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Complexity in Earthquakes, Tsunamis, and Volcanoes, and Forecast and Warning, Introduction
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This Introduction is intended to serve as a ‘road map’
for readers to navigate through the 42 Encyclopedia articles on earthquakes, tsunamis, and volcanoes. Selecting the topics and authors was somewhat subjective, as
it is not possible to cover the vast existing literature with
only 42 articles. They are, however, representative of the
wide range of problems investigated in connection with
these natural phenomena. I will introduce these articles
by grouping them into sections and then into subsections.
However, some articles belong to more than one section or
one subsection, reflecting the inter-related nature of earthquakes, tsunamis and volcanoes. For the benefit of the
readers, I will point to certain issues discussed in some of
the articles which, in my view, have not been settled completely. I have also taken the liberty of quoting or paraphrasing sentences from many of these articles when introducing them, but I do not claim to be accurate. It is best
for these articles to speak for themselves.
I wish to thank Bernard Chouet for helping me in planning and reviewing the manuscripts of the volcanoes section. I am grateful to Bernard Chouet, Edo Nyland, Jose
Pujol, Chris Stephens, and Ta-liang Teng for their helpful
comments that greatly improved this manuscript.
away with fatalities exceeding 280,000. The 79 AD eruption of Mount Vesuvius near Naples, Italy buried the
towns of Pompeii and Herculaneum. The 1902 eruption
of Mount Pelée, Martinique, totally destroyed the town of
St. Pierre.
Insurance companies classify major natural catastrophes as storms, floods, or earthquakes (including tsunamis, and volcanic eruptions). Since 1950, about 2.5 million
people have died due to these catastrophes and overall
economic losses have totaled about US $2 trillion in current dollar values. Earthquakes, tsunamis, and volcanic
eruptions have accounted for about half of the fatalities
and more than one third of the total economic losses.
Geoscientists have attempted to predict these events, but
with limited success. There are many reasons for such
slow progress: (1) systematic monitoring of earthquakes,
tsunamis and volcanoes requires large capital investment
for instruments and very long-term support for operation
and maintenance; (2) catastrophic earthquakes, tsunamis
and volcanic eruptions occur rarely, and (3) politicians
and citizens are quick to forget these hazards in the face
of other more frequent and pressing issues. But with continuing rapid population growth and urbanization, the
loss potential from these natural hazards in the world is
quickly escalating.
With advances in nonlinear dynamics and complexity studies, geoscientists have applied modern nonlinear
techniques and concepts such as chaos, fractal, critical
phenomena, and self-organized criticality to the study of
earthquakes, tsunamis and volcanoes. Here we sample
these efforts, mainly in seismicity modeling for earthquake
prediction and forecast, along with articles that review recent progress in studying earthquakes, tsunamis, and volcanoes. Although predictability is desirable, it is also possible to reduce these natural hazards with more practical approaches, such as early warning systems, hazard analysis,
engineering considerations, and other mitigation efforts.
Several articles in this Encyclopedia discuss these practical
solutions.
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Introduction
Earthquakes
Earthquakes, tsunamis, and volcanic eruptions are complex and often inter-related natural phenomena with disastrous impact to society rivaling those caused by the worst
floods or storms. The 1556 Huaxian earthquake in the
Shansi province of China claimed over 830,000 lives. The
total economic loss of the 1995 Kobe earthquake in Japan
was estimated at US $200 billion. The 2004 Indian Ocean
tsunami (triggered by the Sumatra–Andaman earthquake
of December 26) bought devastation thousands of miles
When a sudden rupture occurs in the Earth, seismic waves
are generated. When these waves reach the Earth’s surface, we may feel them as a series of vibrations, which
we call an earthquake. Instrumental recordings of earthquakes have been made since the latter part of the 19th
century by seismographic stations and networks from local to global scales. The observed data have been used, for
example, (1) to compute the source parameters of earthquakes, (2) to determine the physical properties of the
Complexity in Earthquakes,
Tsunamis, and Volcanoes, and
Forecast and Warning, Introduction
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W ILLIAM H.K. LEE
US Geological Survey (Retired), Menlo Park, USA
Article Outline
Introduction
Earthquakes
Tsunamis
Volcanoes
Discussions
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Earth’s interior, (3) to test the theory of plate tectonics,
(4) to map active faults, (5) to infer the nature of damaging ground shaking, (6) to carry out seismic hazard analyzes, and (7) to predict and forecast earthquakes. A satisfactory theory of the complex earthquake process has
not yet been achieved, and realistic equations for modeling earthquakes do not exist at present. There is, however,
good progress towards a physical foundation for the earthquake source process, partly as a result of research directed
toward earthquake prediction.
Earthquake Monitoring,
and Probing the Earth’s Interior
Earthquakes are complex natural phenomena, and their
monitoring requires an interdisciplinary approach, including using tools from other scientific disciplines and
engineering. In Earthquake Monitoring and Early
Warning Systems, W.H.K. Lee and Y.M. Wu presented
a summary of earthquake monitoring, a description of the
products derived from the analysis of seismograms, and
a discussion of the limitations of these products. The basic
results of earthquake monitoring are summarized in earthquake catalogs, which are lists of origin time, hypocenter location, and magnitude of earthquakes, as well as
other source parameters. Lee and Wu describe the traditional earthquake location method formulated as an inverse problem. In Earthquake Location, Direct, Globalsearch Methods, Lomax et al. review a different approach
using direct-search over a space of possible locations, and
discuss other related algorithms. Direct-search earthquake
location is important because, relative to the traditional
linearized method, it is both easier to apply to more realistic Earth models and is computational more stable. Although it has not been widely applied because of its computational demand, it shows great promise for the future
as computer power is advancing rapidly.
