**A Prospect of Earthquake Prediction Research**

Yosihiko Ogata

**Abstract.**

Earthquakes occur on complex faults under
various different scenarios of preparatory processes and under uncertain
stresses in the earth crust. All of these cannot be seen directly. The
deterministic earthquake prediction that is coveted by people is difficult. To
predict the occurrence, comprehensively taking these elements into
consideration, stochastic prediction cannot be avoided. However, it accompanies
a large uncertainty in identifying whether abnormal phenomenon is a precursor
of a large earthquake or not, as well as urgency to the earthquake. Discovery
of potentially useful facts for earthquake prediction is not perfect unless
their quantitative modeling of risk is not involved. This manuscript describes
a prospect of the earthquake predictability research to realize a practical
operational forecasting in near future.

**1. INTRODUCTION**

**1.1 Progress in Geophysics and Earthquake
Prediction**

Public expectations about the earthquake
predictability are too excessive, and on the other hand, the disappointments
for the current situation are too big. However, until half a century ago, we
did not know the cause of the earthquake. Seismologists tried grab a clue
somehow, and statistical seismology had played a major role in earthquake
research by that time to reveal some regularity and examine other phenomena
that were statistically associated with their occurrence (Aki, 1956).

Thanks to the remarkable development of solid
earth science from the late 1960s, our knowledge of the earthquake phenomenon
has increased significantly. The relevant data is also growing by leaps and
bounds, as the study of earthquakes has progressed remarkably in geophysics.
After every major earthquake, they elucidated many facts what mechanisms were.

However, even though detailed analysis and
discussion have been done, diversity and complexity of the earthquake
phenomenon has been noticeable. In fact this is unfortunate for deterministic
earthquake prediction, because it must be exhaustively taken into account of
all processes (scenarios) of earthquake diverse and complex, in order to
realize the prediction of an earthquake by faithfully reflecting their physics.

**1.2 CSEP project and its aim**

It has been growing momentum that, instead of
seeking for a magic bullet for an earthquake prediction, seismologists should
develop a steady earthquake predictable research in an organized manner. So we
are underway in the international cooperative study among major earthquake
countries to explore the possibility of earthquake prediction called as
"Collaboratory for the Study of Earthquake Predictability (CSEP; Jordan,
2006) ". An immediate objective of the project is to encourage the
development of statistical models of seismic activity, and evaluate their
predictive performances in terms of probability. It also aims to develop a
scientific infrastructure to evaluate statistical significance and
"probability gain" (Aki, 1981) of various methods to predict large
earthquakes using observed abnormality such as seismic activity and
electromagnetic phenomena or crustal movements. Here, the probability gain
means ratio of the predicted probability relative to the underlying earthquake
probability. This is an important concept so that I will discuss later.

In fact, some techniques of predicting
earthquake have been proposed based on anomalies of various types, but are
under constantly controversy over their effectiveness (Jordan et al, 2011).
Therefore, it is necessary to evaluate the predictive power objectively.
Otherwise, it is preoccupied with something barren controversy.

First, in order to give a better prediction of
the probability, the CSEP tries to establish standard models that conform to
the various parts of the world, repeating the revisions. The
"likelihood" is used as a measure of the prediction results with
reasonable ones (cf., Bortzmann, 1878; Akaike, 1985). If someone claims that
the new prediction model has incorporated possibly useful information compared
to the standard model, it should be evaluated whether it improved predictive
power. Earthquake forecasting model is that should evolve in this manner.

The author has been mainly working so far, in
the research towards the elucidation and prediction of abnormal seismic
activity. On this occasion, I would like to discuss in more details of the
contents in the above.

**2. PROBABILISTIC SYNTHESIS OF PRECURSORY
PHENOMENA**

**2.1 Earthquake Related Datasets**

The hypocenter catalog includes the records of
earthquake generating position (latitude, longitude, depth), and the magnitude
of the earthquake. According to the current seismology, an earthquake is due to
the rapid destruction of the rocks of the Earth's interior. Looking at the big
picture, this destruction is that rock on both sides of the fault plane move out of
alignment. The position of the earthquake listed in the catalog hypocenter
means the starting location and the start time of the destruction of such
destruction. Moreover, we can make use of catalogs that recorded the
orientations of fault planes of relatively large earthquakes.

Among the various types of geophysical data,
hypocenter catalog is the data with a large amount that is recorded over a
longest period of time. Earthquake country of the world has its own edit the
catalog. For example, the Japan Meteorological Agency compiles earthquakes of
Japan. The world earthquakes are edited by the International Earthquake Center
(ISC) and United States Geological Survey (USGS). There is a Global Centroid
Moment Tensor (CMT) catalog that has been edited in a geophysical group of
Harvard University as a typical earthquake containing information of earthquake
faults in the world. Now, since WEB functions have well developed, we can also
look at real-time data source.

