to study the Benioff strain
rate release of the Aegean area. Moreover an estimate for the timing
of an imminent strong EQ was achieved, with an accuracy of +/ 1.5
years, by using the same methodology for EQs of the Aegean area (Papazachos
et al. 2001). The time to failure model was used as a technique, in
which a failure function fits on a time series of accumulated
Benioff strain, by Di Giovambattista and Tyupkin (2001) in order to
analyse the relation of the timetofailure model to the hypothesis
of fractal structure of seismicity. This method was applied to in
laboratory rock samples fracturing and real strong EQs of Kamchatka
and Italy, as well.
In the early papers, which deal with the “Benioff strain 
accelerated deformation – critical point” method, the seismogenic,
studied area was related to a circle of an optimum radius R and,
lately, to an elliptical area (Papazachos et al. 2001).
The common feature, of all these papers, is the absence of a
physical model that accounts for the time to failure wellknown
equation which is used very often. This equation is an empirical
one, and derives from the Statistical Physics applied to other
fields of Applied Science. Moreover, no tectonic information is
taken into account, as far as it concerns the seismogenic under
study area.
The topic of accelerating deformation is faced from another point
of view and it is analyzed by the use of the “Lithospheric, Seismic
Energy Flow Model” which was presented in section (2.5.1.1).
In this analysis is introduced an important new feature, that, of
the deep, lithospheric, fracture zones (Thanassoulas, 1998). These
zones are the main, seismogenic zones where strong EQs occur and
constrain the extent of the seismogenic areas to be studied.
If we recall the theoretical analysis which was already presented
and summarizing the forms the equation Ecum(t) takes (that
represents the energy flow) the following cases are possible:
a. linear polynomial  constant energy flow
b. higher order polynomial  real acceleration
c. accelerated for a time period, long before the main
seismic event, which is followed by a constant energy flow period,
just before the occurrence of the large EQ.
Cases (b) and (c) are represented very often by the wellknown
“time to failure” function.
Although, mathematically, it is possible to transform any polynomial
to any arbitrary function, i.e. time to failure function, by
calculating the appropriate parameters of the latter, by using LSQ
techniques, still remains the parameter of arbitrarity, as far as it
concerns the validity of physics behind this transformation.
Moreover, the time to failure function depends on two variables.
The first one is the magnitude of the imminent EQ and the second one
is the time to failure left. In order to overcome the problem of
solving a two parametric equation (infinite number of solutions),
the parameter C (Bowman et al. 1998) was introduced, that is the
ratio of power low fit error over the linear fit error, as far as it
concerns the cumulative seismic energy release. Still the notion of
this ratio is totally arbitrarily, set.
Therefore, it is suggested that the magnitude and time to failure,
of a strong imminent EQ, calculated by these methodologies, are not
supported by any validated physical mechanism and should be
rejected.
The validity of the LSEFM model application on seismic accelerating
deformation and energy release phenomena is demonstrated by the
following two examples. The first one refers to Zakynthos, Greece
2002, Ms = 5.8R EQ and the second one refers to an area (called A)
that is in accelerating mode but the EQ has not taken place yet up
to 2004.
The data, which are used in this analysis, are taken from the EQ
files released online at the web site of the National Observatory
of Athens (NOA), Greece (www.gein.noa.gr).
The released cumulative energy was calculated by transforming all
the EQs, of the area under study, into the corresponding energy
release, for each seismic event, regardless of their magnitude.
Zakynthos EQ example.
The postulated methodology was applied over the regional area of
Zakynthos, indicated by a red circle in figure (4.3.7.1.1). In this
area, was observed large accelerated seismic energy release during
the second half of 2002. This ended in a strong (M=5.8R) seismic
event on 3rd December 2002.
Fig. 4.3.7.1.1. Zakynthos regional (red circle),
seismic area is presented.
By taking into account the deep lithospheric fracture zones (Thanassoulas,
1998) that control the seismicity of the regional area, a
trapezoidal area (fig. 4.3.7.1.2), which surrounds the main tectonic
features of Zakynthos area, was selected. It is assumed that, the
energy release, in this area, is due to seismic activity that occurs
in these lithospheric, fracture zones.
Fig. 4.3.7.1.2. The blue frame indicates the area
whose seismic energy release is studied. The brown line
indicates the main lithospheric, deep fracture seismic
zone.
The released energy (fig. 4.3.7.1.3) was calculated for the period
between 2000 and end of November 2002. The sampling interval, which
was used, is 10 days. That is each 10 days the released energy was
summed up to form a data point of the cumulative energy graph. It is
worth to note that the accelerating process was identified well,
before the Zakynthos seismic event.