The most frequently determined parameter after ‘location’ is ‘magnitude’, which is used to characterize the ‘size’
of an earthquake. A brief introduction to the quantification of earthquake size, including magnitude and seismic
moment, is given in Earthquake Monitoring and Early
Warning Systems by Lee and Wu. Despite its various limitations, magnitude provides important information concerning the earthquake source. Magnitude values have an
immense practical value for realistic long-term disaster
preparedness and risk mitigation efforts. A detailed review, including current practices for magnitude determinations, appears in Earthquake Magnitude by P. Bormann and J. Saul.
Besides computing earthquake source parameters,
earthquake monitoring also provides data that can be used
to probe the Earth’s interior. In Tomography, Seismic,
J. Pujol reviews a number of techniques designed to investigate the interior of the Earth using arrival times and/or
waveforms from natural and artificial sources. The most
common product of a tomographic study is a seismic velocity model, although other parameters, such as attenuation and anisotropy, can also be estimated. Seismic tomography generally has higher resolution than that provided
by other geophysical methods, such as gravity and magnetics, and furnishes information (1) about fundamental
problems concerning the internal structure of the Earth on
a global scale, and (2) for tectonic and seismic hazard studies on a local scale.
In Seismic Wave Propagation in Media with Complex Geometries, Simulation of, H. Igel et al. present the
state-of-the-art in computational wave propagation. They
point to future developments, particularly in connection
with the search for efficient generation of computational
grids for models with complex topography and faults, as
well as for the combined simulation of soil-structure interactions. In addition to imaging subsurface structure
and earthquake sources, 3-D wave simulations can forecast strong ground motions from large earthquakes. In
the absence of deterministic prediction of earthquakes, the
calculation of earthquake scenarios in regions with sufficiently well-known crustal structures and faults will play
an important role in assessing and mitigating potential
damage, particularly those due to local site effects.
In addition to the classical parametrization of the
Earth as a layered structure with smooth velocity perturbation, a new approach using scattered waves that reflect
Earth’s heterogeneity is introduced by H. Sato in his article on Seismic Waves in Heterogeneous Earth, Scattering of. For high-frequency seismograms, envelope characteristics such as the excitation level and the decay gradient of coda envelopes and the envelope broadening of
the direct wavelet are useful for the study of small-scale
inhomogeneities within the Earth. The radiative transfer theory with scattering coefficients calculated from the
Born approximation and the Markov approximation for
the parabolic wave equation are powerful mathematical
tools for these analyzes. Studies of the scattering of highfrequency seismic waves in the heterogeneous Earth are
important for understanding the physical structure and
the geodynamic processes that reflect the evolution of the
solid Earth.
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Earthquake Prediction and Forecasting
A fundamental question in earthquake science is whether
earthquake prediction is possible. Debate on this question
has been going on for decades without clear resolution.
Are pure observational methods without specific physical
understanding sufficient? Earthquakes have been instrumentally monitored continuously for about 100 years (although not uniformly over the Earth), but reliable and detailed earthquake catalogs cover only about 50 years. Consequently, it seems questionable that earthquakes can be
predict solely on the basis of observed seismicity patterns,
given that large earthquakes in a given region have recurrence intervals ranging from decades to centuries or
longer. Despite progress made in earthquake physics, we
are still not able to write down all the governing equations for these events and lack sufficient information about
the Earth’s properties. Nevertheless, many attempts have
been and are being made to predict and forecast earthquakes. In this section, several articles based on empirical
and physics-based approaches will be briefly introduced.
In Geo-complexity and Earthquake Prediction,
V. Keilis-Borok et al. present an algorithmic prediction
method for individual extreme events having low probability but large societal impact. They show that the earthquake prediction problem is necessarily intertwined with
problems of disaster preparedness, the dynamics of the
solid Earth, and the modeling of extreme events in hierarchical complex systems. The algorithms considered by
Keilis-Borok et al. are based on premonitory seismicity
patterns and provide alarms lasting months to years. Since
the 1990s, these alarms have been posted for use in testing
such algorithms against newly occurred large earthquakes.
Some success has been achieved, but since the areas for
the predicted earthquakes are very large and the predicted
time windows are very long, it is not clear how to make
practical use of such predictions for the public.
Stochastic models are a practical way of bridging the
gap between the detailed modeling of a complex system
and the need to fit models to limited data. In Earthquake Occurrence and Mechanisms, Stochastic Models
for, D. Vere-Jones presents a brief account of the role
and development of stochastic models of seismicity, from
the first empirical studies to current models used in
earthquake probability forecasting. The author combines
a model of the physical processes generating the observable data (earthquake catalogs) with a model for the errors,
or uncertainties, in our ability to predict those observables.
D.A. Yuen et al. propose the use of statistical approaches and data-assimilation techniques to earthquake
forecasting in their article on Earthquake Clusters over
Multi-dimensional Space, Visualization of. The nature of
the spatial-temporal evolution of earthquakes may be assessed from the observed seismicity and geodetic measurements by recognizing nonlinear patterns hidden in the
vast amount of seemingly unrelated data. The authors endeavor to bring across the basic concept of clustering and
its role in earthquake forecasting, and conclude that the
clustering of seismic activity reflects both the similarity between clusters and their correlation properties.
In Seismicity, Critical States of: From Models to
Practical Seismic Hazard Estimates Space, G. Zoeller et al.
present a combined approach to understanding seismicity
and the emergence of patterns in the occurrence of earthquakes based on numerical modeling and data analysis.
The discussion and interpretation of seismicity in terms
of statistical physics leads to the concept of ‘critical states’,
i. e. states in the seismic cycle with an increased probability for abrupt changes involving large earthquakes. They
demonstrate that numerical fault models are valuable for
understanding the underlying mechanisms of observed
seismicity patterns, as well as for practical estimates of future seismic hazard.
