Nonlinear dynamics of the lithoshere and earthquake prediction

Nonlinear Dynamics of the Lithosphere
and EarthquakePrediction

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SSSyn - An Interdisciplinary Series on Complex Systems
The success of the Springer Series in Synergetics has been made possible by the
contributions of outstanding authors who presented their quite often pioneering
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Indeed, interdisciplinarity is one of the main features of this series. But interdisciplinarity is not enough: The main goal is the search for common features of
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Vladimir 1. Keilis- Borok
Alexandre A. Soloviev (Eds.)

Nonlinear Dynamics
of the Lithosphere
and Earthquake
Prediction
With 133 Figures and 51 Tables

,

Springer


Professor Dr. Vladimir I. Keilis-Borok
Professor Dr. Alexandre A. Soloviev
Russian Academy of Sciences
International Institute of Earthquake Prediction
Theory and Mathematical Geophysics
Warshavskoye sh., 79, kor. 2
117556Moscow, Russia

Library of Congress Cataloging-in-Publication Data
Nonlinear dynamics of the lithosphere and earthquake predictionlVladimir I. Keilis-Borok, Alexandre A.
Soloviev (eds.).
p.cm.- (Springer series in synergetics, ISSN 0172-7389)
Includes biblographical references. ISBN 354043528X (alk. paper)
1. Earthquake prediction. 2. Geodynamics-Mathematical models. I. Keilis-Borok, Vladimir Isaakovich. II.
Soloviev, Alexandre A., 1947- III. Springer series in synergetics (Unnumbered)
QE538.8 .N66 2002 551.22-dc21 2002030442

ISSN 0172-7389
ISBN 3-540-43528-X Springer-Verlag Berlin Heidelberg New York

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Preface

The vulnerability of our civilization to earthquakes is rapidly growing, raising earthquakes to the ranks of major threats faced by humankind. Earthquake prediction is necessary to reduce that threat by undertaking disasterpreparedness measures. This is one of the critically urgent problems whose
solution requires fundamental research. At the same time, prediction is a major tool of basic science, a source of heuristic constraints and the final test of
theories.
This volume summarizes the state-of-the-art in earthquake prediction. Its
following aspects are considered:
- Existing prediction algorithms and the quality of predictions they provide.

- Application of such predictions for damage reduction, given their current
accuracy, so far limited.
- Fundamental understanding of the lithosphere gained in earthquake
prediction research.
- Emerging possibilities for major improvements of earthquake prediction
methods.
- Potential implications for predicting other disasters, besides earthquakes.
Methodologies. At the heart of the research described here is the integration of three methodologies: phenomenological analysis of observations;
"universal" models of complex systems such as those considered in statistical
physics and nonlinear dynamics; and Earth-specific models of tectonic fault
networks. In addition, the theory of optimal control is used to link earthquake
prediction with earthquake preparedness.
Focus. This scope, broad as it is, covers a specific part of the much wider field
of earthquake prediction, which is intrinsically connected with most of the
solid Earth sciences, as well as with many branches of other natural sciences
and mathematics. Specifically, we review the research aimed at unambiguously defined algorithms and their validation by advance prediction. That
focus is central both for a fundamental understanding of the process expressed
in seismicity and for preventing damage from earthquakes, for a scholar in
quest of a theory and a decision-maker with responsibility for escalating or
relaxing disaster preparedness. Both are in dire need of hard facts, which
only prediction can establish.


VI

Preface

Consecutive approximations. The studies presented here regard the seismically active lithosphere as a nonlinear (chaotic or complex) dissipative
system with strong earthquakes for critical transitions. Such systems may be
predictable, up to a limit, only after averaging (coarse-graining). Accordingly,

we consider prediction based on a holistic approach, "from the whole to
details." The problem of prediction is posed then as a successive, step-by-step,
narrowing of the time interval, territory, and magnitude range where a strong
earthquake can be expected. Such division into successive approximations
is dictated by similar step-by-step development of critical transitions. At
the same time, this division corresponds to the needs of disaster preparedness.
Most of the findings described here concern intermediate-term prediction
(with alarms lasting years) based on premonitory seismicity patterns. There
are compelling reasons to expect that these findings are applicable to other
data and other stages of prediction. We also consider the background stage of
prediction the identification of areas where epicenters of strong earthquakes
can be located.
Content. This volume consists of six chapters.
Chapter 1 outlines the fundamentals of earthquake prediction: (i) Hierarchical structure of fault networks. (ii) Origin of the complexity of the lithosphere that is a multitude of mechanisms destabilizing the stress-strength
field. The strength field is particularly unstable, so analysis of the stress
field per se might not always be relevant. (iii) General scheme of prediction,
using the pattern recognition approach. (iv) Four paradigms of earthquake
prediction research concerning basic types of premonitory phenomena, their
common features (long-range correlations, scaling, and similarity), and their
dual nature, partly "universal" and partly Earth-specific.
Chapter 2 explores seismicity generated by hierarchical lattice models
with dynamic self-organized criticality. Modeled seismicity shows the typical
behavior of self-similar systems in a near-critical state; at the same time, it
exhibits major features of observed seismicity, premonitory seismicity patterns included. The heterogeneity of the strength distribution introduced in
the models leads to the discovery of three types of criticality. The predictability of the models varies with time, raising the problem of the prediction of
predictability, and, on a longer timescale, the prediction of the switching of
a seismic regime.
Chapter 3 describes the model of a block-and-fault system; it consists of
rigid blocks connected by thin viscoelastic layers ("faults"). The model is
Earth-specific: it allows us to set up concrete driving tectonic forces, the geometry of blocks, and the rheology of fault zones. The model generates stickslip movement of blocks comprising seismicity and slow movements. Such