**2.3 Prediction model of time evolution of
seismic activity**

So, what should we do to advance the
evaluation of these criteria at first, using earthquake catalogs? Many small
earthquakes occur frequently, but they are not completely chaotic, way of their
occurrence obeys statistically certain laws. First, Gutenberg and Richter
(1944) found that the number of earthquakes increased (decreased) exponentially
as the size (magnitude) of earthquakes decreases (increases), respectively. The
typical aftershock frequency decays according to a reverse power function in
time (Omori, 1894; Utsu, 1961, 1969). Total number of aftershocks is
exponentially proportional to the magnitude of the main shock (Utsu, 1969; Utsu
et al., 1995). From these laws, we can predict the standard base-line
probability of earthquakes, including large ones, of a region from time series
of present and past earthquakes.

**2.4 Observed abnormalities and their precursors
identifications**

Of course, in order to predict a large
earthquake with a high probability gain, comprehensive study of anomalous
phenomena and observations of earthquake mechanism is essential. However, when
something abnormal is found, the identification of whether or not it is the
precursor of a large earthquake it is not easy.@

By the appearance of an anomaly, it may be
impossible to determine whether the anomaly is precursory phenomenon to a large
earthquake or not. Nevertheless, we may become able to say that, as compared
with those of the reference probability, the probability of occurrence of large
earthquakes has increased to a certain extent in a certain period and a certain
region. In this way, it is necessary to estimate the uncertainty of the nature
and urgency of the precursor to the major earthquake of abnormal phenomena. For
this purpose we must study a large number of anomalous cases for potential
links to large earthquakes.

Thus, how to incorporate as the basis of this
information, or to realize the prediction model of the probability of exceeding
the underlying probability; it is important to us.

**2.5 Improving the probability gain by looking
for a statistically significant phenomenon**

We
should pursue more possible algorithms that have predictive power of a large
earthquake by finding specific developmental patterns from seismic catalog. So
far, although many do not, the alarm-type earthquake prediction (Keilis-Borok
et al., 1988, 1966; Rundle et al, 2002; Shebalin et al., 2006; Sobolev, 2001;
Tiampo, et al., 2002a) have been proposed based on the pattern of seismic
activity, and some of them are operationally implemented, and were notified by
e-mail, or was published in an official document (the Center for Analysis and
Prediction, SSB, China; 1990-2003) . In addition, many
papers carried out their own earthquake prediction after the event happened.
Some of them were statistically significance,

However,
unfortunately, their average probability gains were at most several times of
the probability of the case without such information. These forecasts alone are
not enough for disaster prevention. On such evaluations of the alarm-type
predictions, readers refer to the papers by Zechar and Zhuang (2010), Jordan et
al (2011), Zhuang and Ogata (2011), and Zhuang and Jiang (2012).

I myself
also examined whether certain abnormal phenomena are related to the changes in
the rate of earthquake occurrence. Some of them are confirmed to be
statistically significant. For example, we analyzed causal relationship between
earthquake series from two different regions (Ogata et al., 1982; Ogata and
Katsura, 1984). We also examined periodicity (seasonality) of earthquake
occurrences (Ogata and Katsura, 1984; Ma and Vere-Jones). Those issues had been
frequently discussed in statistical seismology, but it was difficult to analyze
such correlations in the conventional method because earthquake clustering
feature leads to an incorrect result (Aki, 1956). On the other hand, we found
it effective to apply statistical models of stochastic point processes
incorporating a clustering component in them (see the review paper, Ogata,
1999, and the references therein). These models can also be applied to examine
whether or not various geophysical anomalies are statistically causal as the
precursory of a forthcoming large earthquake.

We have
to pay following attention. Suppose that significant correlation is observed
between the two series of events. However, it is insufficient from the
standpoint of prediction, and it is necessary to identify the causality. For
example, let us discuss about the data of unusual intensities of ground
electric potential by day that were observed in the vicinity of Beijing, China,
over 16 years from 1982. The issue is whether or not these were useful as
precursors to strong earthquakes of magnitude 4 or larger. It may be that the
electricity anomalies were aftereffect of the strong earthquakes. However, by
comparing the goodness-of-fit model by the AIC, the anomalies were
statistically significant as precursors to the earthquakes (Ogata and Zhuang,
2001; Zhuang et al., 2005). However, as they do not have very high probability
gain, they alone are not enough to become a practical prediction.@

We know
that the occurrence probability of a big earthquake is extremely small compared
to that of a small earthquake (Gutenberg and Richter, 1944). There are also
regional differences between such probabilities. At present, such a large
earthquake probability is estimated from the frequency distribution of
magnitudes of earthquake data in a region. Alternatively, the estimation is
made using recurrence times of a large earthquake on an active fault. In the
past, time independent risk (i.e., stationary Poisson process model) had been
estimated, and the intensity had been classified by degree of fault activity.
Time independent probability (i.e., stationary Poisson process model) had been
considered in old days where the intensity had been classified by degree of
fault activity. To warn the public for example, Japanese seismologists often
said "not strange even if it occurs now" without giving a
probability.