Fig. 4.3.7.1.3. Accelerated, cumulative, seismic
energy release that corresponds to the period 2000 –
2002, for the regional (frame) area of Zakynthos. Sample
interval = 10 days, is presented.
The data presented, in the previous graph (fig. 4.3.7.1.3) were
fitted with a 6th degree polynomial. This is demonstrated in the
following figure (4.3.7.1.4).
Fig. 4.3.7.1.4. Calculated cumulative energy
release data for the area of Zakynthos (brown line)
fitted with a 6th degree polynomial (blue line). The red
arrow indicates when the strong, EQ occurred.
A different point of view of the accelerating energy release is
through the study of its timegradient. This is demonstrated in the
following figure (4.3.7.1.5).
Fig. 4.3.7.1.5. Time gradient (year 2000 – 2002)
of the cumulative energy release of the area of
Zakynthos is presented.
In figure (4.3.7.1.5), the timegradient was calculated,
analytically, after having obtained the polynomial function of
cumulative energy release, presented in figure (4.3.7.1.6).
Fig. 4.3.7.1.6. The analytical presentation of the
polynomial function that represents the cumulative
energy release of the area of Zakynthos for the period
from 2000 to the end of 2002 is shown.
Finally, in figure (4.3.7.1.7), is shown, the location of the area
of Zakynthos EQ in relation to the deep, lithospheric, seismic
fracture zones.
Fig. 4.3.7.1.7. Location of the area of Zakynthos
EQ, Ms = 5.8R, 3/12/2002
The close coincidence of the EQ epicentral location with the
adjacent, deep, lithospheric fracture zone justifies the presence of
the latter, as this was demonstrated by Thanassoulas (1998).
It was stated, earlier, that a decelerating seismic energy release
period of time preceded the last phase of the preparation of a
strong EQ. This last phase of decreased, seismic energy release is
what the seismologists call as a “seismic quiescence”. An example of
such an energy release (accelerating deformation followed by a
seismic quiescence) sequential case was presented by Varnes (1989).
In the following figure (4.3.7.1.8), the accelerating seismic energy
release period of time is more than evident, while at the end of the
graph, the “seismic quiescence” period that preceded Cremasta,
Greece EQ is clearly shown.
Fig. 4.3.7.1.8. The “accelerating, seismic energy
release” and “seismic quiescence”, observed, at Cremasta,
Greece EQ, are shown (after Varnes, 1989).
Seismogenic area (A) example.
Another example for the very same mechanism, which is still in
progress, at a seismogenic area (called A, without location
presentation at present, for preventing social implications), is
presented as follows. In the following figure (4.3.7.1.9) is
presented the cumulative, seismic energy release.
Fig. 4.3.7.1.9. Cumulative, seismic energy release
calculated, for seismic area (A).
The sampling interval is that of a year and the time spans from
1950 to 2004. In this graph three distinct areas can be observed.
The first one extends from 1950 up to 1955 when two steps of abrupt
energy release are observed (1954 – 1955).
The second extends from 1955 up to 1999. Apart from some steps of
seismic energy release (EQs), observed, the main feature of this
time period is in the accelerating mode.
The last part of it that extends from 1999 up to 2004 is, clearly
still, in the “seismic quiescence” mode.
The graph of figure (4.3.7.1.9) is analyzed, in more details, in
the following figures. In figure (4.3.7.1.10) the released
cumulative, seismic energy, for the time period 1955 – 2000, was
fitted by a 6th degree polynomial.
Fig. 4.3.7.1.10. Accelerating, seismic energy
release, fitted by a 6th degree polynomial, calculated
for the period 1995 – 2000. The blue line corresponds to
the original data, while the red one corresponds to the
fitted polynomial.
Although, the polynomial form indicates that acceleration of energy
release is in progress, the calculation of the corresponding rate of
energy release, in time, is an evaluation of the specific process at
any time.
This is demonstrated in the following figure (4.3.7.1.11). The
analytical derivative in time, of the calculated polynomial, was
determined for the same time period.
Fig. 4.3.7.1.11. Evaluation of the cumulative,
seismic energy flowrate is presented, for the same
period of time, 1995 – 2000.
The calculated value for the rate of cumulative energy flow (dEcum/dt)
through the seismogenic area and for the time t=2000y is:
dE_{cum}/dt = 150*1018 erg (t = 2000y).