D. Sornette and M.J. Werner in Seismicity, Statistical Physics Approaches to stress that the term ‘statistical’
in ‘statistical physics’ has a different meaning than as used
in ‘statistical seismology’. Statistical seismology has been
developed as a marriage between probability theory, statistics, and earthquake occurrences without considerations
of earthquake physics. In statistical physics approaches to
seismicity, researchers strive to derive statistical models
from microscopic laws of friction, damage, rupture, etc.
Sornette and Werner summarize some of the concepts
and tools that have been developed, including the leading theoretical physical models of the space-time organization of earthquakes. They then present several examples
of the new metrics proposed by statistical physicists, underlining their strengths and weaknesses. They conclude
that a holistic approach emphasizing the interactions between earthquakes and faults is promising, and that statistical seismology needs to evolve into a genuine physicallybased statistical physics of earthquakes.
In Earthquake Networks, Complex, S. Abe and N.
Suzuki discuss the construction of a complex earthquake
network obtained by mapping seismic data to a growing
stochastic graph. This graph, or network, turns out to exhibit a number of remarkable physical and mathematical
behaviors that share common traits with many other complex systems. The scale-free and small-world natures are
typical examples in complex earthquake networks.
Electromagnetic phenomena associated with earthquakes, such as earthquake light have been reported
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throughout almost all human history. Until rather recently, however, most such observations were unreliable
and best described as folklore. In Earthquakes, Electromagnetic Signals of, S. Uyeda et al. summarize the scientific search for electromagnetic precursors for earthquake
prediction. The presumption is that since earthquakes occur when slowly increasing tectonic stress in the Earth’s
crust reaches a critical level; the same stress may give rise
to some electromagnetic phenomena. Research on possible relationships was initiated in several countries around
the world in the 1980s. Two main approaches are (1) the
monitoring of possible emissions from focal regions in
a wide range of frequency from DC to VHF, and (2) the
monitoring of possible anomalies in the transmission of
man-made electromagnetic waves of various frequencies
over focal regions. Despite much circumstantial evidence,
earthquake-related electromagnetic signals, in particular
those at a pre-seismic stage are not yet accepted to be
associated with earthquakes.
Observational programs focused on searching for reliable precursory phenomena in seismicity, seismic velocities, tilt and strain, electromagnetic signals, chemical emissions and animal behavior, claim some successes but no
systematic precursors have been identified. In Earthquake Forecasting and Verification, J.R. Holliday et al.
stress that reliable earthquake forecasting will require systematic verification. They point out that although earthquakes are complex phenomena, systematic scaling laws
such as the Gutenberg–Richter frequency-magnitude relation have been recognized. The Gutenberg–Richter relation is given by: log N(M) D a bM, where M is the
earthquake magnitude, N(M) is the number of earthquakes with magnitude greater than or equal to M, and a
and b are constants. Since b 1, this means that the number of earthquakes increase tenfold for each decrease of
one magnitude unit. This suggests that large earthquakes
occur in regions where there are large numbers of small
earthquakes. On this basis, the regions where large earthquakes will occur can be forecast with considerable accuracy, but the Gutenberg–Richter relation provides no information about the precise occurrence times.
Earthquake Engineering Considerations
and Early Warning Systems
Since seismic hazards exist in many regions of the world,
three major strategies are introduced to reduce their societal impacts: (1) to avoid building in high seismic-risk
areas, (2) to build structures that can withstand the effects
of earthquakes, and (3) to plan for earthquake emergencies. The first strategy is not very practical because, with
rapid population growth, many economically productive
activities are increasingly located in high seismic-risk areas. However, by mapping active faults and by studying
past earthquakes, we may estimate the risk potential from
earthquakes and plan our land use accordingly. The second strategy depends on the skills of engineers, and also
requires seismologists to provide realistic estimates of the
ground motions resulting from expected earthquakes. The
third strategy includes attempting to predict earthquakes
reliably well in advance to minimize damage and casualties, and also requires the cooperation of the entire society. Although we are far from being able to predict earthquakes reliably, earthquake early warning systems can provide critical information to reduce damage and causalities,
as well as to aid rescuing and recovery efforts.
Accurate prediction of the level and variability of nearsource strong-ground motions in future earthquakes is
one of the key challenges facing seismologists and earthquake engineers. The increasing number of near-source
recordings collected by dense strong-motion networks exemplifies the inherent complexity of near-field ground
shaking, which is governed by a number of interacting
physical processes. Characterizing, quantifying, and modeling ground-motion complexity requires a joint investigation of (1) the physics of earthquake rupture, (2) wavepropagation in heterogeneous media, and (3) the effects
of local site conditions. In Ground motion: Complexity and scaling in the near field of earthquake ruptures,
P.M. Mai discusses briefly the beginnings of strong-motion seismology and the recognition of ground-motion
complexity. Using two well-recorded recent earthquakes,
the author introduces the observational aspects of nearfield ground shaking and describes the basic mathematical
tools used in the computation of ground motion. The key
elements for characterizing and modeling ground-motion
complexity are also explained, supplemented by a concise
overview of the underlying physical processes.
With increasing urbanization worldwide, earthquake
hazards pose ever greater threats to lives, property, and
livelihoods in populated areas near major active faults on
land or near offshore subduction zones. Earthquake earlywarning (EEW) systems can be useful tools for reducing the impact of earthquakes, provided that the populated areas are favorably located with respect to earthquake
sources and their citizens are properly trained to respond
to the warning messages. Under favorable conditions, an
EEW system can forewarn an urban population of impending strong shaking with lead times that range from
a few seconds to a few tens of seconds. A lead time is the
time interval between issuing a warning and the arrival of
the S- and surface waves, which are the most destructive
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due to their large amplitudes. Even a few seconds of advance warning is useful for pre-programmed emergency
measures at various critical facilities, such as the deceleration of rapid-transit vehicles and high-speed trains, the
orderly shutoff of gas pipelines, the controlled shutdown
of some high-technological manufacturing operations, the
safe-guarding of computer facilities, and bringing elevators to a stop at the nearest floor.