After
the 1995 Hyogo-ken Nanbu Earthquake, the Earthquake Research Committee (ERC) of
the Government has been adopted a renewal process model to predict
time-dependent probability estimated based on the last earthquake. This
prediction implementation was preceded by California. It is an improvement such that the
probability gains of the predictions owing to the renewal process model
compared to the Poisson process model prediction are only around 1.7 times in
California, according to Jordan et al (2011).

However,
the probability of the ERC prediction during 30 years period of each active
fault is very small. The probability per day is even smaller, even if it is the
rupture on a plate boundary. Therefore, in addition to that, the use of various
data of potential precursory anomalies is desired.

As described above, it would be difficult that
only an individual precursory anomaly can give a forecast of the high
probability, but the forecasting probability can be enhanced if some anomalies
are simultaneously observed. By a variety of observations, looking for
anomalies that produce medium-term forecast, short-term, estimate the
probability of each prediction, they also predicted that the combination is a
promising solution (Aki, 1981; Utsu, 1979, 1982). For example, identification
of the foreshocks and seismicity quiescence belongs to short- and medium-term
forecast, respectively.

**2.6 Short-term forecasting (1): probabilistic
identification of foreshocks**

There are foreshocks to something we should
take advantage of short-term forecasts. Although the foreshocks observed
considerably, this is a matter to become aware after a major earthquake
happened. Nevertheless, when earthquakes started happening in a local, it is
serious concern of folks to know whether these are a precursory of a
significantly larger earthquake or not. The goal is to determine statistically
from the data of earthquakes that are happening in this ongoing, to predict the
probability of foreshock-type. Since we are using the identification
information of the magnitude sequence and degree of hypocenter concentration, in a composite
manner, the probability gain of the prediction is heightened. In addition, the
short-term prediction in itself, probability gain is quite high. Because there
is a certain amount of progress in this study (Ogata et al, 1995, 1996; Ogata,
2011a, b; Ogata and Katsura, 2012), I expect that these will be put into practical
use in real time in near future.

**2.7 Short-term forecasting (2): probabilistic
forecasting of aftershocks**

After a big earthquake occurs, the Japan
Meteorological Agency and the U.S. Geological Survey (USGS) in California
undertake the operational probability of aftershocks. Computational methods by
the maximum likelihood procedure for the Omori-Utsu aftershock decay formula
have been calculated together with the Gutenberg-Richter law of
magnitude-frequency of aftershocks (Utsu, 1965; Aki, 1965; Ogata, 1983b).

However, they forecast the probability from
the time after the first day elapsed. This is due to observational difficulties
of smaller aftershocks during the early period after the mainshock. Within the
first day after the mainshock, in fact, more than a half of the entire large
aftershocks have already occurred. Therefore, despite the adverse conditions of
data collection, it is desired to give a probabilistic forecast aftershock as
soon as possible within 24 hours mainshock for mitigating secondary disasters
in the affected areas. For this purpose, it is necessary to estimate the
time-dependent missing rates (or detection rate) of aftershocks (Ogata and
Katsura, 1993, 2006; Ogata, 2005c), which enables real-time probabilistic
forecast from immediately after the main shock (Ogata, 2005c; Ogata and
Katsura, 2006).

Similarly, the probability forecast of seismic
intensity at a local is possible. Namely, the Ishimoto-Iida formula (Ishimoto
and Iida, 1939) of maximum amplitude seismographs of earthquakes also follows
exponential distribution like the Gutenberg-Richter formula. This formula
together with the Omori-Utsu aftershock decay is combined with detection rate
of aftershocks for the forecasting intensities during the early period.

**3. EARTHQUAKE DYNAMICS AND EARTHQUAKE
TRIGGERING**

**3.1 Interaction Between Earthquakes**

In order
to explain the chain of earthquakes as well as the quiescence of the activity,
we need the physical concept of the Coulomb failure stress. The interior of the
crust and upper mantle lithosphere is distorted under stress that increases
steadily in a certain direction. Thus, the lithosphere can be considered as an
elastic body in the long run. Fault planes are chinks within lithosphere, or
they are plate boundary interface. There are numerous faults ranging from very
small sizes to the big ones. A fault size is related to magnitude of an
earthquake when it slips. Fault planes are oriented in various directions. For
each fault plane, stress tensor in the lithosphere is decomposed into the two
components; namely, shear stress works in the direction of shifting the fault,
while the normal stress works pressing the fault plane. The orientation of each
fault plane will vary the amount of these ingredients. Critical condition is
determined by the following Coulomb failure stress.

CFS =
(shear stress) – (friction coefficient) x (normal stress + pore fluid pressure)

The
fracture stress increases at a constant rate over time, and when Coulomb
failure stress exceeds a certain threshold, the fault slips dramatically
causing an earthquake. Then, the stress drops to a certain value, and is
accumulated again. The accumulation of the stress takes a period of decades to
recur a large earthquake on the plate boundary, and takes a period of thousands
of years to recur the slip on the inland active faults.