(4.3.7.1.1)
The seismic quiescence period (2000 – 2004), of the graph in figure
(4.3.7.1.9), is enlarged and presented in the following figure
(4.3.7.1.12).
Fig. 4.3.7.1.12. The “seismic quiescence” period
from 2001 to 2004 is presented. Cumulative seismic
energy release graph vs. time.
The analytical derivative, in time, of the calculated polynomial
was determined for the same period of time. A 1st degree polynomial
was fitted in this case. The results of this procedure are shown in
the next figure (4.3.7.1.13).
Fig. 4.3.7.1.13. The analytical derivative in time
of the calculated polynomial was determined for the same
period from 2001 to 2004. The blue line corresponds to
the original data, while the red one corresponds to the
fitted polynomial.
The analytical derivative, in time of the calculated polynomial,
was determined for the same period of time and is shown in figure
(4.3.7.1.14).
Fig. 4.3.7.1.14. The analytical derivative, in
time, is presented, of the calculated 1st degree
polynomial for the same period of time (2001 – 2004).
The calculated value for the rate of cumulative energy flow (dE_{cum}/dt)
through the seismogenic area and for the specific period of time is:
dE_{cum}/dt = 0.47*1018 erg (t_{y}=
2001 2004).
(4.3.7.1.2)
A comparison between equations (4.3.7.1.1) and (4.3.7.1.2) shows
that the cumulative seismic energy flow rate, through the under
study seismogenic area, was decreased about 300 times, during the
“seismic quiescence” period of time. This indicates that the
seismogenic area is under mechanical “locked” and “strain charge”
conditions and therefore, some time in the near future the stored,
strain energy will be released through a strong seismic event. Its
magnitude can be calculated by the application of the “Lithospheric,
Seismic Energy Flow Model” (Thanassoulas and Klentos, 2001). The
results are shown in the next figure (4.3.7.1.15).
Fig. 4.3.7.1.15. Magnitude calculation of the
expected, seismic event is shown. The black line
indicates the normal, seismic, cumulative energy
release, the blue line indicates the current level of
the cumulative energy release, while the red line
indicates the theoretical cumulative seismic energy
release under normal conditions for time t=150 days,
elapsed, in year 2004. The calculated magnitude for this
time of occurrence is Ms = 5.99 R.
If the time (teq), when the seismic event occurs, is set to teq =
150 days from the start of 2004, then the seismic event will occur
in a magnitude of Ms = 5.99 R.
Summarizing what was already presented it can be said that the
mechanical processes that take place in any seismogenic area,
mainly, control the balance of the energy flow through it.
Consequently, the study of the seismic energy flow, through a
seismogenic area, is capable to provide the necessary time functions
that will describe what was observed in nature and was studied by
statistical methods to date.
The physical mechanism of the “lithospheric energy flow model”,
introduced by Thanassoulas and Klentos (2001), justifies the
“accelerated deformation”, the “seismic quiescence” methods used to
date and the calculation of the expected magnitude of the seismic
event that will take place in a seismically, activated, area.
In contrast to the statistical / empirical “time to failure”
equation, which is used by other researchers for studying the
accelerated, seismic energy release, the model of the lithospheric,
seismic energy flow and its mathematical analysis results, according
to the specific mechanical conditions met in the seismogenic area,
leads, in a mathematical way, directly to the models used to date
empirically.
The mathematical analysis of the lithospheric, energy flow model
does not justify, neither the use of the parameter tteq (the
remaining time to the event), nor the parameter M (magnitude). These
parameters are deliberately included in the “time to failure”
functions, used to date, without any physical justification. These
parameters are calculated by other methodologies. Therefore, the
real value of this analysis is indicative for the seismic activation
of a seismogenic area that will end up with a strong event.
Quite often, a seismic quiescence (linear polynomial energy
release) period of a seismogenic area is preceded by a larger period
of accelerated (higher order polynomial energy release) deformation.
This is the case of the last example of area A, while the same was
observed in the Cremasta, Greece case (Varnes, 1989). The combined
use of both methodologies increases the degree of certainty that a
strong EQ will occur at the under study seismogenic area.
Since the methodology depends on the sampling interval of the
released energy, fine details, as far as it concerns the seismic
status of the seismogenic area to be studied, can be investigated by
choosing a finer sampling interval.
Finally, the physical mechanism of the lithospheric, seismic energy
flow model behaves in a fractal way, as it is shown from the two (2)
presented examples. At the first model (area of Zakynthos), the
accelerated deformation had, fully, developed within three (3)
years, while at area A, the second example, this took almost 45
years.