models provide a very straightforward tool for a broad range of problems:
(i) the connection between seismicity and geodynamics; (ii) the dependence
of seismicity on the general properties of fault networks, i.e. the fragmentation


Preface

VII

of structures, the rotation of blocks, the direction of the driving forces, etc.;
(iii) obviously, direct modeling of earthquake prediction.
Chapter 4 describes a family of earthquake prediction algorithms and
their applications worldwide. Several algorithms are put to the test, unprecedented in rigor and scale. By and large, about 80% of earthquakes
are anticipated by alarms, and alarms occupy 10 to 30% of the time-space
considered. Particularly successful is the advance prediction of the largest
earthquakes of magnitude 8 or more. Recently, advance predictions have
been posted on web sites, along with accumulating scores of their outcomes,
successes, and failures alike: see .html
and />Chapter 5 connects earthquake prediction with earthquake preparedness.
The general strategy of the response to predictions consists of escalation or
deescalation of safety measures, depending on the expected losses and the
accuracy of the prediction. The mathematical solution of that problem is
based on the theory of optimal control. Much can be done by applying this
strategy on a qualitative level.
Chapter 6 concerns background prediction: the recognition of still unknown areas, where epicenters of strong earthquakes may be situated, i.e.
where strong earthquakes can nucleate. These are densely fragmented structures, nodes, formed about fault intersections. Recognition is based on geological and geophysical data, satellite observations included. Maps of such areas
have been published since the early 1970s for numerous regions of the world,
including such well-studied ones as California and the Circumpacific. Subsequent seismic history confirmed these maps: 90% of the new earthquakes
(61 out of 68) occurred within predicted areas; in 19 of these areas, such
earthquakes had been previously unknown. This method is among the best

validated and less widely known, illustrating an awareness gap in earthquake
prediction studies.
.

Collaboration. The findings reviewed here were obtained because of broad
cooperation comprising about 20 institutions in 12 countries and several international projects. The authors have been privileged to have permanent collaboration with the Abdus Salam International Center for Theoretical Physics,
the Universities of Rome ("La Sapienza") and Trieste (Italy), the Institute of
the Physics of the Earth, Paris, and the Observatory of Nice (France), Cornell
and Purdue Universities, the University of California, Los Angeles, and the
United States Geological Survey (USA). The authors are deeply grateful to
our colleagues: C.J. Allegre, B. Cheng, V. Courtillot, J.W. Dewey, J. Filson,
U. Frisch, A.M. Gabrielov, LM. Gelfand, M. Ghil, A. Giesecke, J.H. Healy,
L.V. Kantorovich, L. Knopoff, LV. Kuznetsov, J.-L. Le Mouel, B.M. Naimark,
W. Newman, E. Nyland, Yu.S. Osipov, G.F. Panza, L. Pietronero, V.F. Pisarenko, F. Press, A.G. Prozorov, LM. Rotwain, D.V. Rundqvist, M.A. Sadovsky, D. Sornette, D.L. Turcotte, S. Uyeda, LA. Vorobieva, LV. Zaliapin
and A. Zelevinsky.


VIII

Preface

We worked in the fascinating environment of the International Institute
of Earthquake Prediction Theory and Mathematical Geophysics, the Russian
Academy of Sciences, and can hardly describe our eternal debt to its faculty
and staff.
Acknowledgements. Considerable part of the work was done under the
auspices of the International Decade of Natural Disasters Reduction (ICSU
Project "Non-linear Dynamics of the Lithosphere and Intermediate-term
Earthquake Prediction"). We received invaluable support from the James
S. McDonnell Foundation (the 21st Century Collaborative Activity Award

for Studying Complex Systems); the International Science and Technology
Center (projects 1293 and 1538); the US Civilian Research & Development
Foundation for the Independent States of the Former Soviet Union (projects
RMO-1246 and RG2-2237); the US National Science Foundation (grants
EAR-9804859 and EAR-9423818); the Russian Foundation for Basic Research
(grant 00-15-98507); the NATO Science for Peace Program (project 972266);
UNESCO (UNESCO-IGCP project 414); and the International Association
for the Promotion of Cooperation with Scientists from the Independent States
of the Former Soviet Union (projects INTASjRFFI-97-1914, INTAS-94-232,
INTAS-93-457 and INTAS-93-809).
The studies described in the volume were intensely discussed at the Workshops on Nonlinear Dynamics and Earthquake Prediction organized by the
Abdus Salam International Center for Theoretical Physics; the last one convened in October 2001, right before this volume went to Springer-Verlag;
it was supported by the European Commission (Contract HPCFCT-200000007).