In
recent years, a sudden change of much stress has been attracting many
seismologistsf attention. When an earthquake occurs near, displacement of the
fault brings sudden Coulomb stress changes (CFS) in the crust.
They decrease or increase, depending on the orientation of each fault plane of
the peripheral portion of the fault system. On fault of increased CFS,
an earthquake occurs earlier than expected. On fault of decreased CFS,
the occurrence procrastinates. If there are many faults of similar orientations
dominating the region, we expect seismic activation or seismic quiescence in
there.

Here, the fluid pressure of the gap fault
related to CFS is usually a constant value. However, its changes may play a
major role. For example, the pressure changes in the fluid magma gap affect
swarm activity in volcanic area (Dietrich et al., 2000; Toda et al., 2002).
Another example is that earthquakes are induced due to the increase pore
pressure in a fault system (Hainzl and Ogata, 2005). This is caused by
drastically heavy rainfalls, or by strong seismic waves. Seasonal nature of
seismic activity is also studied (annual change). Statistical model and its
application to validate data from the earthquake-induced phenomena such,
reference is made to the review paper (Ogata, 1993, 1999), for example. Also,
see the study of seismicity changes that were induced by injection of water
using the ETAS model (Lei et al., 2008, 2011).

**3.2 Predicting seismic activity in the
peripheral area by sudden stress changes**

In order to explain the phenomena of induction
of earthquakes, or suppressing seismic activity, it has been useful to see the
increase or decrease in the Coulomb failure stress (CFS) by a rapid
faulting (big earthquake). When a large earthquake occurs, we observe seismic
waves or GPS crustal displacement. From the observations, we can solve the
fault mechanisms of the earthquake; namely, its size, orientation and vector of
the fault shift. Okada (1992) made a computer program to perform the
calculation of CFS
in a receiver fault system from the source fault has become, so the studies on
the induction of earthquake based on CFS recently become
popular. See Special Issue volumes on this subject edited by Harris (1998) and
Steacy (2005), for example.

For example, Ogata (2004b) examined regional
increase or decrease of the CFS in southwestern Japan inland, by massive
earthquake of the 1944 Tonankai earthquake east of M7.9 and the 1946 Nankai
earthquake of M8.1. Conventionally, some seismic quiescence here was considered
as either the genuine precursor or the artifact due to incompletely detected
earthquakes during the last war period. The positive and negative CFS
is compatible well with seismic activation and quiescence, respectively. In
particular, that paper classified the seismicity anomalies into pre-seismic,
coseismic and post seismic before and after the massive earthquakes. The
scenarios that are classified in this study might be helpful in interpreting
seismic activity in western Japan before the next great earthquakes along the
Nankai Trough.

**3.3 ETAS
model and seismic activity**

Interactions among earthquakes are generally
fairly complex. Once an earthquake occurs somewhere, the CFS of fault system adjacent
to the fault is extremely increased, and many earthquake are induced. These are
called aftershocks in most cases. Some of them are also induced outside the
aftershock region, and they are called the aftershocks in broad sense. A big
change in stress brings many aftershocks, and small change can even induce
aftershocks to some extent. However, we cannot see the complex fault system in
the crust. Hence, detailed calculations of the stress changes are difficult and
impractical.

Therefore, statistical model to describe the
actual macroscopic outcome of the interactions is required. For example, the
ETAS model that consists of the empirical laws of aftershocks quantifies the
dynamic forecasting of the induced effects. By fitting to the selected data from
the catalog earthquake, the ETAS model determines their parameters by the
maximum likelihood method. Thus we can predict the incidence of the earthquake,
conforming to regional diversity.

By the way, the friction law of Dieterich which
is constructed based on rock fracture experiment with controlled stresses, has
some links to statistical laws of
earthquake occurrences (Dieterich, 1994). Namely, it reproduces the temporal
and spatial distribution of attenuation rate of aftershocks such as the Omori's
law. However, because of the seismicity diversity, predictions adapting well to
the development of seismic activity seems to be difficult at the moment.

Among the plotting figures to indicate the
seismic activity from the data source, very often used ones include a plot of
earthquake magnitudes series against occurrence times (M-T plot), and a plot of
cumulative number of earthquakes against the occurrence time (the cumulative
function). The seismicity transition can hardly be understood simply by looking
at these plots of earthquake series. These show a complex form generation due
to successive occurrences of the earthquakes (clustering). The clustering
feature was the main difficult factor against the application of conventional
statistical tests that assume the uniformly random earthquake generation
(stationary Poisson process) as the null hypothesis. The complexity due to the
clustering feature makes it difficult to reveal anomalies of seismic activity
due to the subtle stress changes; hence, we may have missed the various
signals.

For this reason, seismologists devised various
de-clustering methods that leave isolated earthquakes and the largest
earthquake in a clustering group (the mainshock), deleting the other
earthquakes. Based on the de-clustered data, statistical significance of
seismic quiescence was tested against the Poisson process. Sometimes, however,
the result of the analysis depends on the choice of the criteria of the adopted
de-clustering algorithm (van Stiphout et al., 2012). Hence, they will have a
haunting worry whether or not the result is caused by artificial treatment
method. In addition, de-clustering methods result in significant loss of
information since it throws away a large amount of data from the original catalog.