Recent advances in early warning methodologies are
summarized by W.H.K Lee and Y.M. Wu in the second part of their article, Earthquake monitoring and
early warning systems. In Earthquake early warning
system in southern Italy, A. Zollo et al. analyze and illustrate the main scientific and technological issues related to the implementation and management of the earthquake early warning system under development in the
Campania region of southern Italy. The system is designed
to issue alerts to distant coastal targets using data from
a dense seismic network deployed in the Apennine belt
region. The authors note that earthquake early warning
systems can also help mitigate the effects of earthquakeinduced disasters such as fires, explosions, landslides, and
tsunamis. Earthquake early warning systems can be installed at relatively low cost in developing countries, where
even moderate-size earthquakes can cause damage comparable to that caused by much larger earthquakes in developed countries.
Nonlinear problems in structural earthquake engineering deal with the dynamic response of meta-stable,
man-made buildings subjected to strong earthquake shaking. During earthquakes, structures constructed on soft
sediments and soils deform together with the underlying
soil. Strong shaking forces the soil-structure systems to
evolve through different levels of nonlinear response, with
continuously changing properties that depend upon the
time history of excitation and on the progression and degree of damage. In Earthquake engineering, Nonlinear
problems in, M.D. Trifunac first briefly discuss the literature on complex and chaotic dynamics of simple mechanical oscillators, and then introduces the dynamic characteristics and governing equations of the meta-stable structural dynamics in earthquake engineering. He describes
the nature of the solutions of the governing equations in
terms of both the vibrational and the wave representations.
The author also addresses the dynamic instability, material
and geometric nonlinearities, and complexities of the governing equations associated with nonlinear soil-structure
interaction.
Structural health monitoring and structural damage
detection refers to the processes of determining and tracking the structural integrity and assessing the nature of
damage in a structure. An important and challenging
problem is being able to detect the principal components
of damage in structures (as they occur during or soon after the earthquake) before physical inspection. In the article, Earthquake damage: Detection and early warning in
man-made structures, M.I. Todorovska focuses on global
methods and intermediate-scale methods, which can point
to the parts of the structure that have been damaged. Recently, structural identification and health monitoring of
buildings based on detecting changes in wave travel time
through the structure has received renewed attention and
has proven to be very promising.
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Brittle deformation, which is the primary mode of deformation of the Earth’s crust in response to tectonic stress, is
manifested by faulting at the long timescale and by earthquakes at the short timescale. It is one of the best-known
examples of a system exhibiting self-organized criticality.
A full understanding of this system is essential for evaluating earthquake hazards, but our current understanding is
sketchy. In Brittle tectonics: A nonlinear dynamical system, C.H. Scholz shows that an earthquake dynamic system has two characteristic length scales, W and W . An
earthquake nucleates within the seismogenic zone and initially propagates in all directions along its perimeter, acting as a 3D crack. When its dimension exceeds W*, the
rupture is restricted to propagating in the horizontal direction, acting as a 2D crack. Thus a symmetry breakage
occurs at the dimension W . Small earthquakes, with dimensions smaller than W , are not self-similar with large
earthquakes, those with lengths larger than W . The same
occurs for suprafaults at the dimension W (a suprafault
is the shear relaxation structure that includes a fault and
its associated ductile shear zone).
Earthquake prediction is desirable for reducing seismic hazards, but we lack an understanding of how and
why earthquakes begin and grow larger or stop. Theoretical and laboratory studies show that a quasi-static rupture growth precedes dynamic rupture. Thus, detecting
the quasi-static rupture growth may lead to forecasting
the subsequent dynamic rupture. In Earthquake Nucleation Process, Y. Iio reviews studies that analyze the
early portions of observed waveforms, and summarizes
what we presently understand about earthquake nucleation process. An earthquake initiates over a small patch
of a fault, and then their rupture fronts expand outward
until they stop. Some large earthquakes have a rupture extent greater than 1000 km, while fault lengths of small microearthquakes range over only a few meters. Surprisingly,
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the concept that earthquakes are self-similar is widely accepted despite fault length ranging over 6 orders of magnitude. One example of such similarity is the proportionality
of average fault slip to fault length, which implies a constant static stress drop, independent of earthquake size.
The self-similarity law raises a fundamental question,
namely what is the difference between large and small
earthquakes? One end-member model represents earthquakes as ruptures that grow randomly and then terminate
at an earlier stage for smaller earthquakes, but continue
longer for larger earthquakes. This type of model has been
proposed mainly to explain the frequency–magnitude distribution of earthquakes (the Gutenberg–Richter relation),
but it implies that it is impossible to forecast the final size
of an earthquake at the time the rupture initiates. However, the other end-member model predicts that larger
earthquakes have a larger ‘seed’ than smaller earthquakes,
and that large and small earthquakes are different even at
their beginnings.
Geoscientists have long sought an understanding of
how earthquakes interact. Can earthquakes trigger other
earthquakes? The answer is clearly yes over short time and
distance scales, as in the case of mainshock–aftershock sequences. Over increasing time and distance scales, however, this question is more difficult to answer. In Earthquakes, Dynamic triggering of, S.G. Prejean and D.P. Hill
explore the most distant regions over which earthquakes
can trigger other earthquakes. This subject has been the
focus of extensive research over the past twenty five years,
and offers a potentially important key to improving our
understanding of earthquake nucleation. In this review,
the authors discuss physical models and give a description
of documented patterns of remote dynamic triggering.
Models of the earthquake source have been successfully used in predicting many of the general properties of
seismic waves radiated from earthquakes. These general
properties can be derived from a simple omega-squared
spectral shape. In Earthquake scaling laws, R. Madariaga
derives general expressions for energy, moment and stress
in terms of measured spectral parameters, and shows that
earthquake sources can be reduced to a single family with
the three parameters of moment, corner frequency and
radiated energy. He suggests that most of the properties
of the seismic spectrum and slip distribution can be explained by a simple crack model. Whether an earthquake
is modeled as a simple circular crack or as a complex distribution of such cracks, the result is the same.