A strong EQ, of a magnitude of M = 5.99 R, is expected to occur in
area A, if this seismic event takes place up to the 150th day from
the start of 2004 (around May, 2004)
4.3.7.2. The “Seismic potential map”. Its application
example in Greece.
The terms “seismic hazard” and “seismic risk”, are very often,
referred to in the seismological and engineering geology studies.
The term “seismic hazard”, at any place, refers to quantity (H),
its magnitude being the expected intensity of the ground motion at
this place. The latter, can be expressed as (Papazachos et al 1985,
1989, Tselentis 1997) the expected ground acceleration, ground
velocity, ground dislocation and the expected, macroseismic
intensity (l).
The term “seismic risk” (R) refers to the expected results (damages
in buildings, deaths etc) from the occurrence of an earthquake and
depends strongly on the seismic hazard of the same place. The term
(R) of the seismic risk can be expressed as the convolution of the
seismic hazard (H) to the vulnerability (V) of a technical
construction. Therefore, the following equation holds:
R = H * V
(4.3.7.2.1)
Tselentis (1997) presents the following, holding equation for the
seismic risk:
R = H(e, μ, s)*T
(4.3.7.2.2)
Where, (R) is the seismic risk, (H) is a nonlinear parametric (e,
μ, s) equation with (e) being the earthquake source parameters, (μ)
is the propagating elastic waves media, (s) is the local conditions
and (T) is the vulnerability of the technical constructions.
A seismic risk study, at a certain place, has a strong
probabilistic – stochastic character and therefore all parameters
that can contribute to an excess ground motion at a probabilistic
level, are taken into account.
The results of a seismic risk study are presented in various forms.
Probabilistic graphs vs. Mercalli scale, excess of spectral velocity
and maps of spatial distribution of expected ground velocity are
some of them.
A typical, seismic risk study of a place includes (Tselentis, 1997)
the four following basic steps:
 Identification of the nearby earthquake sources
 Determination of the statistical model that
prescribes the earthquake sources and the expected, maximum
magnitude due to each one of them.
 Determination of the best amplitude decay of the
seismic waves of each seismic source.
 Determination of the probability for nonexceeding
any ground motion parameter level.
Maps of the spatial distribution of seismic hazard of Greece were
presented in the past (Makropoulos et al. 1985, Papazachos et al.
1985, 1989). Furthermore, the Greek territory was divided in four
(I, II, III, IV) zones of different expected ground acceleration, as
a function of the recurrence mean time value, and the intensity (I)
of a future, seismic event. The former seismic hazard map of Greece
is presented in the following figure (4.3.7.2.1).
Fig. 4.3.7.2.1. Former, seismic hazard zoning is
presented of the Greek territory (Papazachos et al.
1989, OASP).
This map is now under revision, due to the large seismic events
that took place in Greece, during the last decade (1990 – 2000).
Following the mathematical analysis which is presented by
Papazachos et al. (1989), it is made clear that the seismic hazard
map of Greece is based mainly on probabilistic seismic data, as far
as it concerns the parameters of the earthquake sources.
The latter was made clear, when Kozani earthquake (6.6R,
13/05/1995) and Athens earthquake (5.9R, 7/9/1989) took place at
areas, which were considered before as, more or less, aseismic.
Therefore, that map should be modified, as soon as possible,
whenever new, seismic data are available from earthquakes that have
already occurred, or even better, it should be modified according to
already known data, from areas that are being highly charged with
strain energy and consequently strong earthquakes are expected to
occur, within some period of time (a few years).
In the recent decade, a seismological research trend was developed
towards earthquake prediction (medium term prediction) by the use of
accelerating seismic energy release or accelerated deformation, as
it is referred very often. Main (1995), studied the earthquakes from
the point of view of a critical phenomenon. Varnes (1987a, b, 1989),
related the released, seismic energy to earthquake foreshock
sequences in an attempt to predict earthquakes by analyzing
accelerating, precursory seismic activity. A simple, in time (t),
empirical power law failure function was postulated by Bufe and
Varnes, (1993) that relates the parameters of the remaining time (tct)
to the occurrence of the imminent strong EQ and its corresponding
magnitude (M) to the seismic moment release. In the same area of
Statistical Physics Main (1996) showed that the cumulative, seismic
strain release increases as a power law time to failure before the
final event. Bowman et al. (1998) used the concept of cumulative,
seismic strain release, increasing, as a power law time to failure,
before the final event. Moreover it was found that the critical
region of radius (R) and the magnitude of the final event (M) are
correlated as Log(R) = 0.5M suggesting that the strongest probable
event, in a given region, scales with the size of the regional fault
network.