The ETAS model uses the original earthquake
data without de-clustering. As I mentioned before, the ETAS model is a point
process model configured so as to conform to the rule of thumb that has been
accumulated in various studies, such as aftershocks in Japan and the time
evolution of the seismicity rate. We can capture the regional characteristic of
earthquake occurrences that can be called the face of seismic activity, so that
this model has been accepted as a standard model of the ordinary seismic activity
by seismologists. The ETAS model can detects a significant deviation from the
normal activities using it like a "yardstick". This is a new and
unique approach alternative to de-clustering. Incidentally, stochastic
de-clustering method has been proposed by using the space-time ETAS model
(Zhuang et al., 2002). Interpretation of this algorithm is clear in stochastic
sense.

**4.
SEISMICITY ANOMALIES**

**4.1
Seismic quiescence**

Therefore, we measure deviation of actual
cumulative number of earthquakes compared with theoretical cumulative function
of the earthquake that is indefinite integral in time of a predicted rate
function of the ETAS model. When actual earthquake occurrence rates
systematically lowered in comparison with the predicted incidence of by ETAS
model, I call the phenomenon the relative quiescence (Ogata, 1992). The
relative quiescence lasted for a number of years were observed in a broad
region before M8-class great earthquakes in and around Japan (Ogata, 1992;
Ogata et al., 2003a). Similar phenomena were observed before M9-class
mega-earthquakes in the world.

The authors (Ogata, 2009, and reference
therein) reported in the Coordinating Committee for Earthquake Prediction of
Japan so far, such as the example of the analysis of the seismic quiescence
which was published in academic journals, is as follows:

i1jStatistical analysis
of seismic activities in and around Tohoku District, northern Japan, prior to
the large interplate earthquakes off the coast of Miyagi Prefecture;i2jSeismicity changes
and stress changes in and around the northern Japan relating to the 2003
Tokachi earthquake of M8.0;i3jSeismic activities in and around Tohoku
District, northern Japan, prior to the 16th August 2005 interplate earthquake
of M7.2 off the coast of Miyagi Prefecture, and the aftershock activity of the
M7.2 earthquake;i4jSeismicity changes in and around Kyushu District before the 2005
earthquake of M7.0 in the western offshore of Fukuoka Prefecture;i5jOn an anomalous
aftershock activity of the 2004 Niigata-ken-Chuetsu earthquake of M6.8, and
intermediate-term seismicity anomalies preceding the rupture around the focal
region;i6jSeismic activities in and around Tohoku District, northern Japan,
prior to the 16th August 2005 interplate earthquake of M7.2 off the coast of
Miyagi Prefecture, and the aftershock activity of the M7.2 earthquake;i7jAnomalies of
seismicity and crustal movement in and around the Noto Peninsula before the
2007 earthquake of M6.9; (8) Long-term probability forecast of the regional
seismicity that was induced by the M9 Tohoku-Oki earthquake

I have also analyzed aftershocks as well.i9jSeismic activities
in and around Tohoku District, northern Japan, prior to the 16th August 2005
interplate earthquake of M7.2 off the coast of Miyagi Prefecture, and the
aftershock activity of the M7.2 earthquake;i10jQuiescence of the 2003 foreshock/aftershock
activities in and off the coast of Miyagi Prefecture, northern Japan, and their
correlation to the triggered stress-changes;i11jAnomalies in the aftershock sequences of the
2003 Tokachi-Oki earthquake of M8.0 and the 2004 Kushiro-Oki earthquake of M7.1
and seismicity changes in the eastern Hokkaido inland;i12jRelative quiescence
reported before the occurrence of the largest aftershock (M5.8) in the
aftershocks of the 2005 earthquake of M7.0 at the western Fukuoka, Kyushu, and
possible scenarios of precursory slips considered for the stress-shadow
covering the aftershock area;i13jSeismicity changes in and around Kyushu
District before the 2005 earthquake of M7.0 in the western offshore of Fukuoka
Prefecture;i14jOn aftershock activity (M7.2) earthquake off the coast of Miyagi
prefecture in 2005;i15jAnomalies of seismicity in space and time measured by the ETAS model
and stress changes;i16jOn the 2007 Chuetsu-Oki earthquake of M6.8: Preceding anomalous
seismicity and crustal changes around the source, and the normal feature of the
aftershock activity;i17jSeismicity changes in northern Tohoku District before the 2008
Iwate-Miyagi Nairiku Earthquake;
(18) Aseismic slip scenario for transient crustal deformations around
the southern fault before the 2008 Iwate-Miyagi Inland earthquake. (For
example, http://www.ism.ac.jp/~ogata/yoti.html, Coordinating Committee for
Earthquake Prediction newsletter http://cais.gsi.go.jp/YOCHIREN/report.html.
Reference [65] "40 Years of Coordinating Committee for Earthquake
Prediction"