Moscow
May 2002

V.I. Keilis-Borok
A.A. Soloviev


Contents

1 Fundamentals of Earthquake Prediction: Four Paradigms
V.1. Keilis-Borok. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.1 Introduction................................................
1.2 Lithosphere as a Complex Hierarchical System . . . . . . . . . . . . . . . . . .

1.2.1 Hierarchy.............................................
1.2.2 "Physical" Instability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 "Geometric" Instability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
1.2.4 Generalization: Complexity and Critical Phenomena. . . . . . ..
1.3 General Scheme of Prediction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
1.3.1 Formulation of the Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . ..
1.3.2 An Early Example .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
1.3.3 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
1.4 Error Diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
1.5 Four Paradigms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
1.5.1 First Paradigm: Basic Types of Premonitory Phenomena. . ..
1.5.2 Second Paradigm: Long-Range Correlations. . . . . . . . . . . . . ..
1.5.3 Third Paradigm: Similarity. . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
1.5.4 Fourth Paradigm: Dual Nature of Premonitory Phenomena..
1.6 Earthquake Prediction and Earthquake Preparedness
1.7 A Turning Point: Emerging Possibilities yet Unexplored. . . . . . . . ..
1.7.1 The Near-at-Hand Research Lines. . . . . . . . . . . . . . . . . . . . . . ..
1.7.2 The Goals

1
5
5
7
10
13
14
15
15
17
19

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21
23
25
27
32
34
34
36

2 Hierarchical Models of Seismicity
M. Shnirman, E. Blanter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

37

2.1 Introduction................................................
2.1.1 Modeling and Hierarchy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
2.1.2 Self-similarity of Seismicity. . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
2.1.3 Inverse Cascade Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
2.1.4 Earthquake Prediction and Synthetic Seismicity
2.2 Static Hierarchical Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
2.2.1 General Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
2.2.2 Phase Transition in a Homogeneous Model. . . . . . . . . . . . . . ..
2.2.3 Heterogeneity and Stable Criticality. . . . . . . . . . . . . . . . . . . . ..

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46


X

Contents

2.3 Dynamic Hierarchical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
2.3.1 General Description of the Dynamic Model. . . . . . . . . . . . . . ..
2.3.2 Stationary Solution and Phase Transition . . . . . . . . . . . . . . . ..
2.3.3 Heterogeneity in the Dynamic Model. . . . . . . . . . . . . . . . . . . ..
2.3.4 The Feedback Relation and the Evolution
of Scaling Properties
2.3.5 Prediction and Predictability of Strong Events. . . . . . . . . . . ..
2.4 Complex Hierarchical Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
2.4.1 Description of the Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
2.4.2 Seismic Patterns in the Model . . . . . . . . . . . . . . . . . . . . . . . . . ..
2.5 Conclusions and Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
3 Models of Dynamics of Block-and-Fault Systems
A. Soloviev, A. Ismail-Zadeh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
3.1 Introduction................................................
3.2 Description of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
3.2.1 Block Structure Geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
3.2.2 Block Movement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
3.2.3 Interaction Between Blocks and the Underlying Medium. . ..
3.2.4 Interaction Between Blocks Along Fault Planes . . . . . . . . . . ..
3.2.5 Equations of Equilibrium

3.2.6 Discretization
3.2.7 Earthquake and Creep. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
3.3 Dependence of a Synthetic Earthquake Flow
on Structure Fragmentation and Boundary Movements . . . . . . . . . ..
3.3.1 Block Structures and Cases of Boundary Movements
Under Consideration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
3.3.2 Results of Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
3.3.3 Discussion of Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
3.4 Space-Time Correlation Between Synthetic Earthquakes
3.4.1 Clustering of Synthetic Earthquakes. . . . . . . . . . . . . . . . . . . . ..
3.4.2 Long-Range Interaction Between Synthetic Earthquakes ....
3.5 Block Models of Seismicity
in Arc Subduction Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
3.5.1 A Model of an Abstract Arc Subduction Zone. . . . . . . . . . . ..
3.5.2 Model of the Sunda Arc
3.6 Models of Block-and-Fault Dynamics of the Vrancea Region
(the Southeastern Carpathians)
3.6.1 Introduction to the Seismicity and Geodynamics
of the Region
3.6.2 Block Structure of the Vrancea Region: Model A
3.6.3 Comparing Vrancea Seismicity with the Results
from Model A

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63

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Contents

3.6.4 Numerical Tests on Model A Parameters
3.6.5 Source Mechanisms of Synthetic Seismicity
3.6.6 Block Structure of the Vrancea Region: Model B
3.6.7 Synthetic Features of Model Band Vrancea Seismicity
3.7 Modeling Block Structure Dynamics of the Western Alps
3.7.1 Block Structure Approximating a Morphostructural Scheme
of the Western Alps
3.7.2 Synthetic Features and the Seismicity of the Region
3.8 Conclusion