Papazachos et al. (2000, 2001, 2002), applied the same methodology
to the Aegean area, Greece. In this case, ellipses were taken into
account for the critical regions, which correspond to circles of
radius (R) with equal area. Di Giovambatista et al. (2001) studied
the accumulated Benioff strain before strong earthquakes, by using
the timetofailure model, and presented examples from strong
earthquakes that occurred at the Kamchatka and in Italy. Tzanis et
al. (2003), related the crustal deformation in SW Hellenic ARC to
distributed powerlaw seismicity changes.
Following this methodology, it is obvious, theoretically, that
areas of increased probability, for the occurrence of a strong EQ,
can be identified in advance and therefore, the expected, maximum
magnitude of an imminent EQ, at any place, will affect, accordingly,
the seismic hazard, calculated, for it.
Such maps, prepared for the entire Greek territory, will modify,
accordingly, the seismic hazard map, proposed by the seismologists,
and are, already, in use by the state authorities.
The above methodology has a main drawback. The acceleration of
seismic energy release is not a universal process that is observed
before all strong earthquakes. The application of the
timetofailure model, for the estimation of the magnitude and
moment of the future, strong earthquake, is possible only in case
when a tendency to acceleration is observed in the release of
seismic energy in the vicinity of its epicenter. Moreover, it does
not distinguish between the earthquake swarm and the foreshock
activation.
This work presents a different approach in preparing such maps.
These maps can be compiled, in particular, by the application, all
over the Greek territory, of the energy flow model of the
lithosphere (Thanassoulas et al. 2001) on the past seismic data.
A. The data.
The used seismic data were downloaded from the National Observatory
of Athens, Institute of Geodynamics, (NOA), Greece.
Greece is, initially, considered as a unit critical region and the
lithospheric energy flow model was applied over it.
The cumulative energy (Ec) vs. time graph (fig. 4.3.7.2.2), for the
period 1950 – 2002, reveals the presence of several (A, B, C) linear
parts in this graph, with different energy flow rate values (EFLs).
These linear parts are intermitted by periods (1, 2, 3, 4) of
intense, seismic activity.
Fig. 4.3.7.2.2. Greece’s cumulative energy release
is presented for the time period 1950 – 2002.
The continuous decrease of the EFL values (energy flow rate), which
is observed from 1950 to 2002, indicates that for the last 52 years,
Greece, is charging continuously with seismic strain energy that
will be released some time in the future, at some seismically prone
areas.
Consequently, two questions must be answered:
 Which areas have been charged, in excess, with
seismic strain?
 What is the expected maximum value of a future
earthquake, for the next i.e. five years period, for each area?
The following procedure was followed, in order to answer these
questions.
B. Application of the method – examples.
The lithospheric energy flow model was applied over the Greek
territory, by using a grid shell of 100 x 100Km. That shell slides
all over Greece, in steps of 50Km from West to East and from North
to South. As a result of this operation, an overlapping of 50% was
applied on the obtained results and a final grid of 50 x 50Km shell
was resulted.
This procedure is presented in the following figure (4.3.7.2.3).
Fig. 4.3.7.2.3. Size of grid shell is shown and
its movement over the Greek territory. A = shell
movement from West to East. B = shell movement from
North to South. Both movements are performed at steps of
50Km.
For each shell position and for the defined area, the
corresponding, cumulative energy versus time function, for the time
period 1950  2000 was calculated. Determinations were made for the
seismic energy strain charge potential, in terms of expected
magnitude, for a future earthquake, by using this graph and
following the lithospheric energy flow model procedure. As a time
basis for these calculations were used the years 1970, 1975, 1980,
1985, 1990, 1995, 2000, while the expected magnitude was calculated
for the next five years. For example, the calculation for the year
1980 indicates the maximum, expected magnitude for a strong
earthquake in the period of 1980 – 1985.
The used shells total to a number of (323) and the obtained
magnitudes for the different time periods were used to compile the
corresponding maps. These maps present the strain charge status
spatial distribution all over Greece, in terms of magnitude of a
potential, future (within the next five years from the date of the
map) earthquake.
Following, are the compiled maps for the corresponding periods of
time. These maps are presented in two forms:
 The first one presents the spatial distribution of
the entire range of the expected magnitude of a possible, future
earthquake over the Greek territory.
 The second presents the same results, as above, but
with a threshold lowlevel of magnitude set at 6 R. This facilitates
to identify more easily the areas which are highly strain charged
and therefore, prone to intense, seismic activity.