Except in the case of (12) that reported
seismic quiescence of aftershock activity before a largest aftershock, these
are all post-analysis report: the (12) case will be mentioned in some detail in
Section 5.2. Also, from the report that I have investigated the cases of 76
aftershocks in Japan, the relative quiescence was observed in 34 cases (Ogata,
2001, Appendix). It will also be mentioned in Section 4.5 how the results of
this aftershock study will be used for a space-time probability prediction of a
neighboring large earthquake of the similar size to the mainshock.Here, I will
mention about remarkable results in aftershock activities of inland earthquakes
of magnitude 6 or larger southwestern Japan that occurred during 30 years
before and after 1946 Nankai earthquake of M8.1. The 1925 Tajima earthquake of
M6.8, The 1927 Kita-Tango earthquake of M6.8, the 1943 eastern Tottori
earthquake of M6.2, the 1943 Tottori earthquake of M7.3, the 1944 Tonankai
earthquake of M7.9 and the 1945 Mikawa earthquake of M6.8; these occurred
preceding the 1946 Nankai earthquake. Among these, the relative quiescence can
be seen in all the aftershock activity except for the Kita-Tango earthquake. On
the other hand, the 1948 Fukui earthquake of M7.1, the 1955 southern Tokushima
Prefecture earthquake of M6.4, the 1961 Kita-Mino earthquake of M7.0, the 1963
Echizen-Misaki-Oki earthquake of M6.6, the 1968 Ehime-Ken Seigan earthquake of
M6.6, the 1969 Gifu-Ken Chubu earthquake of M6.6, and the 1978 Shimane-Ken
Chubu earthquake of M6.6; these earthquakes occurred during 30 years after the
Nankai earthquake. In contrast, in these aftershocks, the relative quiescence
was not seen and aftershock activity was on track.

**4.2 Stress change and seismic quiescence**

After the GPS observation network in Japan has
established, aseismic fault motions (slow-slips) that could not be detected by
seismometers, have been successively identified in the plate boundary region.
We can assume such a slow slip to discuss the relationship between the seismic
quiescence or activation and a weak stress changes in the crust.

Specifically, assume that slow-slips on a
focal fault or its adjacent part have taken place during a period. Then
depending on the distribution of orientations of faults around the focal fault,
the Coulomb failure stress could decrease and accordingly the seismicity is
considered to lower. Such a region is called stress shadow and seismicity shadow,
respectively.

We sometimes observe the case where even
aftershock attenuation rates decay quicker halfway than those predicted by the
Omori-Utsu rate in the earlier period. This is again called the relative
quiescence. Such a mechanism can be observed by the significant difference
between the prediction and the actual occurrence rates of earthquakes in data
analysis by ETAS model. In fact, as seen in most examples I have reported
above, the stress shadows coincide with seismicity shadow.

**4.3 Aseismic slip and seismicity anomalies**

Seismicity rate change can become
systematically less than predicted in some cases, but become systematically
greater than expected in other cases. The latter is called relative activation.
The region of relative quiescence and activation in seismicity coincide with
that of the CFS decrease or increase, respectively.

An example is seen in the seismicity before
the 2004 Chuetsu Earthquake of M6.8. By assuming the precursory slow slip on
the source fault, the region of the periphery was divided into four subregions
according to the increasing or decreasing change in the CFS. Each of the
subregions can theoretically corresponds to the area either to be promoted
seismicity or to be suppressed. Therefore, the ETAS model was fitted to the
earthquake data from each of the four regions in the period till the 2004
earthquake of M6.8 after September 10, 1997. As a result, there was a clear
change in seismic activity in each area. In the stress shadow region, the
seismicity became quieter than those predicted by the ETAS. In contrast, in the
area of the increased CFS, actual seismicity activated relative to the
predicted (Ogata, 2007).

Similarly, the anomaly patterns of seismic
activities are in good agreement with that of the CFS increment relative to its
trend in the following cases. Namely, these are: the seismicity in and around
Kyushu District till the 2005 Fukuoka-Ken-Seiho-Oki earthquake of M7.0 (Ogata,
2010a); the seismicity around the Noto-Peninsula till the 2007 Noto-Peninsula Earthquake
of M6.9 (Ogata, 2011d), and seismicity in and around the Tohoku District till
the 2008 Iwate-Miyagi-Ken Inland earthquake of M7.2 (Kumazawa et al., 2010).

However, the changes in the activity were not
entirely simultaneous. This may mean that aseismic slip is happening
continuously or intermittently. But the seismicity anomalies at the
investigated regions preceding the 2003 Tokachi-Oki earthquake of M8.0, started
at about the same time (Ogata, 2005b). This might mean the start of the
precursory slip as the change was strong enough.

**4.4 Deduce the variation of local stress from
spatio-temporal variation of aftershock activity**

In many cases of aftershock activity, there are anomalous
parts in space-time locations of aftershocks. To see these relatively clearly,
we first apply the Omori-Utsu formula for aftershock decay to data of
occurrence times, and then convert the times using the estimated theoretical
cumulative function. Then, we can look at aftershock occurrences in detail like
watching a video whose projection speed was adjusted to capture the motion that
is too fast or too slow.