4 Earthquake Prediction
V. Kossobokov, P. Shebalin
4.1 Introduction
4.2 What Is an Earthquake Prediction?
4.3 Reproducible Prediction Algorithms
4.3.1 Data for Precursor Detection
4.3.2 General Scheme of Data Analysis
4.3.3 Major Common Characteristics
of Premonitory Seismic Patterns
4.3.4 Statistical Significance and Efficiency of Predictions
4.4 Validated Precursory Seismic Patterns
4.4.1 Pattern E
4.4.2 Burst of Aftershocks or Pattern B
4.4.3 Algorithm M8
4.4.4 Algorithm MSc or "The Mendocino Scenario"
4.4.5 Global Testing of Algorithms M8 and MSc
4.4.6 Algorithm CN
4.4.7 Will a Subsequent Strong Earthquake Occur Soon?
Algorithm SSE
4.5 Seismic Patterns Submitted for Testing

4.5.1 Seismic Reversal (SR)
4.5.2 Premonitory Increase of the Correlation Range
(Pattern ROC)
4.5.3 Premonitory Spreading of Seismicity Across the Network
of Faults: Pattern Accord
4.6 Discussion

XI
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159

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197
201
205

5 Earthquake Prediction Strategies: A Theoretical Analysis
G.M. Molchan

209

5.1 Introduction
5.2 Prediction Involving Two Types of Alert
5.2.1 The Error Diagram
5.2.2 The Optimal Prediction Strategy
5.2.3 Prediction of the Characteristic Earthquake

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211
211
216
218


XII

5.3
5.4

5.5
5.6

Contents
5.2.4 Stability of the Minimax Strategy
5.2.5 Prediction on the San Andreas Fault
Prediction with Multiphase Alerts
Statistical Problems
5.4.1 The Performance of Prediction Algorithms
5.4.2 Estimation of (n, T)
Estimation of r(t)
5.5.1 Comments
Appendix

6 Recognition of Earthquake-Prone Areas
A. Gorshkov, V. Kossobokov, A. Soloviev

220
223
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229
229
230
230
232
233
239

6.1 Introduction

6.2 Unraveling Earthquake-Prone Areas
as a Pattern Recognition Problem
6.2.1 Parameterization of Recognition Patterns
6.2.2 Evaluating the Reliability of Recognition
6.3 Choosing Objects for Recognition
6.3.1 The Basics of Morphostructural Zoning
6.3.2 Objects of Recognition Derived
from Morphostructural Zoning. . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Recognition of Where Strong Earthquakes Can Occur
6.4.1 The Greater Caucasus
6.4.2 The Western Alps
6.4.3 Pattern Recognition Applied to Earthquakes in California
6.4.4 Pattern Recognition of the Great (M ~ 8.2)
Earthquake-Prone Segments of Major Seismic Belts
6.5 Conclusion: Confirmation of Pattern Recognition Results
by Subsequent Large Earthquakes

239

305

References

311

Index

333

240

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252
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282
288
297


List of Contributors

E. Blanter,

A. Gorshkov,

A. Ismail-Zadeh,

V. Keilis-Borok l ,

V. Kossobokov,

G. Molchan,

P. Shebalin,

M. Shnirman,

A. Soloviev


International Institute
of Earthquake Prediction Theory
and Mathematical Geophysics,
Russian Academy of Sciences
Warshavskoye shosse, 79, kor. 2
117556, Moscow-556, Russia

lalso
Institute of Geophysics and
Planetary Physics and Department
of Earth and Space Sciences,
University of California,
Los Angeles,
405 Hilgard av., IGPP
Los Angeles, CA 90095-1567, USA




Fundamentals of Earthquake
Four Paradigms

Prediction:

V.I. Keilis-Borok

1.1

Introduction

About a million earthquakes of magnitude 2 or more are registered each year
worldwide. About a hundred of them cause serious damage and once or twice
in a decade,a catastrophic earthquake occurs. The vulnerability ofour world
to earthquakes is rapidly growing due to well-known global trends: proliferation of high-risk construction, such as nuclear power plants, high dams,
radioactive waste disposals, lifelines, etc.; deterioration of the ground and
destabilization of engineering infrastructures in megacities;destabilization of
the environment; population growth; and other factors, including the escalating socioeconomic volatility of the global village. Today a single earthquake
with subsequent ripple effects may take up to a million of lives; cause material
damage up to $1012;destroy a megacity; trigger a global economic depression
(e.g. if it occurs in Tokyo); trigger ecological catastrophe rendering a large
territory inhabitable; and destabilize the military balance in a region (e.g.,
the Middle East). Regions of low seismicity became highly vulnerable; among
them are the European and Indian platforms and central and eastern United
States. These regions harbor scores of vulnerable megacities such as New
York, Moscow and Rome.
As a result, earthquakes joined the ranks of the major disasters that, in
the vrords of J. Wiesner, became "a threat to civilization survival, as great as
was ever posed by Hitler, Stalin or the atom bomb." Earthquake prediction at
any stage would open the possibility of reducing the damage by undertaking
disaster-preparedness mea,sures.
The problem. The problem of earthquake prediction consists of consecutive, step-by-step, narrowing of the time interval, space, and magnitude
ranges where a strong earthquake should be expected. Five stages of prediction are usually distinguished. The background stage provides maps with the
territorial distribution of the maximum possible magnitude and recurrence
time of destructive earthquakes of different magnitudes. Four subsequent
stages, fuzzily divided, include the time-prediction; they differ in the characteristic time interval covered by an alarm. These stages are as follows:

