Critical states of seismicity [Elektronische Ressource] : modeling and data analysis / von Gert Zöller

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• Publié par: universitat_potsdam
• Publié le: 01 janvier 2006
• Nombre de lectures: 8
• Langue: English
• Poids de l'ouvrage: 18 Mo

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Universitat Potsdam
CRITICAL STATES OF SEISMICITY
Modeling and data analysis
Habilitationsschrift
zur Erlangung des akademischen Grades
Doctor rerum naturalium habilitatus (Dr. rer. nat. habil.)
in der Wissenschaftsdisziplin Theoretische Physik
angenommen an der
Mathematisch{Naturwissenschaftlichen Fakult at
der Universit at Potsdam
von
Dr. Gert Z oller
geboren am 25. Juli 1967
in Ludensc heid
Potsdam, im September 2005Contents
1 Introduction 1
2 Conceptual models for seismicity 6
2.1 Reid’s elastic rebound theory (1910): A model for the Park eld segment? . 6
2.2 Spring-block systems and cellular automata . . . . . . . . . . . . . . . . . . 8
3 Modeling seismicity in real fault regions 10
3.1 Fault geometry and model framework . . . . . . . . . . . . . . . . . . . . . 10
3.2 Plate motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 Friction and coseismic stress transfer; quasidynamic approach . . . . . . . . 13
3.4 Model algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.5 Limits and parameters of the model . . . . . . . . . . . . . . . . . . . . . . 17
3.6 Model extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.7 Data types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 Results 21
4.1 Frequency-size distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2 Temporal occurrence of large earthquakes . . . . . . . . . . . . . . . . . . . 24
4.3 The stress eld for di eren t degrees of disorder . . . . . . . . . . . . . . . . 24
4.4 Aftershocks and foreshocks . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.5 Accelerating moment release . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.6 Critical point analysis of seismicity in California . . . . . . . . . . . . . . . 32
5 Summary and conclusions 38
6 Outlook 40
Bibliography 41
iiiiv CONTENTS
A Self-organization of spatio-temporal earthquake clusters 49
B Seismic quiescence as an indicator for large earthquakes in a system of
self-organized criticality 59
C Observation of growing correlation length as an indicator for critical
point behavior prior to large earthquakes 64
D The role of disorder and stress concentration in nonconservative fault
systems 74
E Detecting premonitory seismicity patterns based on critical point dy-
namics 93
F A systematic test on precursory seismic quiescence in Armenia 100
G A systematic spatiotemporal test of the critical point hypothesis for
large earthquakes 120
H On increase of earthquake correlation length prior to large earthquakes
in California 125
I Earthquake clusters resulting from delayed rupture propagation in nite
fault segments 147
J Emergence of a band-limited power law in the aftershock decay rate of
a slider-block model 158
K Quasi-static and quasi-dynamic modeling of earthquake failure at inter-
mediate scales 163
L The role of heterogeneities as a tuning parameter of earthquake dynam-
ics 180
M Aftershocks resulting from creeping sections in a heterogeneous fault 204
N Earthquake activity related to seismic cycles in a model for a heteroge-
neous strike-slip fault 209Chapter 1
Introduction
In 2003, the geophysicist Vladimir Keilis-Borok, director of the International Institute of
Earthquake Prediction Theory and Mathematical Geophysics in Moscow issued an alarm
for an upcoming earthquake of magnitude 6.4 or greater within a 12.440 square miles
area of southern California that includes portions of the eastern Mojave Desert, Coachella
Valley, Imperial Valley (San Bernardino, Riverside and Imperial Counties) and eastern
San Diego County, during a time interval of nine months (January 5 - September 5, 2004).
This prediction was based on previous observations of microearthquake patterns forming
chains. Keilis-Borok and co-workers claimed to have predicted two earthquakes correctly
by means of such chains { one in Hokkaido, Japan in September 2003 and the second in
San Simeon, California in December 2003. However, the deadline of the recent forecast
passed and no earthquake tting the alarm occurred.