Aftershocks that have occurred normally in the entire
aftershock area will distribute uniformly in such a converted time, and any
anomaly is not seen. In reliance on this, we examine whether or not the spatial
distribution under the converted time remained uniform in each part of the
region. If the non-uniform spatial distribution in certain portions of the
space-time of conversion is observed, this indicates that there are
discrepancies between the official and actual aftershock occurrence of the
Omori-Utsu aftershock decay. There are some possible scenarios for such
discrepancies. Firstly, secondary aftershocks that follow a large aftershock
look remarkable as a cluster of points among uniformly distributed points as a
whole. This cluster of secondary aftershocks shows traces of a new rupture to
extend the peripheral portion of the fault of the main-shock. When we can see
some non-uniform and heterogeneous portions other than the secondary
aftershock, exploring the reasons for them is very important.

Anyway, by such time conversion, we can see some
non-uniformity where it is relatively clearly abnormal against the Omori-Utsu
formula. From a dozen cases of recent large earthquakes, and from the fairly
accurate spatial aftershock arrangement, Ogata (2010b) revealed spatiotemporal
parts of the relative quiescence. This was considered to be associated with
slow-slips in vicinity of a large aftershock fault of destruction or after the
mainshock. These can occur in any of coseismic, post-seismic or preseismic
slips.

These were
systematically investigated on the assumption that as a result of a change of
partial Coulomb failure stress related to these anomalies. In addition,
assuming several scenarios of stress-changes due to slow slips, Ogata and Toda
(2010) and Ogata (2010b) performed simulations to reproduce seismicity
anomalies(relative activation and quiescence) within aftershocks based on the
rate/state friction law of Dieterich.

**4.5 Space-time
probability gain of a large earthquake under relative quiescence of aftershocks**

When we observe
relative quiescence in aftershock activity, the following question arises. What
percentage of the anomaly is linked to a large earthquake, how long after, and
further where? Since these involve many conditions and hence a number of
parameters involved, we cannot easily put out an answer.

But,
based on statistical studies of aftershock sequences in Japan (Ogata, 2001), it
is possible to say as the following on the probability gain that a large
earthquake will occur. First, if a large earthquake occurred somewhere, then
probability per unit area that another earthquake of similar size will occur in
the vicinity is larger than that which will occur in the distant area. This
itself is an simple statistical results, and physically suggests that the neighboring
earthquake will be more likely induced by sudden change of stress on the
periphery due to abrupt slip of the first earthquake.

If aftershocks become relative quiescence, it
becomes more likely that a large aftershocks will occur within and boundary of
aftershock area than the case where aftershock activity has remained decay on
track as expected by the ETAS or the Omori-Utsu formula. Furthermore If the
relative quiescence lasts longer (more than three months, for example), then
probability that another earthquake of similar size will more likely to occur
in the vicinity of the aftershock area (within 200km, for example) within a
period of six years (Ogata, 2001). The probability gain is several times higher
than the case where we have no information about the aftershock activity
mentioned above.

**5. SEISMICITY ANOMALIES
AND GEODETIC ANOMALY**

**5.1 Aseismic slip and
crustal deformation**

If there
is a sliding motion on a fault, we can in principle see geodetic changes on the
ground around it. The GSI compiles the daily geodetic locations of GPS stations
throughout Japan. From the GPS catalog we can calculate baseline distances
between GPS stations. The geodetic time series show that contraction or
extension of the distance between the stations are basically linear with time.
This is because the subducting plate converges with constant speed.

However,
from years 3-4 prior the 2004 Chuetsu Earthquake, the time series of the
baseline distance variation around the Chuetsu Earthquake fault was observed
systematic deviation from a linear trend (Ogata, 2007). With the exception of
the baseline segments connecting to the nearest 3 stations to the fault, these
deviations were correlated significantly with the coseismic displacements of
the Chuetsu Earthquake.

Similar
baseline-distance anomalies between the GPS-stations were observed in and
around the focal regions before the following earthquakes. Namely these are the
2011 Tohoku-Oki earthquake (GSI, 2012), the Iwate-Miyagi-Ken Inland Earthquake
(Kumazawa et al., 2010), Fukuoka-Ken Seiho-Oki earthquake (Ogata, 2010a), the
Noto-Hanto Earthquake (Ogata, 2011d) , and the Chuetsu-Oki Earthquake (Ogata,
2011d). Each deviation of these baselines is consistently explained by slow
slips on earthquake source fault.

The
above is a post-hoc analysis based on the knowledge of the source fault
obtained by coseismic displacements. From predictive viewpoint, it is desirable
to be able to estimate such a fault slip in near real-time when each slip is
taking place. Indeed, some estimates of slips on plate boundary have been so
far obtained by an inversion method from the GPS records. The GSI regularly
reported such estimates of coseismic, post-seismic and large-size habitual
slips at the Coordinating Committee for Earthquake Prediction.

Moreover, zones of locked fault (or slip
deficit) on plate boundary have also been determined taking account of the
rapid slips by large earthquakes and long-term slow slips (Hashimoto et al.,
2009). The 2011 Tohoku-Oki Earthquake and the 2003 Tokachi-oki Earthquake
eventually occurred in such locked areas (Matsufura, 2012).