V.L Keilis-Borok

o
o
c
o

long-term (101 years),
interrnedia,te-tertn (years),
short-temn (I0-r to 10-2 years), and
imrnediate (10-3 years or less).

Such division into stages is dictated by the character of the process that
Ieads to a strong earthquake and by the needs of earthquake preparednessl
the latter comprises an arsenal of safety measures for each stage of prediction,
as in preparedness for war.
Prehistory
(2O-2O hindsight).
New fundamental understanding of the
earthquake prediction problem was formed during the last 40 or so years,
triggering entirely new lines of research. In hindsight, this understanding
stems from the following unrelated developments in the early 1960s.
- F. Press initiated the installation of a state-of-the-art global seismological network augmented by some regional and local ones. Thus, a uniform
database began to accumulate.
E. Lorenz discovered deterministic chaos in an ordinary natural process,
thermal convection in the atmosphere [Lor63]. This triggered the recognition
of deterministic chaos in a multitude of natural and socioeconomicprocesses;
however, the turn of seismicity and geodynamics in general came about
a quarter of a century later [Kei90a,BCT92,T\rr97,NGT94]. The phenomenon
of deterministic chaos was eventually generalized by a wider concept of complexity [CKO+80,Hol95,HSSS98,Gel94].

- I. Gelfand and J. T\rkey, working independently, created a new culture
of exploratory data analysis that allows us to overcome the complexity of
a process considered. Among the essential elements of this culture is a very
robust representation of information and exhaustive numerical tests validating the results of analysis [GGK+76,Tuk77]. Specifically,pattern recognition
of infrequent events developed by the school of I. Gelfand is widely used in
the studies reviewed here.
L. Knopoff and B. Burridge demonstrated that a simple system of
interacting elements may reproduce a realistically complex seismicity, fitting
many basic heuristic constraints [BK67]. That extended to seismology the
abstract models of interacting elements developed in statistical physics.
* L. Malinovskaya found a premonitory seismicity pattern reflecting the
rise of seismic activity [KM64]. This is the first reported earthquake precursor formally defined and featuring long-range correlations and worldwide
similarity.
With broader authorship,
plate tectonics established the connection between seismicity and largescale dynamics of the lithosphere;
- research in experimental mineralogy and mechanics of rocks revealed
a multitude of mechanisms that may destabilize the strength in fault zones.


1

Fundamentals of Earthquake Prediction: Four Paradigms

3

Four paradigms. In the wake of these developments, the following four paradigms have been established at the crossroad between exploratory data analysis, statistical physics, and the dynamics of fault networks [Kei94, Kei96a].
I. Basic types of premonitory phenomena comprising the variation in
relevant observable fields.
II. Long-range correlations in fault system dynamics. Premonitory phenomena are formed not only in the vicinity of the incipient source but also
within a much wider area.

III. Partial similarity of premonitory phenomena in diverse conditions,
from fracturing in laboratory samples to major earthquakes worldwide and
possibly even to starquakes.
IV. The dual nature of premonitory phenomena. Some of them are "universal," common for complex nonlinear systems of different origin; others are
Earth-specific.
Holistic approach to prediction. Complex systems are not predictable
with absolute precision. However, after a coarse-graining (on not too detailed
a scale), premonitory phenomena emerge and a system becomes predictable,
up to the limits [FS87, MFZ+90, Kra93, Ge194, Hol95, Kad76]. Accordingly,
prediction of complex systems requires a holistic approach, "from the whole to
details" in consecutive approximations, starting with the most robust coarsegraining of the processes considered. Table 1.1 compares the holistic approach
with the complementary (but not necessarily contradictory) reductionistic
approach, "from the details to the whole."
The studies reviewed here are based on the holistic approach. It makes
it possible to overcome the complexity itself and the chronic imperfection of
observations as well. This is achieved at an unavoidable price: the accuracy
of prediction is limited.
"With four exponents I can fit the elephant" (E. Fermi). Earthquake
prediction algorithms include adjustable parameters and other elements that
have to be data-fitted retrospectively to "predict" past earthquakes. The
designer of the algorithm does not know whether it will also predict future
earthquakes and has at least to make sure that predictions are not sensitive
to slight variations of adjustable elements. Such sensitivity analysis takes
most of the effort in prediction research. It is based on the error diagram,
a staple of that research (Sect. 1.4), and the link of prediction with disasterpreparedness.
The only final test of an algorithm is advance prediction. A series of
experiments in advance prediction of strong earthquakes in numerous regions
worldwide has been launched (see Chap. 4 and [KS99, MDRD90]).
By and large the algorithms predict 80-90% of strong earthquakes, and
alarms occupy 10-30% of the time-space considered. The major drawbacks

are the rate of false alarms and the limited probability gain, between 3 and
10 for different algorithms.


