Published in “Earthquake Hazard and Seismic Risk Reduction”,

Eds: S. Balasanian, A. Cisternas and
M.Melkumyan. Kluver, 2000, pp127-136.

EARTHQUAKE PREDICTION: PRO AND CONTRA

                  T. CHELIDZE

This report is provoked by the discussion on the fundamental problem
of predictability of earthquakes, which last years became very intensive.
The main arguments of unpredictability proponents are published in the
special section: ”Assessment of schemes of earthquake prediction” in
Geophysical Journal International (v.131, N 3, 1997), namely in papers
of R. Evans, Y. Kagan, P. Leary,   P. Stark and others, presented on
the meeting of the Royal Astronomical Society and Joint Association
of Geophysics, held in London on November 1996. They claim that
the prediction of the time of strong earthquake is principally impossible,
though the validity of seismic hazard assessment procedures is not doubted.

The main arguments against possibility of earthquake forecast are:

i. The Earth’s crust is in the state of self-organized criticality (SOC)
(Bak, Tang and Wiesenfeld, 1988; Sholtz, 1990). In the state of SOC
due to the str ong nonlinearity of system, the smallest change in initial
conditions may cause totally different response. This leads to conclusion
on “ the inherent implausibility of reliable earthquake prediction, because
many small earthquakes occur through any active seismic zone,
demonstrating that the critical conditions for earthquake nucleation
are satisfied almost everywhere. Apparently, any small shock can
grow into a large event. Thus it is likely that the earthquake has no
preparatory stage” (Kagan, 1997).

ii. The second group of arguments is related to the statistical aspects
of forecast. The existing techniques are mainly aimed to obtaining
optimal retrospective prediction and prescribing to forecasts in future
the same reliability. After-the-fact search is not of much predictive
value, as far as for small statistics of strong earthquakes it is possible
to optimize quite satisfactorily the prediction scheme for existing data.
At the same time it can turn out that this optimized approach is not valid
for prediction of following events or for other regions. This can be called
hunchback jacket effect; you can work out the jacket, ideally fitting the
given hunch, but it can be utterly useless for another one, as each hunch is
individual. There are also other doubts, related, for example, to the
problem of correct formulation of null hypothesis (Stark, 1997).

iii. The third group of arguments considers experimental prediction data.
“The 100-years history of attempts shows little or no progress in prediction
of time, magnitude and location of impending earthquake in reasonably
tight limits on the basis of experimental observations”. According to R.
Geller (1997) “extensive searches have failed to find reliable precursors”.

The arguments are serious, but it seems that they are not so firmly
grounded and decisive as the proponents of unpredictability claim
in their reports in very radical forms. There were already some
critical responses to the above position in EOS (Gusev, 1998; Lomnitz, 1998).

Here I would like to present my personal point of view on the problem.
First of all let us consider the consequences of nonlinearity.

i. The statement on absolute unpredictability on nonlinear processes
is not correct. (Lomnitz, 1998). The behaviour of nonlinear system is
predictable on the limited time interval T. The limit of predictability time
is given by the Kolmogorov-Sinai (KS) entropy h(X)where X  is a set
of states. The system became unpredictable after the passage of time T ~ 1/h(X) (Abarbanel et al, 1993) when the X  became equal to the number of
states available for the orbits of the system (this time for seismicity 
can be from several hundreds to several thousands of years). Alternatively,
as KS-entropy equals to the sum of the positive Lyapunov exponents,
“the limited predictability of the chaos is quantified by the set of Lyapunov
exponents,  which can be determined from the measurements itself”
(Abarbanel et al, 1993).

The examples of relatively successful limited predictability are short-term
weather forecasts and volcano eruption forecasts. It has been shown that
(Shaw, Chouet, 1991) that volcano tremors can be described
mathematically by chaotic models which means that volcano areas
are close to the critical state. Nevertheless, volcano eruptions are
successively predicted on the basis of geochemical, deformation and
seismoacoustic observations. As has been mentioned the weather is
also reliably predicted for short time intervals (3-4 days) though the
atmosphere is a typical nonlinear system. Taking into account significant
difference in the rates of atmospheric and tectonic processes due to
different viscosity of media, the 3-4-days predictability period for
atmosphere should correspond to months and years in lithosphere.

 About SOC. The fact of close resemblance of seismic catalogues
and SOC calculations is not a definite proof that the lithosphere is
just in the state of SOC. For example, mathematical analogues of
Gutenberg-Richter relationship can be obtained by different approaches:
from percolation model of fracture (Chelidze, 1987, 1993), from
kinetic model of strength (Petrov, 1984), etc.

In reality, the lithosphere can be not just in the critical state, but close
to it (Kagan, 1997). This is enough to make things quite different. For
example, in systems, which are close to the critical state, there is still a
characteristic size, namely, the largest finite cluster size Lc. The size of
finite clusters grows as the system approaches the critical state and this
allows prediction of the distance to it Dp, because the properties of
system (so called characteristic functions) depend on the size of clusters.
The time, needed to cover the distance Dp can be large enough even
for small Dp , especially if the process follows logarithmic kinetics
(Petrov, 1984).