In each map, a chromatic bar indicates the corresponding earthquake
magnitudes in Richter scale. The compiled maps are presented in the
next pages as follows:
Year 1970
Fig. 4.3.7.2.4. Calculated map, based, on data
from 1950 to 1970 and expected potential earthquake
magnitudes up to year 1975.
Year 1970
Fig. 4.3.7.2.5. The same as above but a threshold
of 6R was used.
Year 1975
Fig. 4.3.7.2.6. Calculated map, based on data from
1950 to 1975 and expected, potential earthquake
magnitudes up to year 1980.
Year 1975
Fig. 4.3.7.2.7a. The same as above but a threshold of
6R was used.
Year 1980
Fig. 4.3.7.2.8. Calculated map, based on data from
1950 to 1980 and expected, potential earthquake
magnitudes up to year 1985.
Year 1980
Fig. 4.3.7.2.9. The same as above but a threshold of
6R was used.
Year 1985
Fig. 4.3.7.2.10. Calculated map, based on data from
1950 to 1985 and expected, potential earthquake
magnitudes up to year 1990.
Year 1985
Fig. 4.3.7.2.11. The same as above but a threshold
of 6R was used.
Year 1990
Fig. 4.3.7.2.12. Calculated map, based on data from
1950 to 1990 and expected, potential earthquake
magnitudes up to year 1995.
Year 1990
Fig. 4.3.7.2.13. The same as above but a threshold
of 6R was used.
Year 1995
Fig. 4.3.7.2.14. Calculated map, based on data from
1950 to 1995 and expected, potential earthquake
magnitudes up to year 2000.
Year 1995
Fig. 4.3.7.2.15. The same as above but a threshold
of 6R was used.
Year 2000
Fig. 4.3.7.2.16. Calculated map, based on data from
1950 to 2000 and expected, potential earthquake
magnitudes up to year 2005.
Year 2000
Fig. 4.3.7.2.17. The same as above but a threshold of
6R was used.
The following maps are presented in order to validate the used
method and the results which are obtained through it. On each map,
which represents a specific period of time, the corresponding strong
earthquakes (Ms >= 6R) which occurred during the following five
years were superimposed. The percentage of the earthquakes that
occurred, in the predefined area (Ms>=6R), is calculated as a
measure of the success of the method. That is the ratio of:
P = EQ_{in} / EQ_{tot }
(4.3.7.2.3)
Where P is the success percentage, EQ_{in} is the number of
earthquakes that occurred in the predefined area and EQ_{tot}
is the total number of the strong EQs that occurred in the specific
period of time in the Greek territory.
Period 1970 – 1975
Fig. 4.3.7.2.18. Strong seismic events (red
circles, Ms> = 6R) during the period 1970 – 1975.
EQ_{tot} = 4, EQ_{in} = 4, P =
EQ_{in} / EQ_{tot} = 100%
Period 1975 – 1980
Fig. 4.3.7.2.19. Strong seismic events (red
circles, Ms>=6R) during the period 1975 –1980.
EQ_{tot} = 8, EQ_{in} = 5, P = EQ_{in}
/ EQ_{tot} = 62.5%
Period 1980 – 1985
Fig. 4.3.7.2.20. Strong seismic events (red
circles, Ms>=6R) during the period 1980 – 1985.
EQ_{tot} = 17, EQ_{in} = 15, P = EQ_{in} /
EQ_{tot} = 88.2%
Period 1985 – 1990
Fig. 4.3.7.2.21. Strong seismic events (red
circles, Ms>=6R) during the period 1985 – 1990.
EQ_{tot} = 3, EQ_{in} = 3, P = EQ_{in} / EQ_{tot}
= 100%
Period 1990  1995
Fig. 4.3.7.2.22. Strong seismic events (red
circles, Ms>=6R) during the period 1990 – 1995.
EQ_{tot} = 9, EQ_{in} = 7, P = EQ_{in} / EQ_{tot}
= 77.7%
Period 1995  2000
Fig. 4.3.7.2.23. Strong seismic events (red
circles, Ms>=6R) during the period 1995 – 2000.
EQ_{tot} = 8, EQ_{in} = 6, P = EQ_{in} / EQ_{tot}
= 75%
Period 2000  2003
Fig. 4.3.7.2.24. Strong seismic events (red
circles, Ms>=6R) during the period 2000 – 2003.
For the most recent period (2000 – 2003), the (P) value has not
been calculated, since the seismic activity is still in progress and
two more years have to elapse.