In Earthquake Source: Asymmetry and Rotation Effects, R. Teisseyre presents a consistent theory describing
an elastic continuum subjected to complex internal processes, considers all the possible kinds of the point-related
motions and deformations, and defines a complex rotation
field including spin and twist. Also included in the discussion is a new description of the source processes, including
the role of rotation in source dynamics, an explanation of
co-action of the slip and rotation motions, and a theory of
seismic rotation waves. Rotational seismology is an emerging field, and a progress report is provided in the Appendix
in Earthquake monitoring and early warning systems by
W.H.K. Lee and Y.M. Wu.
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Some New Tools to Study Earthquakes
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The Global Positioning System (GPS) is a space-based
Global Navigation Satellite System. Using signals transmitted by a constellation of GPS satellites, the positions
of ground-based receivers can be calculated to high precision, making it possible to track relative movements
of points on the Earth’s surface over time. Unlike older
geodetic surveying methods (which involved periodically
but infrequent measuring angles, distances, or elevations
between points), GPS can provide precise 3-D positions
over a range of sampling rates and on a global scale. GPS
equipment is easy to use and can be set up to collect
data continuously. Since its early geophysical applications
in the mid-1980s, this versatile tool, which can be used
to track displacements over time periods of seconds to
decades, has become indispensable for crustal deformation studies, leading to many important insights and some
surprising discoveries. In GPS: Applications in crustal
deformation monitoring, J. Murray-Moraleda focuses on
applications of GPS data to the studies of tectonic, seismic,
and volcanic processes. The author presents an overview
of how GPS works and how it is used to collect data for
geophysical studies. The article also describes a variety of
ways in which GPS data have been used to measure crustal
deformation and investigate the underlying processes.
The concept of a seismic cycle involves processes associated with the accumulation and release of stress on
seismogenic faults, and is commonly divided into three
intervals: (1) the coseismic interval for events occurring
during an earthquake, (2) the postseismic interval immediately following an earthquake, and (3) the interseismic
period in between large earthquakes. In Crustal deformation during the seismic cycle, Interpreting geodetic observations of, R. Lohman explores how we can draw conclusions about fault zone slip at depths far greater than are
directly accessible to us, based on how the Earth’s surface
deforms during, before, and after earthquakes.
Atmospheric sound can be radiated by the displacement or rupture of the Earth’s surface induced by earthquakes, tsunamis, and volcanoes, and by the flow and ex-
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citation of fluids during volcanic eruptions. These complex and potentially cataclysmic phenomena share some
common physics, yet represent different ways of converting energy into atmospheric sound. In Infrasound
from earthquakes, tsunamis and volcanoes, M. Garces and
A. LePichon discuss some of the signal features unique
to earthquakes, tsunamis, and volcanoes captured by the
present generation of infrasound arrays. They also discuss contemporary methods for the analysis, interpretation, and modeling of these diverse signals, and consider
some of the associated geophysical problems that remain
unsolved.
Tsunamis
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Tsunamis are oceanic gravity waves generated by seafloor
deformation due to earthquakes, volcanic eruptions, landslides, or asteroid impacts. Earthquake tsunamis, such as
the 2004 Indian Ocean tsunami (caused by the Sumatra–
Andaman earthquake of December 26), are the most frequent type of tsunamis. However, large volcanic eruptions,
such as the 1883 Krakatau eruption (in the Sunda strait between the islands of Java and Sumatra) also cause oceanwide tsunamis. Landslides (which are often triggered by
earthquakes) cause large tsunamis locally, but their effects
are usually limited to the immediate vicinity of the source.
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putation. The author then summarizes the tsunami observations, including instrumental sea-level data and runup height estimates for modern, historical and prehistoric
tsunamis. He also describes methods for modeling and
quantifying a tsunami source, and for analyzing tsunami
travel times, amplitudes and waveforms. He concludes
with an estimation of earthquake fault parameters derived
from waveform inversion of tsunami data, and a discussion of heterogeneous fault motion and its application for
tsunami warning.
Tsunami inundation is the one of the final stages of
tsunami evolution, when the wave encroaches upon and
floods dry land. It is during this stage that a tsunami is
most destructive and takes the vast majority of its victims.
To gauge the near-shore impact of tsunami inundation,
engineers and scientists rely primarily on three different
methods: (1) field survey of past events, (2) physical experimentation in a laboratory, and (3) numerical modeling.
In Tsunami inundation, Modeling of, P.J. Lynett focuses
on numerical simulations. He reviews tsunami generation
and open ocean propagation, and discusses the physics of
near-shore tsunami evolution, hydrodynamic modeling of
tsunami evolution, moving shoreline algorithms, and effect of topographical features on inundation.
Tsunami Forecasting and Warning
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Forward-modeling of a tsunami starts from given initial
conditions, computes its propagation in the ocean, and
calculates the tsunami arrival times and/or water run-up
heights along the coasts. Once the initial conditions are
provided, the propagation and coastal behavior can be numerically computed for an actual bathymetry. These calculations are useful for early tsunami warning and for
detailed hazard estimations. However, the initial conditions associated with tsunami generation processes are still
poorly known, because large tsunamis are rare and the
tsunami generation in the open ocean is not directly observable. Currently, the tsunami source is estimated indirectly, mostly on the basis of seismological analysis, but
a more direct estimation of the tsunami source is essential
to better understand the tsunami generation process and
to more accurately forecast the effects of a tsunami along
the coasts.