If there are no predictors of the strong event, then there should not
be also after-event effects. The most obvious and undisputable examples
of after-effects are aftershock activity, which lasts months and years, and
water level relaxation in deep wells of the similar duration. Than, if there
is clear evidence of long strain relaxation period after strong event why
should be rejected the possibility of strain accumulation period before it?
If the relaxation of stress takes several years, why the accumulation
process does not need any time? If any small shock can grow into
strong event, why strong events are so rear?

Even proponents of unpredictability agree that the seismic hazard
assessment problem is solvable. But if the strong earthquake can be
triggered by any small event, what sense is in doing seismic zoning?
Why in some places the maximal expected earthquake magnitude
will not exceed 6 if any small shock can trigger event of any magnitude?

The matter is that the unlimited heterogeneity, that is self-similarity to
infinity, is realized only in mathematical models. Real physical and
geological systems are finite. This introduces the another characteristic
size – the size of system, which sets limit to earthquake size and makes
the hypothesis of unbounded heterogeneity (Leary, 1997) unrealistic.

The last but not least in the nonlinear approach is the problem of connectivity.
The fractal models and SOC theory do not consider the problem.
At the same time the analysis of connectivity may be very important if,
say, pore pressure is decisive in nucleation of earthquakes (Sibson, 1994,
Muir Wood, 1994). If the connectivity is essential, percolation theory seems
to be the best tool for assessment of closeness to the critical state, as it is
focused on the analysis of connectivity of elementary objects, such as pores,
fractures or just overstressed volumes (Chelidze, 1987, 1993).

ii.As a rule, all precursors are considered as nonreliable by unpredictability
proponents due to the small statistics of such events as the sequence predictor-earthquake and possibility on non seismic origin of anomalies. At the
same time they do not consider such situations, as appearance of three,
four or more predictive anomalies before a given large earthquake.
Ignoring consistent appearance of several predictors reminds of one
funny story: An undisciplined driver crosses the crossroads on the red
light. When the policemen stopped him, he denied his fault, saying that
there was not the red light on. So, you think, sir – said the policemen -
that all these cars are out of petrol simultaneously?

Indeed, when there is the great chance to misidentify some event due to
the high level of noise, physicist uses the coincidence technique. In the
cosmic ray physics, for example, the particle of cosmic origin is identified,
when several layers of sensors register the particle simultaneously. Thus
the statistical validity of several consistent anomalies in various fields
should be given significant weight in order to make correct statistical
assessments.

Of course the problem of “hunchback’s jacket” is a difficult one, but
shuffling and bootstrap procedures may help to avoid biased assessments.

iii. In laboratory tests of delayed fracture of rocks, both intact and
containing artificial fracture, as well as in stick-slip experiments a plethora
of precursors of main rupture has been found on the basis of simultaneous
monitoring of acoustic, electric, local strain fields, gas emission and other
phenomena (Sobolev, 1996). What is so specific in the seismic process
that leads to taboo on prediction?

I conclude that the statement of unpredictability of strong earthquakes
follows only from abstract mathematical models, which do not adequately
take into account real physical processes, having place in real geological
systems.

It seems that contradiction of competing paradigms of unpredictable
nonlinearity and predictable strain or damage accumulation models can
be resolved by decoupling of these two approaches. That means that
both of them are valid, but they have different limits of validity.

Such models as SOC and cellular automata are mainly focused on

simulation and prediction of fundamental features of seismic regime,
that is for modeling seismic catalogues and are less helpful for prediction
of the next strong event. These models do not allow understanding the

nature of strain-related anomalies in various geophysical fields. But the
preparation of the strong earthquake is not a purely seismic process.
Even during the earthquake only small part of released energy is
transformed into seis
mic waves. During preparation process the seismic component
plays even less role: the main feature here is mostly aseismic deformation
which may cause, nevertheless, strong anomalies in strain-sensitive
geophysical, geochemical and geodynamical fields, due, say, to evolution
of fracture network before strong event and redistribution of pore fluid.
Percolation fracture model (Chelidze, 1987 1993; Herrmann
and Roux, 1990) and kinetic theory of strength (Petrov, 1984)
allow to understand the process of nucleation, coagulation and
growth of clusters of microfractures during delayed fracture and
predict evolution of physical properties of system during destruction.
Theoretical predictions agree quite well with experimental data on
delayed fracture of rocks (Chelidze, 1987). The most important
point is that in percolation and kinetic models closeness to the critical
state can be assessed by analysis of behaviour of characteristic functions,
which depend on the size of finite clusters of defects. It should be stressed
also that percolation model naturally explains the spatio-temporal
heterogeneity of response of geophysical fields to the strain variation
in terms of anomalous strain-sensitivity of objects that are close to
percolation state (Chelidze, 1987, 1993).

We can illustrate the above statement on decoupling of competing
paradigms by the following example: in microscopic studies the
analysis of overall pattern of rock (its stricture, etc) is made at
small magnification (analogue of SOC model), but if the individual
grain is to be studied, quite different magnification should be used
(percolation model).

It seems that it is impossible to elaborate the unique theory, which
explains equally well the overall seismic regime and the process of
preparation of the individual strong event.

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