C. Discussion – Conclusions.
The Greek territory, considered as a unit area, appears to be
charged with seismic energy, continuously, since 1950. This is the
result of the application of the energy flow model that indicates a
continuous decrease, in total, of the seismic energy release in the
Greek area. The latter, is demonstrated, in figure (4.3.7.2.2),
where the energy flow rate (EFL) values decrease, along time, since
1950 and consequently, excess seismic energy is stored in the
lithosphere. Therefore, it is expected that, some time in the
future, the stored, seismic energy will be released through the
occurrence of some strong seismic events.
The detailed study of the prepared maps (fig. 4.3.7.2.4 – fig.
4.3.7.2.17), for consecutive periods of 5 years (1970 – 2000),
reveals the dynamic character of the phenomenon. A significant
increase of seismic, potential charge is observed even in a five
years period.
The observed, increased values of the seismic potential, in all the
prepared maps, are distributed along the axis of the North Anatolian
Fault Zone and the Southern Aegean Seismic Arc. The latter, complies
with the seismological observations which concern the spatial
distribution of the strong seismic events in the Greek territory.
The periods of time, when the seismic potential has reached large
levels, is indicated by expected earthquake magnitudes of levels
above seven (7R). A very good example of the latter is demonstrated
in figure (4.3.7.2.20) for the period 1980 – 1985. The prepared map
for the year 1980 indicates the presence of three centers of large
seismic potential (Ms >7R, Kefalonia island, Korinthos – Alkyonides
– Thiva area, Limnos island). In the next five years (1980 – 1985)
to follow, 17 strong (M>6R) seismic events occurred, releasing a
significant amount of seismic energy. The latter is made clear by
the next prepared map (fig. 4.3.7.2.21, 1985) and the small number
of strong seismic events that occurred (only 3) in the following
five years period (1985 – 1990).
What is more important, as a result of comparing the maps to each
other, is the fact that a period of large seismic activity
discharges the Greek territory for only .5 – 1.0 R. Therefore,
distinct areas can be considered as being at a state of continuous,
large seismic charge (expected EQ levels up to 6R) and slight,
occasional increases of stress, trigger strong seismic events in the
same areas.
In all these prognostic maps, which were prepared for the years
1970, 1975, 1980, 1985, 1990, 1995, 2000, were superimposed the
corresponding large (Ms>6R) EQs for the next five years period of
time. The percentage of success ranges from 62.5%, for the period
1975 – 1980, to a value of 88.2%, which was achieved for the period
1980 – 1985, in a total of 17 strong EQS, which occurred during this
period. Obtained values of 100% for the percentage of success are
based in a small number of strong seismic events and could be no
reliable at all. Nevertheless, these seismic events still verify the
validity of the method, used for the calculation of these seismic,
potential maps.
As far as it concerns the small number of the seismic, strong
events that didn’t occurred in the predefined areas, it could be
attributed to errors in compilation of these maps. A major error can
be introduced by inadequate, available seismic data for the
calculation of the cumulative energy graph (Ec) vs. time, for each
frame, used, during the application of the lithospheric energy flow
model.
The calculated seismic potential maps, for different periods of
time, were compared with the Athens EQ (1999, Ms = 5.9R), Karpathos
(2001, Ms = 6.6R) and ZakynthosKefalonia EQ (2003, Ms = 5.8R)
strong seismic events in Greece.
In the following figure (4.3.7.2.25), the seismic potential map of
Greece, for the year 1995, is shown, along with the strong (Ms >6R)
seismic events that occurred in the period 1995  2000. The red
arrow indicates the place where the Athens EQ occurred (Ms = 5.9R).
It coincides with the narrow area, of expected events of Ms >6.5R,
observed, in the same place. A comparison of this map with the one
in figure (4.3.7.2.22), compiled for the year 1990, indicates that
seismic potential at the regional area of Athens was builtup during
the time span of 1990 – 1995.
Fig. 4.3.7.2.25. Seismic potential spatial
distribution in Greece is presented for the year 1995.
The red arrow indicates the location of Athens (1999) EQ.
A comparison of figure (4.3.7.2.25) with figure (4.3.7.2.24), of
the seismic potential for the year 2000, reveals that there is still
accumulated, large seismic potential, at a rather short distance,
west of Athens.
The next example concerns Karpathos strong EQ (2001, Ms = 6.6R).
The corresponding map of the seismic potential was compiled for the
year 2000. The red arrow indicates the location of the earthquake.
The coincidence of its epicenter with the area of increased, seismic
potential (expected EQ with Ms >6.5R) is more than evident.