4

V.1. Keilis-Borok
Table 1.1. Two complementary approaches to earthquake prediction

"REDUCTIONISM"
(from details to the whole)

"HOLISM"
(from the whole to details)

Premonitory phenomena
preceding an earthquake with linear source dimension L
are formed
near the incipient source

in a network of faults
of linear size on a timescale
- 10 2 L
tens of years
- 10£
years
- L
years to months
- possibly, fractions of L, i.e., in the vicinity of
the hypocenter, on a smaller timescale

Premonitory phenomena
are specific to mechanisms
controlling the strength, e.g.
friction, rock-fluid interaction,
stress corrosion, buckling, etc.

are divided into
- "universal" ones common to many
chaotic systems
- those depending on the geometry of fault
network
- mechanism-specific ones.

Premonitory phenomena in different regions and energy ranges
are different

are to a considerable extent similar
Constitutive equations

are local

are nonlocal
Triggering of earthquakes is controlled

by a strength-stress
difference in the incipient source

also by geometric incompatibility near
the fault junctions that may supersede

a strength-stress criterion

Indispensable for further research is the unique uniform collection of errors
and correct predictions accumulated during these experiments.
This chapter outlines the fundamentals of earthquake prediction, as a common background for the subsequent chapters. It includes: the physical origin
of complexity in the seismically active lithosphere (Sect. 1.2); the general
scheme of prediction (1.3); the evaluation of prediction algorithms by error
diagrams (1.4); the abovementioned paradigms and classification of premon-


1

Fundamentals of Earthquake Prediction: Four Paradigms

5

itory seismicity patterns (1.5); the link between earthquake prediction and
disaster-preparedness (1.6); and emerging possibilities of developing the next
generation of earthquake prediction methods (1.7).

1.2

Lithosphere as a Complex Hierarchical System

Origin of complexity. Two major factors cause complexity of the lithosphere [Kei90a, Tur97]: (i) a hierarchical structure extending from tectonic
plates to the grains of rocks; (ii) instability caused by a multitude of nonlinear
mechanisms controlling the strength-stress field. On a timescale relevant to
earthquake prediction, 102 years or less, these factors, by an inevitable conjecture, turn the lithosphere into a hierarchical dissipative complex system.
Critical transitions. A prominent feature of complex systems is the persistent reoccurrence of abrupt overall changes called critical transitions or
critical phenomena.

Strong earthquakes may be regarded as critical phenomena in the lithosphere. Note that an earthquake may be a critical phenomenon in a certain
volume of the lithosphere and part of the background seismicity in a larger
volume.
1.2.1

Hierarchy

Blocks. The structure of the lithosphere presents a hierarchy of volumes,
or blocks, that move relative to each other. The largest blocks are the major
tectonic plates, of continental size, 103 -10 4 km in linear dimension. They are
divided into smaller blocks, such as shields or mountain belts. After 15 - 20
consecutive divisions, we come to about 1025 grains of rocks of millimeter
size.
Boundary zones. Blocks are separated by less rigid "boundary zones,"
whose width is 10 - 100 times smaller than the characteristic size of the blocks
they separate. Boundary zones are named differently, depending on size. They
are called fault zones, high in the hierarchy; then faults; sliding surfaces;
and, finally, interfaces between grains of rock. Except at the lowest level of
the hierarchy, a boundary zone presents a similar hierarchical structure with
more dense division: it consists of blocks, divided by boundary zones, etc.
Nodes. Even more densely fractured mosaic structures, called nodes, are
formed in the vicinity of the intersections and junctions of faults. Their
origin is due, roughly speaking, to the collision of the corners of blocks
[GKJ96, Kin83, Kin86]. The formalized definition of nodes is given in
[AGG+77]. Nodes playa singular role in the dynamics of the lithosphere.