In Tsunamis, Inverse problem of, K. Satake reviews
inverse methods used in the quantification of tsunami
sources from the observations. The author describes the
tsunami generation by earthquakes, with an emphasis on
the fault parameters and their effects on tsunami propagation, including shallow water theory and numerical com-
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The original definition of ‘tsunami earthquake’ was given
by H. Kanamori (Phys Earth Planet Inter 6:346–359,
1972) as “an earthquake that produces a large-size tsunami
relative to the value of its surface wave magnitude (MS )”.
The true damage potential that a tsunami earthquake represents may not be recognized by conventional near realtime seismic analysis methods that utilize measurements
of relatively high-frequency signals, and thus the threat
may only become apparent upon the arrival of the tsunami
waves on the local shores. Although tsunami earthquakes
occur relatively infrequently, the effect on the local population can be devastating, as was most recently illustrated by
the July 2006 Java tsunami earthquake, which was quickly
followed by tsunami waves two to seven meters high, traveling as far as two kilometers inland and killing at least
668 people.
It is important to note that the definition of ‘tsunami
earthquake’ is distinct from that of ‘tsunamigenic earthquake’. A tsunamigenic earthquake is any earthquake that
excites a tsunami. Tsunami earthquakes are a specific subset of tsunamigenic earthquakes. In Tsunami earthquakes, J. Polet and H. Kanamori describe the characteristics of tsunami earthquakes and the possible factors involved in the anomalously strong excitation of tsunamis by
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these events. They also discuss a possible model for these
infrequent, but potentially very damaging events.
Tsunamis are among nature’s most destructive hazards. Typically generated by large, underwater shallow
earthquakes, tsunamis can cross an ocean basin in a matter
of hours. Although difficult to detect, and not dangerous
while propagating in open ocean, tsunamis can unleash
awesome destructive power when they reach coastal areas.
With advance warning, populations dwelling in coastal areas can be alerted to evacuate to higher ground and away
from the coast, thus saving many lives.
Tsunami travels at about the same speed of a commercial airliner, however, seismic waves can travel at speeds
more than 40 times greater. Because of this large disparity in speed, scientists rely on seismic methods to detect
the possibility of tsunami generation and to warn coastal
populations of an approaching tsunami well in advance of
its arrival. The seismic P-wave for example, travels from
Alaska to Hawaii in about 7 min, whereas a tsunami will
take about 5.5 h to travel the same distance. Although over
200 sea-level stations reporting in near-real time are operating in the Pacific Ocean, it may take an hour or more,
depending on the location of the epicenter, before the existence (or not) of an actual tsunami generation is confirmed. In other ocean basins where the density of sealevel instruments reporting data in near real-time is less,
the delay in tsunami detection is correspondingly longer.
However, global, regional, and local seismic networks, and
the infrastructure needed to process the large amounts of
seismic data that they record, are well in place around the
world. For these reasons, tsunami warning centers provide
initial tsunami warnings to coastal populations based entirely on the occurrence of a large shallow offshore earthquake. It is well-known, however, that large shallow offshore earthquakes may or may not be tsunamigenic.
In Tsunami forecasting and warning, O. Kamigaichi
discusses the complexity problem in tsunami forecasting
for large local events, and describes the Tsunami Early
Warning System in Japan. Tsunami disaster mitigation
can be achieved effectively by the appropriate combination of software and hardware countermeasures. Important issues for disaster mitigation includes: (1) improving
people’s awareness of the tsunami hazards, (2) imparting
the necessity of spontaneous evacuation when people notice an imminent threat of tsunami on their own (feeling strong shaking near the coast, seeing abnormal sea
level change, etc), (3) giving clear directions on how to respond to the tsunami forecast, and (4) conducting tsunami
evacuation drills. The author notes that in tsunami forecasting, a trade-off exists between promptness and accuracy/reliability.
In Earthquake source parameters, Rapid estimates
for tsunami warning, B. Hirshorn and S. Weinstein describe the basic method used by the Pacific Tsunami
Warning Center (PTWC) mainly for large teleseismic
events. Software running at the PTWC processes in real
time seismic signals from over 150 seismic stations worldwide provided by various seismic networks. Automatic
seismic event detection algorithms page the duty scientists for any earthquake occurring worldwide over about
Magnitude 5.5. Other automatic software locates these
events, and provides a first estimate of their magnitude
and other source parameters in near real time. Duty scientists then refine the software’s automated source parameter estimates and issue a warning if necessary. The authors
also describe their ongoing efforts to improve estimates of
earthquake source parameters.
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Wedge Mechanics, Submarine Landslides
and Slow Earthquakes
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A study of the mechanics of wedge-shaped geological bodies, such as accretionary prisms in subduction zones and
fold-and-thrust belts in collision zones, is interesting because they enable us to use the observed morphology and
deformation of these bodies to constrain properties of the
thrust faults underlying them. The fundamental process
described in wedge mechanics is how gravitational force,
in the presence of a sloping surface, is balanced by basal
stress and internal stress. The internal state of stress depends on the rheology of the wedge. The most commonly
assumed wedge rheology for geological problems is perfect
Coulomb plasticity, and the model based on this rheology
is referred to as the Coulomb wedge model.
The connection between wedge mechanics and great
earthquakes and tsunamis at subduction zones is an
emerging new field of study. In their article, Wedge mechanics: Relation with subduction zone earthquakes and
tsunamis, Wang et al. cover the topics of stable and critical
Coulomb wedges, dynamic Coulomb wedge, stress drop
and increase in a subduction earthquake, and tsunamigenic coseismic seafloor deformation. Better constraints
are needed to quantify how stresses along different downdip segments of the subduction fault evolve with time
throughout an earthquake cycle and how the evolution impacts wedge and seafloor deformation. Submarine monitoring in conjunction with land-based monitoring at subduction zones that are currently in different phases of
earthquake cycles will allow us to better understand the
evolution of fault and wedge stresses during the interseismic period. In this regard, cabled seafloor monitoring
networks including borehole observatories being designed
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or implemented at different subduction zones will surely
yield valuable data in the near future.