Fig. 4.3.7.2.26. Seismic, potential spatial
distribution, in Greece is presented, for the year 2000.
The red arrow indicates the location of Karpathos (2001)
EQ.
The last example refers to Zakynthos  Kefalonia (2003, Ms = 5.8R).
The red arrow indicates the location of this EQ. Even if this EQ is
not of a magnitude larger than 6R, it is still considered as a
rather strong one and of significant magnitude since it occurred
near inhabited areas.
Fig. 4.3.7.2.27. Seismic, potential spatial
distribution in Greece is shown for the year 2000. The
red arrow indicates the location of Zakynthos 
Kefalonia (2003) EQ.
Apart from the previous, presented examples, a statistical study
was applied on the, obtained, results, as follows:
a. the total number of strong seismic events, during
the period 1970 – 2000, is equal to 50.
b. the total number of the seismic events that occurred, in
the predefined as seismically active areas, is 41.
c. For the total period between 1970 – 2000 the P value
is calculated as:
P = 41/50 = 82%
For the last compiled map (fig. 4.3.7.2.24), for the year 2000, it
is not possible to calculate a P value, since two more years are
left for completing the five years time interval, needed. Therefore,
only a statistical extrapolation, as follows, can be made, based, on
the previous results.
Since only one strong earthquake occurred in the period 2000 –
2003, and assuming the value of 82% is the correct one, then 5 more
strong EQs are expected, within the next two years, four of them
must occur in the predefined areas, so that the P value is: P = 5/6
= 83% that is very close to the calculated 82% (average value,
calculated, for the entire time period of the study), and it is the
result of the smallest pair of integer numbers found.
If another scenario is followed, for a minimum P value found of
62.5% (period 1975 – 1980), then, by following the above procedure,
it is found that four more strong EQs must occur, two of them in the
predefined area, so that the P value is: P = 3/5 = 60% and it is
very close to the assumed value of 62.5%. Regardless the used
statistical hypothesis, 4 – 5 strong (Ms > 6R) seismic events are,
theoretically, expected, to occur within the next period of time up
to 2005, included (Thanassoulas et al. 2003).
Four years have elapsed, at the time of writing this book, since
the time (2003) the latter scenarios had been presented. Therefore,
it is possible to present the entire 2000 – 2005 seismic potential
map and to compare it with the “guesses”, made in 2003. This is
shown in the following figure (4.3.7.2.28).
Fig. 4.3.7.2.28. Strong seismic events (blue
circles, Ms>=6R) during the period of time 2000 – 2005.
The number of strong (M > 6R) seismic events that took place is
seven (7) and four (4) of them are located in seismically charged
areas. The calculated P value is:
P = 4/7 or 57%
If the double, seismic event of Hios Island (eastern Greece), is
considered as of marginal success, then the P value becomes:
P = 6/7 or 86%
Actually, both hypothetical scenarios were superceded by a larger
number of earthquakes (6) verifying thus the number of expected
strong EQs in the period 2000 – 2005.
Finally, the compiled map for the year 2000, that is the current
map used for the seismic potential evaluation of the period of time
2000 – 2005, is compared with the seismicity in Greece (April, 2003,
Ms > 4.5 R). This map is presented in the following figure
(4.3.7.2.29).
In this map, the black solid lines indicate the location of the
deep fracture zones of the lithosphere. The red circles indicate the
location of the earthquakes of magnitude Ms > 4.5R that occurred
during the period 1st April – 24th April 2003.
It is clearly shown that, the epicenters coincide with the
predefined areas, where intense seismic activity is expected in the
future. Moreover, these epicenters are very closely located to the
deep fracture zones of the lithosphere, while the predefined areas
of peak large seismic potential are closely related to the deep
fracture lithospheric zones.
Fig. 4.3.7.2.29. Seismic, potential map is shown,
for the year 2000, along with the April, 2003 seismicity
(red circles) with Ms > 4.5 R.
It is worth to compare the current, seismic hazard map (fig.
4.3.7.2.1), compiled by seismological data only, with the seismic,
potential maps, compiled, by the application of the energy flow
model of the lithosphere. The latter indicates, in medium term
periods of time, the dynamic change of the seismic potential charge
of the lithosphere and therefore, it can be used so that medium term
measures against any seismic event, can be taken, by the State
Authorities, in areas prone to intense, seismic activity.
Consequently, the seismic hazard map of Greece should be recompiled
more frequently, since it changes dynamically, in medium time
intervals, along the time span.