6

V.I. Keilis-Borok

- A special type of instability is concentmted within nodes (Sect. 1.2).
- Strong earthquakes nucleate in nodes. As demonstrated in a series of
studies, the epicenters of strong earthquakes worldwide are located within
nodes, more precisely, within some nodes that can be identified by pattern
recognition ( [GGK+76], Chap. 6).
Nodes are well known in structural geology and geomorphology and play
a prominent textbook role in geological prospecting. However, their connection with earthquakes is sometimes overlooked in earthquake studies.
Is the division "blocks:::::? faults ee- nodes" always complete? We
have stipulated above the division of a tectonic region into blocks separated by
closed contours of faults. Such a division has developed throughout geological
history and may be not complete, particularly in tectonically young regions.
For example, some faults comprise a bundle of small ruptures that are not
(or not yet) evolved into a hierarchical network; the boundary of a block may
be a flexure not yet ruptured, etc.
Fault networks. Systems of boundary zones and nodes are called here fault
networks; this term sounds more familiar, though it is less precise.
Fault network, a stockpile of instability. Boundary zones of different
rank, from the Circumpacific seismic belt, with giant triple junctions for
nodes, to interfaces between rock grains, with the corners of grains for nodes,
their great diversity notwithstanding, playa similar role in lithosphere dynamics. Specifically, although tectonic energy is stored in the whole volume of
the lithosphere and well beneath, energy release is to a large extent controlled
by the processes in relatively thin fault networks. This contrast is due to the
following reasons.
First, the strength of a fault network is smaller than the strength of the
blocks it separates: fault networks are weakened by denser fragmentation
and higher permeability to fluids. For that reason, tectonic deformations are
concentrated in fault networks, whereas blocks move essentially "as a whole,"
with a relatively smaller rate of internal deformations. In other words, on the
timescale directly relevant to earthquake prediction, tens of years or less, the

major part of lithosphere dynamics is realized through deformation of fault
networks and the relative movement of blocks.
Second, the strength of a fault network is not only smaller, but also
highly unstable, sensitive to many processes there. This instability, central
for understanding seismicity, is discussed below.
Physical and geometric instabilities. We term as "physical" the instability originated by a physical or chemical mechanism at the elementary (micro)
level, and as "geometric," the instability controlled by the geometry of the
fault network on a global (macro) level. These instabilities largely control the
dynamics of seismicity, including the occurrence of strong earthquakes.


1

1.2.2

Fundamentals of Earthquake Prediction: Four Paradigms

7

"Physical" Instability [Kei90a]

As in any solid body, deformation and fracturing in the lithosphere are
controlled by the strength-stress field. Strength is in turn controlled by
a great multitude of interdependent mechanisms concentrated in the fault
network. We describe, for illustration, several such mechanisms starting with
the impact of fluids.
Rehbinder effect, or stress corrosion [GK83, Tra85].
Mechanism. Many solid substances lose their strength when they come in
contact with certain surface-active liquids. The liquid diminishes the surface
tension J1 and consequently the strength, which is proportional to Vii by

Griffits criteria. When the strength drops, cracks may emerge under small
stress, even gravity might suffice. This triggers expansion of fatigue: liquid
penetrates cracks, they grow, and drops of liquid propel forward, until they
dissipate. This mechanism requiring very little energy to generate fracturing
was first discovered in metals and ceramics. Then such combinations of solid
substances and surface-active liquids were recognized among common ingredients of the lithosphere, e.g., basalt and sulfur solution. When they meet,
the basalt is permeated by a grid of cracks, and the efficient strength may
instantly drop by a factor of 10 or more due to this mechanism alone.
Geometry of weakened areas. Orientation of cracks at each point depends
on the stress field; it is normal to the main tensile stress. The stress field
in the lithosphere may be exceedingly diverse. Strictly limited, however, is
the geometry of weakened areas where cracks concentrate; such areas may be
of only a few types, determined by the theory of singularities. Some examples are shown in Fig. 1.1, where thin lines show the trajectories or cracks.
Each separatrix (a heavy line) separates the areas with different patterns of
trajectories.
When the source of a liquid appears in a place such as shown in Fig. 1.1
by arrows, the liquid that penetrates the cracks concentrates in the shaded
area, and its strength plummets. A slight displacement of the source across
the separatrix may lead to a strong change in the geometry of such fatigue;
it may be diverted to quite a different place and take quite a different shape,
although not an arbitrary one.
A new dimension is brought into this picture by the evolution of the stress
field, which is changing all the time for many reasons, including the feedback
from this very effect. Such evolution may change the type of a singularity,
make it disappear or create a new one, and the geometry of fatigue will follow
suit.
Sensitivity to chemical composition. The Rehbinder effect is highly sensitive to the chemical ingredients of the fluid, even in microconcentrations. For
example, gabbro and dolerite are affected only in the presence of iron oxides;
Kamchatka ultrabasic rocks are affected by andesite lava liquids only in the
presence of copper oxide, etc.

V.I. Keilis-Borok

/N t,

a/t
--Nt

:+>$$:Y

-r..\\

I I

t I

Fig.1.1. Instability caused by stress corrosion. The geometry of weakened areas
depends on the type of singularity and the place where the chemicallv active fluid
comes in. After lGK83]