Apart from the social and the economic dimension, this failed prediction raises also basic
scienti c questions in earth sciences: Is a prediction of earthquakes solely based on the
emergence of seismicity patterns reliable? In other words, is there a \magic parameter",
which becomes anomalous prior to a large earthquake? Is it necessary that such a parame-
ter is based on a physical model? Are pure observational methods without speci c physical
understanding, like the pattern recognition approach of Keilis-Borok, also su cien t? Tak-
ing into account that earthquakes are monitored continuously only since about 100 years
and the best available data sets (\earthquake catalogs") cover only a few decades, it seems
questionable to forecast earthquakes solely on the basis of observed seismicity patterns,
because large earthquakes have recurrence periods of decades to centuries; consequently,
data sets for a certain region include not more than ten large events making a reliable
statistical testing questionable.
The relation between frequency and magnitude of earthquakes in a large seismically active
region is given by the empirical Gutenberg-Richter law [Gutenberg and Richter, 1956]
log N = bM a; (1.1)
where N is the frequency of earthquakes with magnitude equal to or greater than M; a is
a measure of the overall seismicity level in a region and the slope b is the Richter b value,
which determines the relation between large and small earthquakes.
A key problem of the present work is the evaluation of the relevance of observed seismicity
patterns. First, it is important to decide whether an observed pattern has a physical
12 CHAPTER 1. INTRODUCTION
origin or is an artifact, arising for example from inhomogeneous reporting or from man-
made seismicity, like quarry blasts or explosions. Second, the non-arti cal events have
to be analyzed with respect to their underlying mechanisms. This leads to an inverse
problem with a non-unique solution, which can be illustrated for the most pronounced
observed seismicity pattern, the occurrence of aftershocks. It is empirically known that the
_earthquake rate N after a large event at time t follows the modi ed Omori law [Omori,M
1894; Utsu et al., 1995]
c1_N = ; (1.2)
p(c + t t )2 M
where t is the time, c and c are constants, and the Omori exponent p is close to unity.1 2
In particular, aftershocks are an almost universal phenomenon; that is, they are observed
nearly after each mainshock. The underlying mechanisms leading to aftershocks are, how-
ever, unknown. Various physical models have been designed in order to explain aftershock
occurrence following Eq. (1.2). These models assume physical mechanisms including vis-
coelasticity [Hainzl et al., 1999], pore uid o w [Nur and Booker, 1972], damage
rheology [Ben-Zion and Lyakhovsky, 2003; Shcherbakov and Turcotte, 2004],
and special friction laws [Dieterich, 1994]. The question, which mechanism is realistic
in a certain fault zone, remains open. Detailed comparisons of observed and modeled
seismicity with respect to the aftershock rate, the duration of aftershock sequences, the
dependence on the mainshock size, and other features are necessary to address this prob-
lem. Additionally, the results from lab experiments on rupture dynamics, and satellite
observations in fault zones, provide important constraints for the evaluation of such mod-
els.
Apart from aftershock activity, other seismicity patterns are well-known from observations,
e.g. foreshocks [Jones and Molnar, 1979], seismic quiescence [Wyss and Haber-
mann, 1988; Hainzl et al., 2000b; Zoller et al., 2002], and accelerating seismic moment
release [Bufe and Varnes, 1993; Jaume and Sykes, 1999]. These patterns have been
documented in several cases before large earthquakes. They occur, however, less frequent
than aftershocks. For example, foreshocks are known to preceed only 20-30% of large
earthquakes [Wyss, 1997]. Therefore, their predictive power is questionable. Moreover,
it is not clear whether or not these ndings can be attributed to physical processes or
to random uctuations in the highly noisy earthquake catalogs. This problem can be
addressed by using conceptual fault models which allow to simulate long earthquake se-
quences over at least 1000 years. If the models are to some extent physical, the occurrence
of seismicity patterns can be studied with reasonable statistics. The main ingredients of
such models are the geometry of a fault region, empirically known friction laws, quenched
spatial heterogeneities, and stress and displacement functions in accordance to dislocation
theory [Chinnery, 1963; Okada, 1992] . In order to allow for detailed studies of the
relations between the imposed mechanisms and the observed seismicity functions, it is im-
portant that the number of adjustable parameters is limited. It is emphasized that these
models do not aim to reproduce an observed earthquake catalog in detail. Instead, the
main goal is to address questions like: Why is the Park eld segment of the San Andreas
fault characterized by relatively regular occurrence of earthquakes with magnitude M 6,
while on the San Jacinto fault in California