However,
it is difficult to obtain (especially inland slip) fine image of small slip,
although the GPS stations inland are arranged closely enough. This is due to
not only GPS observation errors, but also high seismic activity. Since strong
earthquakes occur frequently, various effects of the slips are mixed into the
GPS records. It is urgent to develop statistical models and methods to separate
the such signals.

In any case, to estimate slow-slips more
precisely, the combined modeling and analysis of the seismicity anomalies and
the geodetic anomalies will be useful. Analyzing the both seismic activities
and transient geodetic movement in a number of areas, and locate the
whereabouts of aseismic slip is very important, is likely to eventually help to
increase the probability of occurrence prediction gain of a large earthquake.

**5.2 Considering the
scenario of an earthquake from aseismic slip**

Anomaly
of crustal movement and seismic activity, if they are observed, set the
scenario assumptions about the fault mechanism and location of the slip
precursor for the prediction probability, must estimate the uncertainty of
them. We further need to estimate the likelihoods of considered scenarios.
These are not easy. A possible method is to consider the logic tree of various
scenarios regarding the destruction of the fault system, attaching appropriate
subjective or objective probabilities to the tree components as has been done
in the long-term prediction of California and Japan. Hence such a scenario
ensemble gives a forecast probability. Similarly, there is also a need to
consider the medium-term and short-term prediction logic tree of different
scenarios.

At the Coordinating
Committee for Earthquake Prediction of April 6, 2005, I reported the relative
quiescence of aftershocks of the Fukuoka-Ken Seiho-Oki earthquake (Ogata,
2005d). Additionally, I assumed several slow-slip scenarios on the active
faults around the aftershock region for the cause of the quiescence. Namely, I
looked for a potential slow-slip part on nearby active faults that might have
created stress shadow causing relative quiescence in the aftershock sequence.

Among
them Kego fault, traversing Fukuoka City, was the large positive CFS
by the mainshock rupture, and was in easy circumstances that slow-slip being
induced. Furthermore, the seismogenic zone along the Kego fault had already
activated before the Fukuoka-Ken Seiho-Oki Earthquake occurred (Ogata, 2010a).
Therefore, I set up the slow-slip scenario on this fault that may have
happened, and examined the causing pattern of stress variation to the
aftershock area. However, in the aftershock area, there was no stress shadow
being caused by it. Therefore I think the probability that the slow-slip had
occurred on the Kego fault was quite low.

A few
potential slow slips in the neighboring active faults could make a stress
shadow that covered the aftershock region. However, no large earthquake has occurred
there so far.

Actually,
after about a month later, the largest aftershock occurred at the south-east
end of the aftershock zone. By post-mortem examination based on the information
in the fault mechanism of the largest aftershock in addition to detailed
aftershock data, it was able to give a detailed scenario. That is to say, by
assuming a slow slip into the gap between the fault of the largest aftershock
and the mainshock, we can well explain the relative quiescence of activity in
the deeper part of the aftershock zone (Ogata, 2006a). At the same time, the
slip can also explain the relative quiescence in the induced swarm activity
that occurred away from the aftershock area (Ogata, 2006a).

The setting as a prediction of future
scenarios is much more vague and difficult, even if we can draw ex post
scenario in this way. Moreover we must predict time of occurrence, not just the
place. This is more difficult. Even if a slow slip was revealed somewhere, many
papers suggest that it does not always indicate a proximate precursory of a the
fault corruption.

**6. CONCLUDING REMARKS**

In order
to predict major earthquakes with high probability gain, and also to obtain
good evaluations showing the progress of such predictions, comprehensive study
of anomalous phenomena and observations of earthquake mechanism is essential.
Incorporating those to achieve the predicted probability of exceeding the
predictions of the typical statistical model seismic activity, study of seismic
activity for that must be carried steadily as carrying bricks.

Furthermore
to see the urgency and uncertainty of a major earthquake against abnormal
phenomena, we must accumulate a lot of research examples. Based on those, we
must provide possible prediction scenarios and their likelihoods. In order to
adapt well to the diversity of earthquake generation process, it is useful to
adopt Bayesian prediction (Akaike, 1980; Nomura et al., 2011). There is also a
need to consider region-specific models.

I can
say from my experience so far is that the method of statistical science is
essential to elucidate the movement leading to prediction of a complex system
of global phenomenon. There is a need to forecast using a hierarchical Bayesian
model to build a model that reflects the diversity of the vast amount of
information on the basis of seismic activity of various data. Space-time model
for seismic activity has become more complicated than ever (Ogata, 1998, 2004a,
2011c; Ogata et al., 2003b; Ogata and Zhuang, 2006).

A similar evolution is required for statistical
models of geodetic GPS data as described above. So, without the professionals
involved in earthquake statistics (statistical seismology) the research itself
is difficult. In this way, I believe that statistical seismology is essential
for the study of complex systems of the earth. Education for citizens
understanding forecast probability of complex phenomena is also the duty of
researchers and practitioners who engage in statistical science.