Self-erci'tation.The impact of chemically active fluids increaseswith stress
in rocks, thus becoming self-exciting, because stress is always concentrated
near the corners of rock grains.
summ'ing up, the Rehbinder effect brings a strong and specific instability
into the dynamics of the lithosphere. This instability is controlled by the stress
field and by the geochemistry of fluids. The migration of fluids is accompanied
by the observable variations of the "fluids regime" and of electromagnetic and
geochemicalfields.
This effect might explain many premonitory seismic patterns. such an

explanation, however, has at least two limitations.
(i) The basic configurations of fatigue, as shown in Fig. 1.1, might be
realized only in small areas. The inhomogeneity of stress and strength fields
and the dissipation of fluids may destroy the formation of such configurations
on the scale of the observed premonitory patterns, which is tens to hundreds
of kilometers. More likely, these configurations are the elements composing
a more complicated infrastructure of fatigue.
(ii) The Rehbinder effect is not a single major mechanism by which fault
zones control the dynamics of the lithosphere. Even fluids alone may generate
other equally strong mechanisms.
Nonlinear

filtration [BKM8B].
Mechan'ism. one of the competing mechanisms is the more conventional filtration of fluids through fault zones. This processis modeled in
lBKMg3] as
the relative movement of impermeable blocks separated by a porous layer.
The latter is connected with a source of fluid migrating along the gradient
of


1 Fundamentalsof Earthquake Prediction: Four Paradigms

I

pressure. The fluid acts as a lubricant that reduces the friction and triggers
episodesof fast slip.
Further development brings in strong instability illustrated by Fig. 1'2.
when the porosity is subcritical (below a certain threshold), the slip, once
started, causes an increase in friction and self-decelerates. At most, the fluid
will trigger vacillating creep or a slow earthquake. However, when the porosity

exceeds a critical threshold, the slip causes a decrease in friction and the
incessantly forming microcracks start to self-accelerate, grow, and merge at
an escalating rate. The porosity can be raised above the critical threshold by
infiltration of a fluid itself; this will increase the tension, and the pores will
expand.

FaultZone

of Fluid

o
'o
c
lt

Porosity> C
f-accelerating)

Sliprate

Fig. 1.2. Instability caused
by the infiItration of a Iubricating fluid. A change of
porosity causes an abruPt
change in the slip rate. After lBKM83l

uaue. The propagation of critical porosity is described by
Destabi,ti,zati,on
the equation
0e l\t : V2 Lso ,

I : I,Lp; V2 : kopol(poqo),

a ) 2,

where p is porosity; p is the density of the fluid; and ko, po, pe, and 4s
are the characteristic values of permeability, pressure, porosity, and viscosity,
respectively. A is the Laplace Operator.
This is the famous nonlinear parabolic equation studied by Ya. Zeldovich
and I.Barenblatt [Bar96]. In the specific case considered here, nonlinearity
reflects the change of porosity and permeability from pressure'
Due to the nonlinearity, perturbations of g(r,t) propagate at a final velocity proportional to V. The values of V computed for realistic parameters
of Earth's crust include the range 10 102 kilometers per year, the same as
for the observed migration of seismicity along fault zones'


10

V.I. Keilis-Borok

A model of an earthquake source. The source is modeled as a residual
pocket of a fluid, where high background pressure raises the velocity
of filtration. The filtration front may quickly cross and destabilize such a pocket.
turning it into an earthquake source.
summing up, instability caused by nonlinear filtration also explains many
features of real seismicity,e.g., its migration, seismic cycle, and certain earthquake precursors, such as the rise of seismic activity and earthquake
clustering. It also suggests some premonitory changes in the fluid regime and the
electromagnetic field.
However, one can see the same limitations as in stress corrosion. First,
such instabilities may rise simultaneously within boundary zones of different rank and interact along the hierarchy. Thus, this is not a stand-alone
model but, like stress corrosion, has an element of some infrastructure of

filtration-generated instability. And, again, this is not a single major source
of instability.
other mechanisms of instability. Boundary zones feature several other
mechanisms, potentially as important and certainly as complicated. A few
more examples follow.
"Fingers of fi,u'ids" springing out at the front of the fluid migrating in
a porous media [Bar96]. The fluids may act as lubricants and create the
destabilization described above.
D'issolution of rocks. Its impact is magnified by the ,,R,ieckeeffect,', an
increase in the solubility of rocks with pressure. This effect leads to mass
transfer. solid material is dissolved under high stress and carried out in solution along the stress gradient to areas of lower stress, where it precipitates.
The Riecke effect might be triggered in a crystalline massif at the corners of
rock grains, where stress is likely to concenrrate.
Petrochem'icaltransiti,ons.some of them tie up or releasefluids, as in the
formation or decomposition of serpentines. other transitions cause a rapid
drop in density, such as in the transformation of calcite into aragonite. (This
would create a vacuum and unlock the fault; the vacuum will be closed at
once by hydrostatic pressure, but the rupture may be triggered.)
sensi,ti'ui'ty of dynam'ic fri.ction to locar phgsi.cal enuiriiment
[Lomg1].
Mechan'ical processeslsuch as multiple fracturing, buckling, viscous flow,
etc.
The impact of pressure and temperature on most of the abouemechanisms.
This list, by no means complete, illustrates the diversity of mechanisms
that cause the physical instability.
1.2.3

66Geometric" fnstability

[GKJ96]

The geometry of fault networks might be, and often is, incompatible
with tectonic movements, including earthquakes. This leads to stress accumulation.