The term ‘submarine landslide’ encompasses a multitude of gravitational mass failure features at areal scales
from square meters to thousands of square kilometers. The
term ‘slow earthquake’ describes a discrete slip event that
produces millimeter to meter-scale displacements identical to those produced during earthquakes but without the
associated seismic shaking. Recently, a GPS network on
the south flank of Kilauea volcano, Hawaii, recorded multiple slow earthquakes on the subaerial portion of a large
landslide system that extends primarily into the submarine environment. Since catastrophic failure of submarine
landslides can cause a tsunami they represent significant
hazards to coastal zones. Because submarine landslide systems are among the most active as well as spatially confined deforming areas on Earth, they are excellent targets for understanding the general fault failure process.
In Submarine landslides and slow earthquakes: Monitoring motion with GPS and seafloor geodesy, B.A. Brooks
et al. present a review of this interdisciplinary topic of interest in geodesy, seismology, tsunamis, and volcanology.
Volcanoes
About 1,500 volcanoes have erupted one or more times
during the past 10,000 years, and since A.D. 1600, volcanic
disasters have killed about 300,000 people and resulted in
property damage and economic loss exceeding hundreds
of millions of dollar. Articles in this section are intended
to summarize recent research in: (1) volcano seismology,
(2) physical processes involved in volcanoes, and (3) modeling volcanic eruptions and hazards warning.
Volcano Seismology
Magma transport in a volcano is episodic due to the inherent instability of magmatic systems at all time scales.
This episodicity is reflected in seismic activity, which originates in dynamic interactions between gas, liquid and solid
along magma transport paths that involve complex geometries. The description of the flow processes is governed
by the nonlinear equations of fluid dynamics. In volcanic
fluids, further complexity arises from the strong nonlinear
dependence of magma rheology on temperature, pressure,
and water and crystal content, and nonlinear characteristics of associated processes underlying the physico-chemical evolution of liquid-gas mixtures constituting magma.
In Volcanoes, Nonlinear processes in, B. Chouet
presents a brief review of volcano seismology and addresses basic issues in the quantitative interpretation of
processes in active volcanic systems. Starting with an in-
troduction of the seismic methodology used to quantify
the source of volcano seismicity, the author then focuses
on sources originating in the dynamics of volcanic fluids. A review of some of the representative source mechanisms of Long-Period (LP) and Very Long-Period (VLP)
signals is followed by a description of a mesoscale computational approach for simulating two-phase flows of complex magmatic fluids. Refined understanding of magma
and hydrothermal transport dynamics therefore requires
multidisciplinary research involving detailed field measurements, laboratory experiments, and numerical modeling. Such research is fundamental to monitoring and interpreting the subsurface migration of magma that often
leads to eruptions, and thus would enhance our ability to
forecast hazardous volcanic activity.
Volcano seismicity produces a wide variety of seismic signals that provide glimpses of the internal dynamics of volcanic systems. Quantitative approaches to analysis and interpret volcano-seismic signals have been developed since the late 1970s. The availability of seismic equipments with wide frequency and dynamic ranges since the
early 1990s has revealed a variety of volcano-seismic signals over a wide range of periods. Quantification of the
sources of volcano-seismic signals is crucial to achieving
a better understanding of the physical states and dynamics of magmatic and hydrothermal systems. In Volcano seismic signals, Source quantification of, H. Kumagai provides the theoretical basis for a quantification of the
sources of volcano-seismic signals. The author focuses on
the phenomenological representation of seismic sources,
waveform inversion to estimate source mechanisms, spectral analysis based on an autoregressive model, and physical properties of fluid-solid coupled waves.
Among various eruptive styles, Strombolian activity
is easier to study because of its repetitive behavior. Since
Strombolian activity offers numerous interesting seismic
signals, a growing attention has been devoted to the application of waveform inversion for imaging conduit geometry and retrieving eruption dynamics from seismological recordings. Quantitative models fitting seismological
observations are a powerful tool for interpreting seismic
recordings from active volcanoes. In Slug flow: Modeling in a conduit and associated elastic radiation, L. D’Auria
and M. Martini discuss the mechanism of generation of
Very-Long Period (VLP) signals accompanying Strombolian explosions. This eruptive style, occurring at many
basaltic volcanoes worldwide, is characterized by the ascent and the bursting of large gas slugs. The mechanism of
formation, ascent and explosion of bubbles and slugs and
their relation with eruptive activity has been studied theoretically and by analogue simulations. The authors report
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results from numerical simulations, focusing on the seismic signals generated by pressure variations applied to the
conduit walls.
Physical Processes in Volcanoes
The dynamics of solid-liquid composite systems are relevant to many problems, including how melts or aqueous
fluids migrate through the mantle and crust toward the
surface, how deformation and fracture in these regions are
influenced by the existence of fluids, and also how these
fluids can be observed in seismic tomographic images.
In Earth’s crust and upper mantle, Dynamics of solidliquid systems in, Y. Takei introduces a general continuum
mechanical theory for macroscopic dynamics of solid-liquid composite systems, and emphasizes on how such interactions with pore geometry can be studied. The author
then discusses the determinability of porosity and pore geometry from seismic tomographic images, and presents
a practical method to assess porosity and pore geometry
from tomographic VP and VS images.
A volcano consists of solids, liquids, gases, and intermediate materials of any two of these phases. Mechanical
and thermodynamical interactions between these phases
are essential in the generating a variety of volcanic activities. In particular, the gas phase is mechanically distinct
from the other phases and plays an important role in dynamic phenomena in volcanoes. In Pressure impulses
generated by bubbles interacting with ambient pressure
perturbation, M. Ichihara and T. Nishimura discuss several bubble dynamics phenomena from the viewpoint that
a bubbly fluid acts as an impulse generator of observable
signals, such as earthquakes, ground deformations, airwaves, and an eruption itself. The authors focus on the notion that the impulse is excited by non-linear coupling between internal processes in a bubbly fluid and an external
perturbation. The importance of these processes has recently become noticed as a possible triggering mechanism
of eruptions, earthquakes, and inflation of a volcano.
Our capability to mitigate volcano hazards relies in
large part on forecasting explosive events, a process which
requires a high degree of understanding of the physicochemical factors operating during explosive volcanism.
The approaches taken to gain an understanding of explosive volcanism have relied on a combination of field observations, theoretical models and laboratory models of materials and mechanisms. In Volcanic eruptions, Explosive: Experimental insights, S.J. Lane and M.R. James first
review aspects of the volcanic materials literature, with the
aim of illustrating the nature of molten rock, the complexity of which underpins most explosive volcanic pro-
cesses. Experimental modeling of these processes can then
build on the materials understanding. Such experiments
involve investigation of the behavior of natural volcanic
products at laboratory time and length scales, including
the response of magma samples to rapid changes in pressure and temperature, the fall behavior of silicate particles
in the atmosphere, and the generation and separation of
electrostatic charge during explosive eruptions.
In Volcanic eruptions: Cyclicity during lava dome
growth, O. Melnik et al. consider the process of slow extrusion of very viscous magma that forms lava domes.
Dome-building eruptions are commonly associated with
hazardous phenomena, including pyroclastic flows generated by dome collapses, explosive eruptions, and volcanic
blasts. These eruptions commonly display fairly regular alternations between periods of high and low or no activity
with time scales from hours to years. Usually hazardous
phenomena are associated with periods of high magma
discharge rate. Hence, understanding the causes of pulse
activity during extrusive eruptions is an important step
towards forecasting volcanic behavior, and especially the
transition to explosive activity when magma discharge rate
increases by a few orders of magnitude. In recent years the
risks have escalated because the population density in the
vicinity of many active volcanoes has increased.
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Modeling Volcanic Eruptions and Hazards Warning
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While a wide range of complex deterministic models exists to model various volcanic processes, these provide little in the way of information about future activity. Being
the (partially) observed realization of a complex system,
volcanological data are inherently stochastic in nature, and
need to be modeled using statistical models. In Volcanic eruptions: Stochastic models of occurrence patterns,
M.S. Bebbington considers models of eruption occurrence,
omitting techniques for forecasting the nature and effect of
the eruption. As the track record of a potentially active volcano provides the best method of assessing its future longterm hazards, the author first briefly reviews the provenance and characteristics of the data available, and then
discusses various taxonomies for stochastic models. The
examples of Mount Etna and Yucca Mountain are selected
for more detailed examination partly because many, somewhat contradictory, results exist. Different models make
different assumptions, and vary in how much information
they can extract from data. In addition, the data used often
varies from study to study, and the sensitivity of models to
data is important, but too often ignored.
In Volcano hazards and early warning, R.I. Tilling
highlights the range in possible outcomes of volcano un-
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rest and reviews some recent examples of the actual outcomes documented for several well-monitored volcanoes.
The author also discusses the challenge for emergencymanagement authorities, as well as challenges in achieving refined predictive capability. To respond effectively to
a developing volcanic crisis, timely and reliable early warnings are absolutely essential; they can be achieved only by
a greatly improved capability for eruption prediction. This
in turn depends on the quantity and quality of volcanomonitoring data and the diagnostic interpretation of such
information.
Discussions
The terms ‘Prediction’ and ‘forecasting’ are often used interchangeably. However, the commonly accepted definition of an ‘earthquake prediction’ is a concise statement,
in advance of the event, of the time, location, and magnitude of a future earthquake. To be practically useful to
the society, the time window must be short (in days or
months), the location extent small (within tens of kilometers), and the magnitude precise (˙ 0.5 unit). A ‘forecast’,
on the other hand, is more loosely defined as the probability of an occurrence of a large earthquake in a given region
(e. g., southern California) during the coming decades or
centuries. The broader time intervals associated with forecasts allows society to consider and implement mitigation
efforts over a large region.
As an observational seismologist and on a personal
note, I am skeptical that earthquakes can be reliably predicted before (1) we have collected accurate data of their
occurrences over a sufficiently long period of time, and
(2) we have a good understanding of the physical processes that create them. Although earthquakes have been
known from antiquity, accurate earthquake catalogs exist
only since about the 1960s. Since the recurrence of a damaging earthquake in a given area is often more than 100
years (some even thousands of years), it is obvious that we
lack the necessary observed data. C. Lanczos (Linear Differential Operators, Van Nostrand-Reinhold, 1961) said it
well in general: “a lack of information cannot be remedied
by any mathematical trickery”. Nevertheless, we must apply new concepts and tools to extract as much useful information as possible from the existing data. Indeed, we must
thank many pioneers for enlightening us with many interesting and tentative results about earthquakes, tsunamis
and volcanoes that they managed to extract from inadequate and insufficient data.
Because most tsunamis are generated by earthquakes,
successes in predicting tsunamis depend on predicting
earthquakes and recognizing them as tsunamigenic. Pre-
dicting a volcanic eruption is a little easier, as the location
is known and there are often some observable phenomena
preceding it. However, the exact time and the intensity and
extent of an eruption are difficult to predict because the
volcanic processes are very complex involving gas, liquid
and solid phases.
Fortunately, earthquake, tsunami and volcano hazards
can be reduced by employing sound engineering practices,
early warning systems, and hazard analysis, using many
of the tools and concepts that were developed for prediction. Since fatalities and economic loss from a single catastrophic event can reach 100,000 or more, and $100 billion
or more, respectively, it is imperative that governments
should support long-term monitoring with modern instruments and research, including complexity studies of
earthquakes, tsunamis and volcanoes.
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